10th Standard CBSE Maths CBSE - study material, free online tests, previous year question papers, answer keys, topper answers, centum question paper, exam tips

CBSE 10th Maths Probability Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Statistics Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Surface Areas And Volumes Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Areas Related To Circles Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Circles Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Some Applications Of Trigonometry Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Introduction To Trigonometry Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Coordinate Geometry Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Triangles Chapter Case Study Question with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Arithmetic Progressions Chapter Case Study Questions with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Quadratic Equations Chapter Case Study Questions with Answers - by users_admin - Jan 22, 2024 - View & Read

CBSE 10th Maths Pair Of Linear Equation In Two Variables Chapter Case Study Question with Answers - by users_admin - Jan 06, 2024 - View & Read

CBSE 10th Maths Polynomials Case Study Question & Answers - by users_admin - Jan 06, 2024 - View & Read

CBSE 10th Maths Real Numbers Case Study Question & Answers - by users_admin - Jan 06, 2024 - View & Read

10th Maths Model Question Paper 2023 - by users_admin - Mar 03, 2023 - View & Read

CBSE 10th Standard Maths Subject Probability HOT Questions 2 Mark Questions With Solution 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
A bag contains 12 marbles out of which y are white.
(i)If one marble is drawn at random from the bag, what is the probability that it will be white marble?
(ii)If 6 more white marbles are put in the bag, the probability of drawing a white marble will double than in part (i), find y.
2)
Two dice are thrown at the same time.Find the probability of getting different numbers on the dice.
3)
From a group of 3 Girls and 2 Boys, two children are selected at random.Find the probability such that at least one boy is selected.
4)
In a bag-A, there are four cards numbered 1,3,5 and 7 respectively.In another bag-B, there are three cards numbered 2, 4 and 6 respectively.A card is drawn at random from each bag.
(i)Write the possible outcomes i.e., sample space
(ii)Find the probability that the sum of these two cards drawn is:
(a)7
(b)even
(c)odd
(d)more than 7

CBSE 10th Standard Maths Subject Circles HOT Questions 2 Mark Questions With Solution 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
A \(\Delta\)ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of length 8 cm and 6 cm respectively. Find the sides AB and AC.
2)
In the given figure, AB is a diameter of the circle, with centre O and AT is a tangent. Calculate the numerical value of x.
3)
In given figure, find the perimeter of \(\angle ABC\), if AP = 10 cm.
4)
Two circles intersect each other at two points A and B. From point A, tangents AP and AQ are drawn to two circles which intersect the circles at the pointsP and Q respectively. Prove that AB is the bisector of \(\angle PBQ\).
5)
Let A be a point of intersection of two intersecting circles with centres O and O'. The tangents at A to the two circles meet the circles at B and C respectively. Point P is located so that AOPO; is a parallelogram. Prove that P is the circumcentre of \(\triangle ABC\).

CBSE 10th Standard Maths Subject Arithmetic Progressions HOT Questions 2 Mark Questions With Solution 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
For what value of k, 2k - 7, k+5 and 3k + 2 are three consecutive terms of an A.P.?
2)
If the sum of the first n terms of an A.P. is given by 3n²+5n, find the common difference of the A.P.
3)
The ratio of the sum of m and n terms of an A.P, is m²:n². Show that the ratio of the m^th and n^th term is (2m-1):(2n-1).
4)
If a₁, a₂, a₃, ....., be an A.P. of non-zero terms, prove that: \(\frac { 1 }{ { a }_{ 1 }{ a }_{ 2 } } +\frac { 1 }{ { a }_{ 2 }{ a }_{ 3 } } +......+\frac { 1 }{ { a }_{ n-1 }{ a }_{ n } } =\frac { n-1 }{ { a }_{ 1 }{ a }_{ n } } .\)

CBSE 10th Standard Maths Subject Areas Related to Circles HOT Questions 2 Mark Questions With Solution 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
The figure given shows a kite, in which BCD is in the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and \(\triangle CEF\) is an isosceles right-angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
2)
Four cows are tethered at the four corner of a squares plot of size 50 m. So that they just cannot reach one another. What area will be left ungrazed?
3)
In the adjoining figure, ABCD is a square of side 6cm.Find the area of the shaded region.
4)
In the figure alongside, crescent is formed by two circles which touch at the point A, O is the centre of the point A, O is the centre of the bigger circle.If CB=9cm and ED=5cm, find the area of the shaded region.[Take \(\pi\)=3.14]
5)
ABCD is a field in the shape of a trapezium.AB||DC and \(\angle\)ABC=60⁰,\(\angle\)DAB=90⁰.Four sector are formed with centres A, B, C and D.THe radius of each sector is 17.5m.Find:
(i)the total area of the four sectors
(ii)the area of remaining portion, given that AB=75m and CD=50m.

CBSE 10th Standard Maths Subject Areas Related to Circles HOT Questions 2 Mark Questions 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
A round table cover has six equal designs as shown in figure on the side (shaded one). If the radius of the cover is 28 cm, find the cost of making the design at the rate of Rs, 0.85 per cm² . \([Use \ \ \sqrt{3}=1.7]\).
2)
Two circles touch each other externally and the sum of their areas is \(52\pi { cm }^{ 2 }\) . If the distance between the centres of two circles is 10 cm, find the radii of the two circles.
3)
In the given figure, from each corner of a square ABCD, of side 4 cm, quadrant of a circle of radius 1 cm each is cut and a circle of radius 1 cm is cut from the centre. Find the area of the shaded region.
4)
Find the area of the shaded region which contains two semicircles and a rectangle of breadth 1 cm.
5)
In the adjoining figure, O is the centre of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm; find the area of the shaded region.

CBSE 10th Standard Maths Subject HOT Questions 4 Mark Questions With Solution 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
A pole 5m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60⁰ and the angle of depression of the point A from the top of the tower is 45^o . Find the height of the tower.
2)
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see the fig). Find the length TP.
3)
In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 min after she starts playing. What is the probability that the music will stop within the first half-minute after starting?

CBSE 10th Standard Maths Subject HOT Questions 3 Mark Questions With Solution 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
Find the equation of the perpendicular bisector of AB, where A and B are the points (3, 6) and (-3, 4). respectively. Also, find its point of intersection with
(i) X-axis
(ii) Y-axis.
2)
Find the coordinates of the circumcenter of the triangle whose vertices are (8,6), (8,- 2) and (2, - 2).Also, find its circumradius.
3)
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one- fourth of the water flows out. Find the number of lead shots dropped in the vessel.
4)
How many metres of cloth 1.1 m wide will be required to make a conical tent, whose vertical height is 12 m and base radius is 16 m ? Find also the cost of the cloth used at the rate of Rs. 14 per metre.

CBSE 10th Standard Maths Subject HOT Questions 2 Mark Questions With Solution 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
If a₁, a₂, a₃, ....., be an A.P. of non-zero terms, prove that: \(\frac { 1 }{ { a }_{ 1 }{ a }_{ 2 } } +\frac { 1 }{ { a }_{ 2 }{ a }_{ 3 } } +......+\frac { 1 }{ { a }_{ n-1 }{ a }_{ n } } =\frac { n-1 }{ { a }_{ 1 }{ a }_{ n } } .\)
2)
The angles of depression of top and bottom of tower as seen from the top of a 100m high cliff are 30⁰ and 60⁰ respectively.Find the height of the tower.
3)
Draw a triangle PQR, with PQ = 4 cm, angle \(\angle\) Q = 60^o and the median PL = 3.6 cm. Draw another triangle PQ'R' similar to given triangle \(\Delta\)PQR, such that PQ' = \(\frac { 4 }{ 3 } \) PQ.
4)
Construct a triangle whose perimeter is 13.5 cm and the ratio of the three sides is 2 : 3 : 4.
5)
In the given figure, from each corner of a square ABCD, of side 4 cm, quadrant of a circle of radius 1 cm each is cut and a circle of radius 1 cm is cut from the centre. Find the area of the shaded region.

CBSE 10th Standard Maths Subject HOT Questions 2 Mark Questions 2021 Part - II - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
If the sum of the first n terms of an A.P. is given by 3n²+5n, find the common difference of the A.P.
2)
A man on the deck of a ship is 10m above water level.He observes that the angle of elevation of the top of a hill is 60⁰ and the angle of depression of the base of the hill is 30⁰.Calculate the distance of the hill from the ship and the height of the hill.
3)
A bird is sitting on the top of a tree which is 60m high.The angle of elevation of the bird from a point on the ground is 45⁰.the bird flies away from the point o observation horizontally and remains at a constant height.After 2seconds, the angle of elevation of the bird from the point of observation becomes 30⁰ .Find the speed of flying of bird.
4)
In the given figure, AB is a diameter of the circle, with centre O and AT is a tangent. Calculate the numerical value of x.
5)
Draw an equilateral triangle of altitude 4 cm. Construct another triangle similar to it such that its sides are \(\frac { 2 }{ 3 } \) of the given triangle.

CBSE 10th Standard Maths Subject HOT Questions 2 Mark Questions 2021 - by QB365 - Question Bank Software - May 29, 2021 - View & Read

1)
If the sum of the first n terms of an A.P. is given by 3n²+5n, find the common difference of the A.P.
2)
Show that A (6,4), B (4,- 3)and C (8,- 3) are the vertices of an isosceles triangle. Also, find the length of the median through A.
3)
The angles of depression of top and bottom of tower as seen from the top of a 100m high cliff are 30⁰ and 60⁰ respectively.Find the height of the tower.
4)
A \(\Delta\)ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of length 8 cm and 6 cm respectively. Find the sides AB and AC.
5)
In given figure, find the perimeter of \(\angle ABC\), if AP = 10 cm.

CBSE 10th Standard Maths Subject Probability Ncert Exemplar 3 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Box A contains 25 slips of which 19 are marked Rs. 1 and other are marked Rs. 5 each. Box B contains 50 slips of which 45 are marked Rs 1 each and others are marked Rs 13 each. Slips of both boxes are poured into a third box and reshuffled. A slip is drawn at random. What is the probability that it is marked other than Rs 1?
2)
A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded.
(i) How many different scores are possible?
(ii) What is the probability of getting a total of 7?
3)
A lot consists of 48 mobiles phones of which 42 are good, 3 have only minor defects and 3 have major defects. Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is
(i) acceptable to Varnika?
(ii) acceptable to the trader?
4)
A carton of 24 bulbs contains 6 defective bulbs.One bulb is drawn at random.What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?
5)
Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is
(i) 6
(ii) 12
(iii) 7

CBSE 10th Standard Maths Subject Probability Ncert Exemplar 3 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Box A contains 25 slips of which 19 are marked Rs. 1 and other are marked Rs. 5 each. Box B contains 50 slips of which 45 are marked Rs 1 each and others are marked Rs 13 each. Slips of both boxes are poured into a third box and reshuffled. A slip is drawn at random. What is the probability that it is marked other than Rs 1?
2)
A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded.
(i) How many different scores are possible?
(ii) What is the probability of getting a total of 7?
3)
A lot consists of 48 mobiles phones of which 42 are good, 3 have only minor defects and 3 have major defects. Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is
(i) acceptable to Varnika?
(ii) acceptable to the trader?
4)
A carton of 24 bulbs contains 6 defective bulbs.One bulb is drawn at random.What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?
5)
Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is
(i) 6
(ii) 12
(iii) 7

CBSE 10th Standard Maths Subject Probability Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.
2)
A ticket is drawn at random from a bag containing tickets numbered from 1 to 40. Find the probability that the selected ticket has a number,
(i) which is a multiple of 7
(ii) which is a multiple of 5.
3)
At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player select one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that
(i) the first player wins a prize?
(ii) the second player wins a prize, if the first has won?
4)
There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs. 100 each, 100 of them contain a cash prize of Rs. 50 each and 200 of them contain a cash and an envelope is picked up out, what is the probability that it contains no cash prize?
5)
A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since this situation has only two possible outcomes, so, the probability of each is \(\frac{1}{2}\). Justify.

CBSE 10th Standard Maths Subject Probability Ncert Exemplar 2 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.
2)
A ticket is drawn at random from a bag containing tickets numbered from 1 to 40. Find the probability that the selected ticket has a number,
(i) which is a multiple of 7
(ii) which is a multiple of 5.
3)
There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs. 100 each, 100 of them contain a cash prize of Rs. 50 each and 200 of them contain a cash and an envelope is picked up out, what is the probability that it contains no cash prize?
4)
A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since this situation has only two possible outcomes, so, the probability of each is \(\frac{1}{2}\). Justify.
5)
In a family having three children, there may bo no girl, two girls or three girls. So, the probability of each is \(\frac{1}{4}\). Is this correct? Justify your answer.

CBSE 10th Standard Maths Subject Statistics Ncert Exemplar 4 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Calculate the mean of the scores of 20 students in a Mathematics test.

Marks 10-20 20-30 30-40 40-50 50-60

Number of students 2 4 7 6 1

Marks	10-20	20-30	30-40	40-50	50-60
Number of students	2	4	7	6	1

2)

Determine the mean of the following distribution.

Marks	Number of students
Below 10	5
Below 20	9
Below 30	17
Below 40	29
Below 50	45
Below 60	60
Below 70	70
Below 80	78
Below 90	83
Below 100	85

3)
An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table:

Number of seats 100-104 104-108 108-112 112-116 116-120

Frequency 15 20 32 18 15

Determine the mean number of seats occupied over the flights.
4)
The mileage (in km/L) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below:

Mileage (in km/L) 10-12 12-14 14-16 16-18

Number of cars 7 12 18 13

Find the mean mileage. The manufacturer claimed that the mileage of the model was 16 km/L. Do you agree with this claim?
5)
The mean of the following frequency distribution is 50, but the frequencies f₁ and f₂ in classes 20-40 and 60-80 respectively are missing. Find the missing frequencies.

Class interval 0-20 20-40 40-60 60-80 80-100 Total

Frequency 17 f₁ 32 f₂ 19 120

Number of seats	100-104	104-108	108-112	112-116	116-120
Frequency	15	20	32	18	15

Mileage (in km/L)	10-12	12-14	14-16	16-18
Number of cars	7	12	18	13

Class interval	0-20	20-40	40-60	60-80	80-100	Total
Frequency	17	f₁	32	f₂	19	120

CBSE 10th Standard Maths Subject Statistics Ncert Exemplar 4 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Calculate the mean of the following data.

Class 4-7 8-11 12-15 16-19

Frequency 5 4 9 10
2)
Calculate the mean of the scores of 20 students in a Mathematics test.

Marks 10-20 20-30 30-40 40-50 50-60

Number of students 2 4 7 6 1

Class	4-7	8-11	12-15	16-19
Frequency	5	4	9	10

Marks	10-20	20-30	30-40	40-50	50-60
Number of students	2	4	7	6	1

3)

Determine the mean of the following distribution.

Marks	Number of students
Below 10	5
Below 20	9
Below 30	17
Below 40	29
Below 50	45
Below 60	60
Below 70	70
Below 80	78
Below 90	83
Below 100	85

4)
The mileage (in km/L) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below:

Mileage (in km/L) 10-12 12-14 14-16 16-18

Number of cars 7 12 18 13

Find the mean mileage. The manufacturer claimed that the mileage of the model was 16 km/L. Do you agree with this claim?
5)
The mean of the following frequency distribution is 50, but the frequencies f₁ and f₂ in classes 20-40 and 60-80 respectively are missing. Find the missing frequencies.

Class interval 0-20 20-40 40-60 60-80 80-100 Total

Frequency 17 f₁ 32 f₂ 19 120

Mileage (in km/L)	10-12	12-14	14-16	16-18
Number of cars	7	12	18	13

Class interval	0-20	20-40	40-60	60-80	80-100	Total
Frequency	17	f₁	32	f₂	19	120

CBSE 10th Standard Maths Subject Areas Related to Circles Ncert Exemplar 4 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
In the given figure, arcs have been drawn with radius 14 cm each and with centres P,Q and R. Find the area of the shaded region.
2)
In the given figure, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.
3)
Find the area of the segment of a circle of radius 12 cm, whose corresponding sector has a central angle of 60^o . [Take, \(\pi =3.14\)].
4)
Four circular cardboard pieces of radius 7 cm are placed on a paper in such a way that each piece touches other two pieces, Find the area of the portion enclosed between these pieces.
5)
In the figure given alongside, a circle is inscribed in a square of side 4 ern and another circle is circumscribing the square. Prove that the area of the circumscribed circle is two times the area of the inscribed circle.

CBSE 10th Standard Maths Subject Areas Related to Circles Ncert Exemplar 4 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
In the given figure, arcs have been drawn with radius 14 cm each and with centres P,Q and R. Find the area of the shaded region.
2)
In the given figure, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.
3)
Four circular cardboard pieces of radius 7 cm are placed on a paper in such a way that each piece touches other two pieces, Find the area of the portion enclosed between these pieces.
4)
In the figure given alongside, a circle is inscribed in a square of side 4 ern and another circle is circumscribing the square. Prove that the area of the circumscribed circle is two times the area of the inscribed circle.
5)
Find the area of the shaded region given in figure.

CBSE 10th Standard Maths Subject Areas Related to Circles Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 \(cm^2\) (Use \(\pi\) = 3.14).
2)
Find the number of revolutions made by a circular wheel of area 1.54 \(m^2\) in rolling a distance of 176 m.
3)
An archery target has three regions formed by three concentric circles as shown in Fig. If the diameters of the concentric circles are in the ratio 1 : 2 : 3, then find the ratio of the areas of three regions.
4)
Find the radius of a circle whose circumference is equal to the sum of the circumference of two circles of radii 15cm and 18 cm.
5)
In the given figure, arcs are drawn by taking vertices A. B and C of an equilateral triangle of side 10 cm, to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region.

CBSE 10th Standard Maths Subject Areas Related to Circles Ncert Exemplar 2 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 \(cm^2\) (Use \(\pi\) = 3.14).
2)
Find the number of revolutions made by a circular wheel of area 1.54 \(m^2\) in rolling a distance of 176 m.
3)
An archery target has three regions formed by three concentric circles as shown in Fig. If the diameters of the concentric circles are in the ratio 1 : 2 : 3, then find the ratio of the areas of three regions.
4)
Find the area of the largest circle that can be drawn inside the given rectangle of length 'a' cm and breadth 'b' cm (a>b).
5)
In the given figure, arcs are drawn by taking vertices A. B and C of an equilateral triangle of side 10 cm, to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region.

CBSE 10th Standard Maths Subject Circles Ncert Exemplar 3 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
The tangent at a point C of a circle and a diameter AB when extended intersect at P.If \(\angle PCA=110^0\), find \(\angle CBA\) [see figure] Join C with centre O
2)
In figure, AB and CD are common tangents to two circles of unequal radii.Prove that AB=CD.
3)
If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in figure.Prove that \(\angle BAT=\angle ACB\)
4)
If an isosceles ∆ABC in which AB = AC = 6 cm is inscribed in a circle of radius 9 cm, then find the area of the triangle
5)
AB is a diameter of a circle and AC is its chord such that \(\angle BAC=30°\). If the tangent at C intersects AB extended at D, then prove that BC = BD.

CBSE 10th Standard Maths Subject Circles Ncert Exemplar 3 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
The tangent at a point C of a circle and a diameter AB when extended intersect at P.If \(\angle PCA=110^0\), find \(\angle CBA\) [see figure] Join C with centre O
2)
In figure, AB and CD are common tangents to two circles of unequal radii.Prove that AB=CD.
3)
From an external point P, two tangents, PA and PB are drawn to a circle with centre O.At one point E on the circle tangent is drawn which intersect PA and PB at C and D, respectively.If PA = 10cm, find the perimeter of the triangle PCD.
4)
If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in figure.Prove that \(\angle BAT=\angle ACB\)
5)
AB is a diameter of a circle and AC is its chord such that \(\angle BAC=30°\). If the tangent at C intersects AB extended at D, then prove that BC = BD.

CBSE 10th Standard Maths Subject Introduction to Trigonometry Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Name the type of triangle formed by the points A(-5, 6), B(-4, 2) and C(7, 5).
2)
Find the value of m if the points (5, 1), (-2, -3) and (8, 2m) are collinear.
3)
The points A(2, 9), B(a, 5) and C(5, 5) Are the vertices of \(\triangle ABC\) right angled at B. Find the value of a and hence the area of \(\triangle ABC\).
4)
Name the type of triangle PQR formed by the points \(P(\sqrt { 2 } ,\sqrt { 2 } ),Q(-\sqrt { 2 } ,-\sqrt { 2 } )\) and \(R(-\sqrt { 6 } ,\sqrt { 6 } )\)
5)
Show that \(\Delta \)ABC with vertices A(-2, 0), B(0, 2) and C(2,0) is similar to \(\Delta \)DFE with vertices D(- 4, 0), E(4, 0) and F(0, 4).

CBSE 10th Standard Maths Subject Introduction to Trigonometry Ncert Exemplar 2 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
If \(\sin ^{ 2 }{ \theta } -\cos ^{ 2 }{ \theta } =2,\) find the value of \(\theta\)
2)
Prove that \(\sqrt { \sec ^{ 2 }{ \theta } +{ cosec }^{ 2 }\theta } =\tan { \theta } +\cot { \theta } .\)
3)
If cos 9 \(\alpha\) = sin \(\alpha\) and value of tan 5 \(\alpha\) is 9 \(\alpha\) < 90°, then the
4)
If sin \(\theta\) + 2 cos \(\theta\) = 1. prove that 2 sin \(\theta\) - cos \(\theta\) = 2.
5)
If 1 + sin² \(\theta\) = 3 sin \(\theta\) cos \(\theta\), prove that \(\tan \theta=1 \text { or } \frac{1}{2}\)

CBSE 10th Standard Maths Subject Introduction to Trigonometry Ncert Exemplar 1 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Given that \(\sin { \alpha } =\frac { 1 }{ 2 } \) and \(\cos { \beta } =\frac { 1 }{ 2 } ,\) what is the value of \((\alpha +\beta )?\)
2)
If \(\cos { 9\alpha } =\sin { \alpha } \) and \(9\alpha <{ 90 }^{ 0 },\) find the value of \(\tan { 5\alpha } .\)
3)
Prove \((\tan { \theta } +2)(2\tan { \theta } +1)=5\tan { \theta } +2\sec ^{ 2 }{ \theta } .\)
4)
Find the value of \(\left[ \frac { \sin ^{ 2 }{ { 22 }^{ 0 } } +\sin ^{ 2 }{ { 68 }^{ 0 } } }{ \cos ^{ 2 }{ { 22 }^{ 0 } } +\cos ^{ 2 }{ { 68 }^{ 0 } } } +\sin ^{ 2 }{ { 63 }^{ 0 } } +\sin { { 27 }^{ 0 } } \cos { { 63 }^{ 0 } } \right] .\)
5)
If \(\cos { A } +\cos ^{ 2 }{ A } =1,\) find the value of \(\sin ^{ 2 }{ A } +\sin ^{ 4 }{ A } .\)

CBSE 10th Standard Maths Subject Introduction to Trigonometry Ncert Exemplar 1 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Given that \(\sin { \alpha } =\frac { 1 }{ 2 } \) and \(\cos { \beta } =\frac { 1 }{ 2 } ,\) what is the value of \((\alpha +\beta )?\)
2)
If \(\cos { 9\alpha } =\sin { \alpha } \) and \(9\alpha <{ 90 }^{ 0 },\) find the value of \(\tan { 5\alpha } .\)
3)
Prove \((\tan { \theta } +2)(2\tan { \theta } +1)=5\tan { \theta } +2\sec ^{ 2 }{ \theta } .\)
4)
Find the value of \(\left[ \frac { \sin ^{ 2 }{ { 22 }^{ 0 } } +\sin ^{ 2 }{ { 68 }^{ 0 } } }{ \cos ^{ 2 }{ { 22 }^{ 0 } } +\cos ^{ 2 }{ { 68 }^{ 0 } } } +\sin ^{ 2 }{ { 63 }^{ 0 } } +\sin { { 27 }^{ 0 } } \cos { { 63 }^{ 0 } } \right] .\)
5)
If \(\cos { A } +\cos ^{ 2 }{ A } =1,\) find the value of \(\sin ^{ 2 }{ A } +\sin ^{ 4 }{ A } .\)

CBSE 10th Standard Maths Subject Coordinate Geometry Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Name the type of triangle formed by the points A(-5, 6), B(-4, 2) and C(7, 5).
2)
Find the value of m if the points (5, 1), (-2, -3) and (8, 2m) are collinear.
3)
The points A(2, 9), B(a, 5) and C(5, 5) Are the vertices of \(\triangle ABC\) right angled at B. Find the value of a and hence the area of \(\triangle ABC\).
4)
Name the type of triangle PQR formed by the points \(P(\sqrt { 2 } ,\sqrt { 2 } ),Q(-\sqrt { 2 } ,-\sqrt { 2 } )\) and \(R(-\sqrt { 6 } ,\sqrt { 6 } )\)
5)
Show that \(\Delta \)ABC with vertices A(-2, 0), B(0, 2) and C(2,0) is similar to \(\Delta \)DFE with vertices D(- 4, 0), E(4, 0) and F(0, 4).

CBSE 10th Standard Maths Subject Coordinate Geometry Ncert Exemplar 2 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Name the type of triangle formed by the points A(-5, 6), B(-4, 2) and C(7, 5).
2)
Find the value of m if the points (5, 1), (-2, -3) and (8, 2m) are collinear.
3)
The points A(2, 9), B(a, 5) and C(5, 5) Are the vertices of \(\triangle ABC\) right angled at B. Find the value of a and hence the area of \(\triangle ABC\).
4)
Name the type of triangle PQR formed by the points \(P(\sqrt { 2 } ,\sqrt { 2 } ),Q(-\sqrt { 2 } ,-\sqrt { 2 } )\) and \(R(-\sqrt { 6 } ,\sqrt { 6 } )\)
5)
Show that \(\Delta \)ABC with vertices A(-2, 0), B(0, 2) and C(2,0) is similar to \(\Delta \)DFE with vertices D(- 4, 0), E(4, 0) and F(0, 4).

CBSE 10th Standard Maths Subject Coordinate Geometry Ncert Exemplar 1 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the distance of the point P(2, 3) from the x-axis.
2)
Find the distance between the points A(0, 6) and B(0, -2).
3)
Find the distance between the points (0, 5) and (-5, 0).
4)
If (-4, 0), (4, 0) and (0, 3) are the vertices of a triangle, then write the shape of the triangle.
5)
Find the distance of the point P(-6, 8) from the origin.

CBSE 10th Standard Maths Subject Coordinate Geometry Ncert Exemplar 1 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the distance between the points (0, 5) and (-5, 0).
2)
If (-4, 0), (4, 0) and (0, 3) are the vertices of a triangle, then write the shape of the triangle.
3)
Find the distance of the point P(-6, 8) from the origin.
4)
If point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then write the relation between AP and AB.
5)
Does the point P(-2, 4) lie on a circle of radius 6 units and centre C(3, 5)?

CBSE 10th Standard Maths Subject Triangles Ncert Exemplar 4 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
A 15 m high tower casts a shadow 24 m long at a certain time and at the same time, telephone pole caste a shadow 16 m long. Find the height of the telephone pole.
2)
Shweta prepared two posters on National Integration for decoration on Independence day on triangular sheets (say ABC and DEF). The sides AB and AC and the perimeter P₁ of \(\triangle ABC\) are respectively four times the corresponding sides DE and DF and the perimeter P₂ of \(\triangle DEF\). Are the two triangular sheets similar? If yes, find \(\frac { ar\left( \triangle ABC \right) }{ ar\left( \triangle DEF \right) } \). What values can be indicated through celebration of national festivals?
3)
In \(\triangle PQR,PD\bot QR\) such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, then prove that (a + b) (a - b) = (c + d) (c - d).
4)
In the given figure, IIIm and line segments AB, CD and EF are concurrent at point P. Prove that \(\frac{A E}{B F}=\frac{A C}{B D}=\frac{C E}{F D}\)
5)
In the given figure, if PQRS is a parallelogram and AB || PS, prove that OC II SR.

CBSE 10th Standard Maths Subject Triangles Ncert Exemplar 4 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
A 15 m high tower casts a shadow 24 m long at a certain time and at the same time, telephone pole caste a shadow 16 m long. Find the height of the telephone pole.
2)
Shweta prepared two posters on National Integration for decoration on Independence day on triangular sheets (say ABC and DEF). The sides AB and AC and the perimeter P₁ of \(\triangle ABC\) are respectively four times the corresponding sides DE and DF and the perimeter P₂ of \(\triangle DEF\). Are the two triangular sheets similar? If yes, find \(\frac { ar\left( \triangle ABC \right) }{ ar\left( \triangle DEF \right) } \). What values can be indicated through celebration of national festivals?
3)
In the given figure, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find PQ, QR and RS.
4)
In the adjoining figure, ABC is a triangle right angled at B and \(BD\bot AC\) . If AD = 4 cm and CD = 5 cm. find BD and AB.
5)
In the given figure, if PQRS is a parallelogram and AB || PS, prove that OC II SR.

CBSE 10th Standard Maths Subject Triangles Ncert Exemplar 3 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3 m, find how far is she away from the base of the pole?
2)
If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, find the length of the sides of the rhombus.
3)
\(\triangle ABC\) and \(\triangle AMP\) are two right angled triangles. right angled at B and M, respectively. Prove that CA x MP = PA x BC
4)
In the given figure, if \(AB\parallel DC\) and AC, PQ intersect each other at the point O, then prove that OA. CQ = OC.AP.
5)
If \(\triangle ABC\sim \triangle QRP\), \(\frac { ar\left( \triangle ABC \right) }{ ar\left( \triangle QRP \right) } =\frac { 9 }{ 4 } \), AB = 18 cm and BC = 15 cm, then find PR.

CBSE 10th Standard Maths Subject Triangles Ncert Exemplar 3 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3 m, find how far is she away from the base of the pole?
2)
If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, find the length of the sides of the rhombus.
3)
For going to city B from city A, there is a route via city C such that \(AC\bot CB\) , AC = 2x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway, which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction on the highway?
4)
It is given that \(\triangle ABC\sim \triangle EDF\) such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.
5)
If \(\triangle ABC\sim \triangle QRP\), \(\frac { ar\left( \triangle ABC \right) }{ ar\left( \triangle QRP \right) } =\frac { 9 }{ 4 } \), AB = 18 cm and BC = 15 cm, then find PR.

CBSE 10th Standard Maths Subject Triangles Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the third side of a right angled triangle whose hypotenuse is of length p cm, one side of length q cm and p - q = 1.
2)
ABCD is a trapezium in which \(AB\parallel DC\). P and Q are points on sides AD and BC respectively such that \(PQ\parallel AB\). If PD = 18 cm, BQ = 35 cm and QC = 15 cm, find the value of AD.
3)
In the given figure, if \(\angle1=\angle2\) and \(\triangle NSQ\cong \triangle MTR\) , prove that \(\triangle PTS\sim \triangle PRQ\)
4)
In the given figure, if \(\angle A=\angle C, A B=6\) cm BP = 15 cm, AP = 12 cm and CP = 4 cm, find the lengths of PD and CD.
5)
In the given figure PA, QB, RC and SD are all perpendiculars to a line 1, AB = 6 cm, BC = 9 cm,CD = 12 cm and SP = 36 cm. Then, find the PQ,QR and RS.

CBSE 10th Standard Maths Subject Triangles Ncert Exemplar 2 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the third side of a right angled triangle whose hypotenuse is of length p cm, one side of length q cm and p - q = 1.
2)
ABCD is a trapezium in which \(AB\parallel DC\). P and Q are points on sides AD and BC respectively such that \(PQ\parallel AB\). If PD = 18 cm, BQ = 35 cm and QC = 15 cm, find the value of AD.
3)
In the given figure, if \(\angle1=\angle2\) and \(\triangle NSQ\cong \triangle MTR\) , prove that \(\triangle PTS\sim \triangle PRQ\)
4)
In the given figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm. PB = 3 cm, PC = 2.5 cm, PD = 5 cm \(\angle A P B=50^{\circ} \text { and } \angle C D P=30^{\circ} . \text { Then find } \angle P B A\)
5)
In the given figure, if \(\angle A=\angle C, A B=6\) cm BP = 15 cm, AP = 12 cm and CP = 4 cm, find the lengths of PD and CD.

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar 4 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
2)
Kanoka was given her pocket money on Jan 1st, 2008. She puts Rs.1 on day 1, Rs.2 on day 2, Rs.3 on day 3, and continued doing so til the end of the month, from this money into her piggy bank. She also spent Rs.204 of her pocket money, and found that at the end of the month she still had Rs.100 with her. How much was her pocket money for the month?
3)
The sum of the first five terms of an AP and the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
4)
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first five terms to the sum of the first 21 terms.
5)
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to \(\frac{(a+c)(b+c-2a)}{2(b-a)}\).

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar 4 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the sum of the integers between 100 and 200 that is not divisible by 9.
2)
If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
3)
The sum of the first five terms of an AP and the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
4)
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to \(\frac{(a+c)(b+c-2a)}{2(b-a)}\).
5)
Jaipal Singh repays the total loan of Rs 118000 by paying every month starting with the first instalment of Rs 1000. If the increases the instalment by Rs 100 every month, then what amount will be paid by him in the 30th instalment? What amount of loan does he still have to pay after 30th instalment?

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar 3 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the sum: \(\frac{a - b}{a + b}+\frac{3a - 2b}{a + b}+\frac{5a - 3b}{a + b}+...\) to 11 terms.
2)
The sum of first three terms of an A.P. is 33. If the product of the first and third term exceeds the second term by 29, find the A.P.
3)
The sum of the first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. whose first term is -30 and the common difference is 8. Find n.
4)
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on day, 1, Rs 2 on day 2, Rs 3 on day 3 and continued doing so till the end of the month, from this money into her piggy back she also spent Rs 204 of her pocket money and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
5)
Find the sum of those integers between 1 and 500, which are multiples of 2 as well as of 5.

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar 3 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on day, 1, Rs 2 on day 2, Rs 3 on day 3 and continued doing so till the end of the month, from this money into her piggy back she also spent Rs 204 of her pocket money and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
2)
The sum of the first five terms and the sum of the first seven terms of an AP is 167. If the sum of the first ten terms of this AP is 235. then find the sum of its first twenty terms.
3)
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.
4)
Find the sum of first 17 terms of an AP, where 4th and 9th terms are -15 and - 30, respectively.
5)
Find the sum of those integers between 1 and 500, which are multiples of 2 as well as of 5.

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
The eighth term of an AP is half its second term and the eleventh term exceeds one-third of its fourth term by 1. Find the 15th term.
2)
Justify whether it is true to say that -1,\(-\frac{3}{2}\) -2,\(-\frac{5}{2}\)..... forms an AP as a₂ - a₁ = a₃ - a₂.
3)
Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?
4)
The taxi fare each km, when the fare is Rs.15 for the first km and Rs.8 for each additional km, does not form an AP as the total fare (in Rs) after each km is 15, 8, 8, 8,.............
5)
In which of the following situations do the lists of numbers involved form an AP? Give reasons for your answers.
(i) The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs.400.
(ii) The fee charged every month by a school from classes I to XII, when the monthly fee for class I is Rs.250, and it increased by Rs.50 for the next higher class.
(iii) The amount of money in the account of Varun at the end of every year when Rs.1000 is deposited at simple interest of 10% per annum.
(iv) The number of bacteria in a certain food after each second, when they double in every second.

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar 2 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?
2)
The taxi fare each km, when the fare is Rs.15 for the first km and Rs.8 for each additional km, does not form an AP as the total fare (in Rs) after each km is 15, 8, 8, 8,.............
3)
In which of the following situations do the lists of numbers involved form an AP? Give reasons for your answers.
(i) The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs.400.
(ii) The fee charged every month by a school from classes I to XII, when the monthly fee for class I is Rs.250, and it increased by Rs.50 for the next higher class.
(iii) The amount of money in the account of Varun at the end of every year when Rs.1000 is deposited at simple interest of 10% per annum.
(iv) The number of bacteria in a certain food after each second, when they double in every second.
4)
Find the sum of the two middle terms of the AP: \(-\frac{ 4}{3 },-1,-\frac{ 2}{ 3},....,4\frac{ 1}{ 3}.\)
5)
How many terms of the AP: -15, -13, -11,.... are needed to make the sum -55? Explain the reason for double answer.

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar 1 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the 6th term from the end of the A.P. -11, -8, -5, ...., 49
2)
If the first term of an A.P. is -5 and the common difference is 2, then find the sum of the first 6 terms.
3)
If 7 times the 7th term of A.P. is equal to 11 times the 11th term, then find the 18th term.
4)
If the common difference of an A.P. is 5, then find the value of a₁₈ - a₁₃ .
5)
Name the famous mathematician associated with finding the sum of the first 100 natural numbers.

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar 1 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
In an A.P., if a = 1, a_n= 20 and S_n = 399, then find the value of n.
2)
If 7 times the 7th term of A.P. is equal to 11 times the 11th term, then find the 18th term.
3)
If the common difference of an A.P. is 5, then find the value of a₁₈ - a₁₃ .
4)
Find the sum of first five multiples of 3.
5)
If a_n = 3 - 4n, show that a₁, a₂, a₃,.......form an A.P.

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar MCQ Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
If an AP have 8 as the first term and -5 as the common difference and its first three terms are 8, A. B, then (A + B) is equal to
2)
Let a be a sequence defined by a₁ = 1, a₂ = 1 and an = a_{n - 1} + a_{n - 2} for all n > 2, then the value of \(\frac{a_{4}}{a_{3}}\) is
3)
Which term of the AP 5, 15,25, ... will be 130 more than its 31st term?
4)
The 10th term of an AP is 52 and 16 th term is 82, then 32nd term of the AP is
5)
Is an sequence defined by a_n = 2n² +1 forms an AP?

CBSE 10th Standard Maths Subject Arithmetic Progressions Ncert Exemplar MCQ Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
If an AP have 8 as the first term and -5 as the common difference and its first three terms are 8, A. B, then (A + B) is equal to
2)
Let a be a sequence defined by a₁ = 1, a₂ = 1 and an = a_{n - 1} + a_{n - 2} for all n > 2, then the value of \(\frac{a_{4}}{a_{3}}\) is
3)
Which term of the AP 5, 15,25, ... will be 130 more than its 31st term?
4)
The 10th term of an AP is 52 and 16 th term is 82, then 32nd term of the AP is
5)
Is an sequence defined by a_n = 2n² +1 forms an AP?

CBSE 10th Standard Maths Subject Quadratic Equations Ncert Exemplar 3 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
At t minutes past 2 p.m. the time needed by the minutes hand of a clock to show 3 p.m. was found to be 3 minutes less than \(t^2\over 4\)minutes. Find t.
2)
Find whether \(5x^{2} - 2x - 10 = 0\) has real roots. If real roots exist, find them.
3)
Find whether \({1\over {2x - 3}} + {1\over {x - 5}} = 1 , \ x \neq {3\over 2} , 5\) has real roots. If real roots exist , find them.
4)
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
5)
Find the roots of the following quadratic equations by the factorisation method
(i) \(2x^{ 2 }+\frac { 5 }{ 3 } X-2=0\)
(ii) \(\frac { 2 }{ 5 } x^{ 2 }-x-\frac { 3 }{ 5 } =0\)

CBSE 10th Standard Maths Subject Quadratic Equations Ncert Exemplar 3 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find whether \(5x^{2} - 2x - 10 = 0\) has real roots. If real roots exist, find them.
2)
Find whether \({1\over {2x - 3}} + {1\over {x - 5}} = 1 , \ x \neq {3\over 2} , 5\) has real roots. If real roots exist , find them.
3)
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
4)
Find the roots of the following quadratic equations by the factorisation method
(i) \(2x^{ 2 }+\frac { 5 }{ 3 } X-2=0\)
(ii) \(\frac { 2 }{ 5 } x^{ 2 }-x-\frac { 3 }{ 5 } =0\)
5)
What is/are the value(s) of k for which the quadratic equation \(2x^{ 2 }-kx+k=0\) has equal root ?

CBSE 10th Standard Maths Subject Quadratic Equations Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the roots of the quadratic equation \(3\sqrt {2}x^{2} - 5x - \sqrt {2} = 0\) by factorisation method.
2)
If \(\frac { 1 }{ 2 } \) is a root of the equation x² +kx-\(\frac{5}{4}\)=0, then find the value of k.
3)
Find the value of k for which the quadratic equation 2x²-kx+k=0 has equal roots.
4)
Which of the following is not a quadratic equation?
(i) \((\sqrt{2} x+\sqrt{3})^{2}=3 x^{2}-5 x\)
5)
A and B are centres of two circles of radii 9 cm and 2 cm respectively and AB = 17 cm. C is the centre of a circle of radius x em, which touches the above circles externally. Given that ∠ACB = 90°, write an equation in x and solve it for x.

CBSE 10th Standard Maths Subject Quadratic Equations Ncert Exemplar 2 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the roots of the quadratic equation \(-3x^{2} + 5x + 12 = 0\) by using the quadratic formula.
2)
Find the roots of the quadratic equation \(x^{2} + 2 {\sqrt {2}}x - 6 = 0\) by using the quadratic formula.
3)
Find the roots of the quadratic equation \(2x^{2} + {5\over3}x -2 = 0\) by factorisation method.
4)
If \(\frac { 1 }{ 2 } \) is a root of the equation x² +kx-\(\frac{5}{4}\)=0, then find the value of k.
5)
A and B are centres of two circles of radii 9 cm and 2 cm respectively and AB = 17 cm. C is the centre of a circle of radius x em, which touches the above circles externally. Given that ∠ACB = 90°, write an equation in x and solve it for x.

CBSE 10th Standard Maths Subject Quadratic Equations Ncert Exemplar 1 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
State whether the following quadratic equations have two different real roots. Justify your answer. \(\sqrt2 x^2-{3\over\sqrt2}x+{1\over\sqrt2}=0\)
2)
State whether the following quadratic equations have two different real roots. Justify your answer. (x-1)(x+2)+2=0
3)
A quadratic equation with integral coefficient has integral roots. Justify your answer
4)
Find the roots of the quadratic equation \(3\sqrt {2}x^{2} - 5x - \sqrt {2} = 0\) .
5)
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

CBSE 10th Standard Maths Subject Quadratic Equations Ncert Exemplar 1 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
State whether the following quadratic equations have two different real roots. Justify your answer. \((x-\sqrt2)^2-2(x+1)=0\)
2)
State whether the following quadratic equations have two different real roots. Justify your answer. \(\sqrt2 x^2-{3\over\sqrt2}x+{1\over\sqrt2}=0\)
3)
State whether the following quadratic equations have two different real roots. Justify your answer. (x-1)(x+2)+2=0
4)
Which constant should be added or subtracted to solve the quadratic equation \(4x^{2} - \sqrt {3 }x -5 = 0\) by the method of completing the square?
5)
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

CBSE 10th Standard Maths Subject Quadratic Equations Ncert Exemplar MCQ Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
The sum of the squares of three consecutive integers is 110, then the smallest positive integer is
2)
Is -8 is a solution of the equation 3x² + 8x + 2 = 0?
3)
A line segment AB is 8 cm in length. AB is produced to P such that Bp² = AB· AP. Then, the length of BP is
4)
If α and β are roots of equation ax² + bx + c = 0, then \(\frac{\alpha}{a \beta+b}+\frac{\beta}{a \alpha+b}\) equals
5)
If x = \(\frac{1}{\sqrt{3}}\) IS root of the equation Px² + ( \(\sqrt3\) - \(\sqrt{2}\)) x - 1 = 0, then the value of p² + 1 is

CBSE 10th Standard Maths Subject Quadratic Equations Ncert Exemplar MCQ Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
The sum of the squares of three consecutive integers is 110, then the smallest positive integer is
2)
Is -8 is a solution of the equation 3x² + 8x + 2 = 0?
3)
A line segment AB is 8 cm in length. AB is produced to P such that Bp² = AB· AP. Then, the length of BP is
4)
If α and β are roots of equation ax² + bx + c = 0, then \(\frac{\alpha}{a \beta+b}+\frac{\beta}{a \alpha+b}\) equals
5)
If x = \(\frac{1}{\sqrt{3}}\) IS root of the equation Px² + ( \(\sqrt3\) - \(\sqrt{2}\)) x - 1 = 0, then the value of p² + 1 is

CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Ncert Exemplar 4 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Write a pair of linear equations which has the unique solution x=-1 and y=3. How many such pairs can you write?
2)
Find the solution of the pair of equations \(\frac { x }{ 10 } +\frac { y }{ 5 } -1=0\) and \(\frac { x }{ 8 } +\frac { y }{ 6 } =15\) and find \(\lambda ,\) if \(y=\lambda x+5.\)
3)
Reduce the following pair of equations into a pair of linear equations and solve them
\(\frac { 2xy }{ x+y } =\frac { 3 }{ 2 } ,\quad \frac { xy }{ 2x-y } =\frac { -3 }{ 10 } ;\quad x+y\neq 0,\quad 2x-y\neq 0\)
4)
Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour, if she travels 2 km by rickshaw and the remaining distance by bus.
On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 min longer. Find the speed of rickshaw and of the bus.
5)
Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs.1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would received Rs.20 more as annual interest. How much money did she invest in each scheme?

CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Ncert Exemplar 4 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the solution of the pair of equations \(\frac { x }{ 10 } +\frac { y }{ 5 } -1=0\) and \(\frac { x }{ 8 } +\frac { y }{ 6 } =15\) and find \(\lambda ,\) if \(y=\lambda x+5.\)
2)
Reduce the following pair of equations into a pair of linear equations and solve them
\(\frac { 2xy }{ x+y } =\frac { 3 }{ 2 } ,\quad \frac { xy }{ 2x-y } =\frac { -3 }{ 10 } ;\quad x+y\neq 0,\quad 2x-y\neq 0\)
3)
Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs.1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would received Rs.20 more as annual interest. How much money did she invest in each scheme?
4)
For which values of p and q, will the following pair of linear equations have infinitely many solutions?
4x+5y=2, (2p+71)x+(p+8q)y=2q-p+1
5)
Form the pair of linear equation in the following problems and find their solutions graphically.
The cost of 4 pens and 4 pencil boxes is Rs.100. Threetimes the cost of a pen is Rs.15 more than the cost of a pencil box. Find the cost of a pen and a pencil box.

CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Ncert Exemplar 3 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Draw the graph of the pair of linear equation x-y+2=0 and 4x-y-4. Calculate the area of the triangle formed by the lines so drawn and the X-axis.
2)
Solve the following pair of linear equations.
\(\frac { x }{ 7 } +\frac { y }{ 3 } =a+b;\frac { x }{ { a }^{ 2 } } +\frac { y }{ { b }^{ 2 } } =2,\quad a,b\neq 0\)
3)
Show that the following system of equations has a unique solution. 3x+5y=12, 5x+3y=4 Also, find the solution of the given system of equations.
4)
Two chairs and three tables cost Rs.5650 whereas three chairs and two tables cost Rs.7100. Find the cost of a chair and a table separately.
5)
The angles of a cyclic quadrilateral ABCD are \(\angle A={ (6x+10) }^{ 0 },\angle B={ (5x) }^{ 0 },\angle C={ (x+y) }^{ 0 }\) and \(\angle D={ (3y-10) }^{ 0 }\) Find x and y and then the values of the four angles.

CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Ncert Exemplar 3 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Show that the following system of equations has a unique solution. 3x+5y=12, 5x+3y=4 Also, find the solution of the given system of equations.
2)
Two chairs and three tables cost Rs.5650 whereas three chairs and two tables cost Rs.7100. Find the cost of a chair and a table separately.
3)
The angles of a cyclic quadrilateral ABCD are \(\angle A={ (6x+10) }^{ 0 },\angle B={ (5x) }^{ 0 },\angle C={ (x+y) }^{ 0 }\) and \(\angle D={ (3y-10) }^{ 0 }\) Find x and y and then the values of the four angles.
4)
Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x - y = 1. How many such lines can we find?
5)
Determine algebraically, the vertices of the triangle formed by the lines
3x-y=3, 2x-3y=2 and x+2y=8.

CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.
2)
If a motorboat can travel 30 km upstream and 28km down stream in 7 h, it can travel 21 km upstream and return in 5 h. Find the speed of the boat in still water and the speed of the stream.
3)
There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.
4)
If the angles of a triangle are x, y and 40⁰ and the difference between the two angles x and y is 30⁰ . Then, find the values of x and y.
5)
Find the values of x and y in the given rectangle.

CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Ncert Exemplar 2 Marks Questions 2021 - by Prerna - Bangalore - May 26, 2021 - View & Read

1)
Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.
2)
If a motorboat can travel 30 km upstream and 28km down stream in 7 h, it can travel 21 km upstream and return in 5 h. Find the speed of the boat in still water and the speed of the stream.
3)
There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.
4)
If the angles of a triangle are x, y and 40⁰ and the difference between the two angles x and y is 30⁰ . Then, find the values of x and y.
5)
Find the values of x and y in the given rectangle.

CBSE 10th Standard Maths Subject Real Number Ncert Exemplar 4 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
The product of two consecutive positive integers is divisible by 2. Is this statement true or false? Give reason.
2)
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
3)
Show that the square of an odd positive integer is of the form 8m + 1, where m is some whole number.
4)
Find the least number that is divisible by all the numbers from 1 to 10 (both inclusive).
5)
For any positive integer n, prove that n³ - n is divisible by 6.

CBSE 10th Standard Maths Subject Real Number Ncert Exemplar 4 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
The product of two consecutive positive integers is divisible by 2. Is this statement true or false? Give reason.
2)
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
3)
Show that the square of an odd positive integer is of the form 8m + 1, where m is some whole number.
4)
If two positive integers a and b are written as a = x³y² and b = xy³; where x, y are prime numbers, find the HCF of a and b.
5)
Find the least number that is divisible by all the numbers from 1 to 10 (both inclusive).

CBSE 10th Standard Maths Subject Real Number Ncert Exemplar 3 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Show that the square of any positive odd integer, is of the form 4m + 1, for some integer m.
2)
Explain, why (3 x 5 x 7) + 7 is a composite number?
3)
Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.
4)
Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.
5)
Prove that (\( \sqrt{p} \) + \( \sqrt{q} \) is irrational, where p and q are primes.

CBSE 10th Standard Maths Subject Real Number Ncert Exemplar 3 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Show that the square of any positive odd integer, is of the form 4m + 1, for some integer m.
2)
Explain, why (3 x 5 x 7) + 7 is a composite number?
3)
Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.
4)
Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.
5)
Prove that (\( \sqrt{p} \) + \( \sqrt{q} \) is irrational, where p and q are primes.

CBSE 10th Standard Maths Subject Real Number Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q. when this number is expressed in the form \(\frac{p}{q}\)? Give reason.
2)
Use Euclid's division algorithm to find the HCF of the following three numbers
2, 7 and 12
3)
Use Euclid's division algorithm to find the HCF of the following three numbers
1620,1725 and 255
4)
Use Euclid's division algorithm to find the HCF of the following three numbers
4407,2938 and 1469
5)
Use Euclid's division algorithm to find the HCF of the following three numbers
625,3125 and 15625

CBSE 10th Standard Maths Subject Real Number Ncert Exemplar 2 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q. when this number is expressed in the form \(\frac{p}{q}\)? Give reason.
2)
Use Euclid's division algorithm to find the HCF of the following three numbers
2, 7 and 12
3)
Use Euclid's division algorithm to find the HCF of the following three numbers
1620,1725 and 255
4)
Use Euclid's division algorithm to find the HCF of the following three numbers
4407,2938 and 1469
5)
Use Euclid's division algorithm to find the HCF of the following three numbers
625,3125 and 15625

CBSE 10th Standard Maths Subject Real Number Ncert Exemplar 1 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the largest number which divides 70 and 125 leaving remainders 5 and 8. respectively.
2)
In Euclid's division lemma, the value of r, when a positive integer a is divided by 3, are 0 and 1 only. Is this statement true or false? Justify your answer.
3)
Can the number 6ⁿ, where n being a natural number, ends with digit 5? Give reason.
4)
The product of three consecutive positive integers is divisible by 6. Is this statement true or false? Justify your answer.
5)
If the HCF of 65 and 117 is expressible in the form 65 m - 117, then find the value of m.

CBSE 10th Standard Maths Subject Real Number Ncert Exemplar 1 Marks Questions 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Find the largest number which divides 70 and 125 leaving remainders 5 and 8. respectively.
2)
In Euclid's division lemma, the value of r, when a positive integer a is divided by 3, are 0 and 1 only. Is this statement true or false? Justify your answer.
3)
Can the number 6ⁿ, where n being a natural number, ends with digit 5? Give reason.
4)
The product of three consecutive positive integers is divisible by 6. Is this statement true or false? Justify your answer.
5)
If the HCF of 65 and 117 is expressible in the form 65 m - 117, then find the value of m.

CBSE 10th Standard Maths Subject Ncert Exemplar 4 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
2)
Show that the square of an odd positive integer is of the form 8m + 1, where m is some whole number.
3)
If two positive integers a and b are written as a = x³y² and b = xy³; where x, y are prime numbers, find the HCF of a and b.
4)
Find the least number that is divisible by all the numbers from 1 to 10 (both inclusive).
5)
For any positive integer n, prove that n³ - n is divisible by 6.

CBSE 10th Standard Maths Subject Ncert Exemplar 4 Marks Questions 2021 Part - II - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
2)
Show that the square of an odd positive integer is of the form 8m + 1, where m is some whole number.
3)
If two positive integers a and b are written as a = x³y² and b = xy³; where x, y are prime numbers, find the HCF of a and b.
4)
Find the least number that is divisible by all the numbers from 1 to 10 (both inclusive).
5)
Find the zeroes of the polynomial x²-3 and verify the relationship between the zeroes and the coefficients.

CBSE 10th Standard Maths Subject Ncert Exemplar 4 Marks Questions 2021 Part - I - by QB365 - Question Bank Software - May 26, 2021 - View & Read

1)
The product of two consecutive positive integers is divisible by 2. Is this statement true or false? Give reason.
2)
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
3)
Show that the square of an odd positive integer is of the form 8m + 1, where m is some whole number.
4)
If two positive integers a and b are written as a = x³y² and b = xy³; where x, y are prime numbers, find the HCF of a and b.
5)
Find the least number that is divisible by all the numbers from 1 to 10 (both inclusive).

CBSE 10th Standard Maths Subject Ncert Exemplar 3 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
Given that, \(\sqrt { 2 } \) is a zero of the cubic polynomial \(6x^{ 3 }+\sqrt { 2x^{ 2 } } -10x-4\sqrt { 2 } \). Find its other two zeroes.
2)
What is/are the value(s) of k for which the quadratic equation \(2x^{ 2 }-kx+k=0\) has equal root ?
3)
The sum of first three terms of an A.P. is 33. If the product of the first and third term exceeds the second term by 29, find the A.P.
4)
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on day, 1, Rs 2 on day 2, Rs 3 on day 3 and continued doing so till the end of the month, from this money into her piggy back she also spent Rs 204 of her pocket money and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
5)
The sum of the first five terms and the sum of the first seven terms of an AP is 167. If the sum of the first ten terms of this AP is 235. then find the sum of its first twenty terms.

CBSE 10th Standard Maths Subject Ncert Exemplar 3 Marks Questions 2021 Part - II - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
Explain, why (3 x 5 x 7) + 7 is a composite number?
2)
Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.
3)
Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.
4)
Prove that (\( \sqrt{p} \) + \( \sqrt{q} \) is irrational, where p and q are primes.
5)
For which values of a and b, the zeroes of q(x)=x³+2x²+a are also the zeroes of the polynomial p(x)=x⁵-x⁴-4x³+3x²+3x+b?

CBSE 10th Standard Maths Subject Ncert Exemplar 3 Marks Questions 2021 Part - I - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
Show that the square of any positive odd integer, is of the form 4m + 1, for some integer m.
2)
Explain, why (3 x 5 x 7) + 7 is a composite number?
3)
Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.
4)
Prove that (\( \sqrt{p} \) + \( \sqrt{q} \) is irrational, where p and q are primes.
5)
Given that, \(\sqrt { 2 } \) is a zero of the cubic polynomial \(6x^{ 3 }+\sqrt { 2x^{ 2 } } -10x-4\sqrt { 2 } \). Find its other two zeroes.

CBSE 10th Standard Maths Subject Ncert Exemplar 2 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q. when this number is expressed in the form \(\frac{p}{q}\)? Give reason.
2)
Use Euclid's division algorithm to find the HCF of the following three numbers
2, 7 and 12
3)
Use Euclid's division algorithm to find the HCF of the following three numbers
441, 567 and 693
4)
Check whether 12ⁿ can end with the digit 0 or 5, for any natural number n
5)
If the zeroes of the cubic polynomial x³ - 6x² + 3x + 10 are of the form a, a + b and a + 2b for some real numbers a and b, then find the values of a and b.

CBSE 10th Standard Maths Subject Ncert Exemplar 2 Marks Questions 2021 Part - II - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q. when this number is expressed in the form \(\frac{p}{q}\)? Give reason.
2)
Use Euclid's division algorithm to find the HCF of the following three numbers
2, 7 and 12
3)
Check whether 12ⁿ can end with the digit 0 or 5, for any natural number n
4)
If the zeroes of the cubic polynomial x³ - 6x² + 3x + 10 are of the form a, a + b and a + 2b for some real numbers a and b, then find the values of a and b.
5)
Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

CBSE 10th Standard Maths Subject Ncert Exemplar 2 Marks Questions 2021 Part - I - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q. when this number is expressed in the form \(\frac{p}{q}\)? Give reason.
2)
Use Euclid's division algorithm to find the HCF of the following three numbers
2, 7 and 12
3)
Use Euclid's division algorithm to find the HCF of the following three numbers
441, 567 and 693
4)
Check whether 12ⁿ can end with the digit 0 or 5, for any natural number n
5)
If the zeroes of the cubic polynomial x³ - 6x² + 3x + 10 are of the form a, a + b and a + 2b for some real numbers a and b, then find the values of a and b.

CBSE 10th Standard Maths Subject Ncert Exemplar 1 Marks Questions With Solution 2021 - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
Can the number 6ⁿ, where n being a natural number, ends with digit 5? Give reason.
2)
The product of three consecutive positive integers is divisible by 6. Is this statement true or false? Justify your answer.
3)
If the HCF of 65 and 117 is expressible in the form 65 m - 117, then find the value of m.
4)
Is the following statement True or False? Justify your answer. 'If the zeroes of a quadratic polynomial ax²+bx+c are both negative, then a, b and c all have the same sign.'
5)
If the zeroes of the quadratic polynomial ax²+bx+c, where c\(\neq \)0, are equal, then show that c and a have same sign.

CBSE 10th Standard Maths Subject Ncert Exemplar 1 Marks Questions 2021 Part - II - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
Can the number 6ⁿ, where n being a natural number, ends with digit 5? Give reason.
2)
The product of three consecutive positive integers is divisible by 6. Is this statement true or false? Justify your answer.
3)
If x = a , y = b is the solution of the equations x - y = 2 and x + y = 4, then find the values of Q and b.
4)
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
5)
What is the nature of roots of the quadratic equation 2x²-\(\sqrt { 5 } \)x+1=0?

CBSE 10th Standard Maths Subject Ncert Exemplar 1 Marks Questions 2021 Part - I - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
Find the largest number which divides 70 and 125 leaving remainders 5 and 8. respectively.
2)
In Euclid's division lemma, the value of r, when a positive integer a is divided by 3, are 0 and 1 only. Is this statement true or false? Justify your answer.
3)
Can the number 6ⁿ, where n being a natural number, ends with digit 5? Give reason.
4)
The product of three consecutive positive integers is divisible by 6. Is this statement true or false? Justify your answer.
5)
If the zeroes of the quadratic polynomial ax²+bx+c, where c\(\neq \)0, are equal, then show that c and a have same sign.

CBSE 10th Standard Maths Subject Ncert Exemplar MCQ Questions With Solution 2021 - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
For some integer q, every odd integer is of the form
2)
If two positive integers a and b are written as 0 = x ³y² an d b = xy ³, where x, yare prime numbers, then HCF (a, b) is
3)
If two positive integers p and q can be expressed as p = ab² and q = a³ b;where a, b being prime numbers, then LCM (p, q) is equal to
4)
The product of a non-zero rational and an irrational number is
5)
Which of the following is not the graph of a quadratic polynomial?

CBSE 10th Standard Maths Subject Ncert Exemplar MCQ Questions 2021 Part - II - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
For some integer q, every odd integer is of the form
2)
If two positive integers a and b are written as 0 = x ³y² an d b = xy ³, where x, yare prime numbers, then HCF (a, b) is
3)
If two positive integers p and q can be expressed as p = ab² and q = a³ b;where a, b being prime numbers, then LCM (p, q) is equal to
4)
The product of a non-zero rational and an irrational number is
5)
Which of the following is not the graph of a quadratic polynomial?

CBSE 10th Standard Maths Subject Ncert Exemplar MCQ Questions 2021 Part - I - by QB365 - Question Bank Software - May 25, 2021 - View & Read

1)
For some integer q, every odd integer is of the form
2)
If two positive integers a and b are written as 0 = x ³y² an d b = xy ³, where x, yare prime numbers, then HCF (a, b) is
3)
If two positive integers p and q can be expressed as p = ab² and q = a³ b;where a, b being prime numbers, then LCM (p, q) is equal to
4)
Which of the following is not the graph of a quadratic polynomial?
5)
The pair of equations x + 2y + 5 = 0 and - 3x - 6y + 1= 0 has

CBSE 10th Standard Maths Subject Probability Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)

Two friends Richa and Sohan have some savings in their piggy bank. They decided to count the total coins they both had. After counting they find that they have fifty \(\begin{equation} ₹ \end{equation} \) 1 coins, forty eight \(\begin{equation} ₹ \end{equation} \) 2 coins, thirty six \(\begin{equation} ₹ \end{equation} \) 5 coins, twenty eight \(\begin{equation} ₹ \end{equation} \)10 coins and eight \(\begin{equation} ₹ \end{equation} \) 20 coins. Now, they said to Nisha, their another friends, to choose a coin randomly.
Find the probability that the coin chosen is

(i) \(\begin{equation} ₹ \end{equation} \)5 coin

(a) \(\begin{equation} \frac{17}{55} \end{equation}\)	(b) \(\begin{equation} \frac{36}{85} \end{equation}\)
(c) \(\begin{equation} \frac{18}{85} \end{equation}\)	(d) \(\begin{equation} \frac{1}{15} \end{equation}\)

(ii) \(\begin{equation} ₹ \end{equation} \) 20 coin

(a) \(\begin{equation} \frac{13}{85} \end{equation}\)	(b) \(\begin{equation} \frac{4}{85} \end{equation}\)
(c) \(\begin{equation} \frac{3}{85} \end{equation}\)	(d) \(\begin{equation} \frac{4}{15} \end{equation}\)

(iii) not a \(\begin{equation} ₹ \end{equation} \) 10 coin

(a) \(\begin{equation} \frac{15}{31} \end{equation}\)	(b) \(\begin{equation} \frac{36}{85} \end{equation}\)
(c) \(\begin{equation} \frac{1}{5} \end{equation}\)	(d) \(\begin{equation} \frac{71}{85} \end{equation}\)

(iv) of denomination of atleast \(\begin{equation} ₹ \end{equation} \)10.

(a) \(\begin{equation} \frac{18}{85} \end{equation}\)	(b) \(\begin{equation} \frac{36}{85} \end{equation}\)
(c) \(\begin{equation} \frac{1}{17} \end{equation}\)	(d) \(\begin{equation} \frac{16}{85} \end{equation}\)

(v) of denomination of atmost \(\begin{equation} ₹ \end{equation} \) 5.

(a) \(\begin{equation} \frac{67}{85} \end{equation}\)	(b) \(\begin{equation} \frac{36}{85} \end{equation}\)
(c) \(\begin{equation} \frac{4}{85} \end{equation}\)	(d) \(\begin{equation} \frac{18}{85} \end{equation}\)

2)

In a play zone, Nishtha is playing claw crane game which consists of 58 teddy bears, 42 pokemons, 36 tigers and 64 monkeys. Nishtha picks a puppet at random. Now, find the probability of getting

(i) a tiger

(a) \(\begin{equation} \frac{3}{50} \end{equation}\)	(b) \(\begin{equation} \frac{9}{50} \end{equation}\)
(c) \(\begin{equation} \frac{1}{25} \end{equation}\)	(d) \(\begin{equation} \frac{27}{50} \end{equation}\)

(ii) a monkey

(a) \(\begin{equation} \frac{8}{25} \end{equation}\)	(b) \(\begin{equation} \frac{4}{25} \end{equation}\)
(c) \(\begin{equation} \frac{16}{25} \end{equation}\)	(d) \(\begin{equation} \frac{1}{5} \end{equation}\)

(iii) a teddy bear

(a) \(\begin{equation} \frac{41}{50} \end{equation}\)	(b) \(\begin{equation} \frac{29}{50} \end{equation}\)
(c) \(\begin{equation} \frac{29}{100} \end{equation}\)	(d) \(\begin{equation} \frac{41}{100} \end{equation}\)

(iv) not a monkey

(a) \(\begin{equation} \frac{1}{25} \end{equation}\)	(b) \(\begin{equation} \frac{8}{25} \end{equation}\)
(c) \(\begin{equation} \frac{13}{25} \end{equation}\)	(d) \(\begin{equation} \frac{17}{25} \end{equation}\)

(v) not a pokemon

(a) \(\begin{equation} \frac{27}{100} \end{equation}\)	(b) \(\begin{equation} \frac{43}{100} \end{equation}\)
(c) \(\begin{equation} \frac{61}{100} \end{equation}\)	(d) \(\begin{equation} \frac{79}{100} \end{equation}\)

3)

Rohit wants to distribute chocolates in his class on his birthday. The chocolates are of three types: Milk chocolate, White chocolate and Dark chocolate. If the total number of students in the class is 54 and everyone gets a chocolate, then answer the following questions.

(i) If the probability of distributing milk chocolates is 1/3, then the number of milk chocolates Rohit has, is

(a) 18	(b) 20
(c) 22	(d) 30

(ii) If the probability of distributing dark chocolates is 4/9, then the number of dark chocolates Rohit has, is

(a) 18	(b) 25
(c) 24	(d) 36

(iii) The probability of distributing white chocolates is

(a) \(\begin{equation} \frac{11}{27} \end{equation}\)	(b)\(\begin{equation} \frac{8}{21} \end{equation}\)
(c) \(\begin{equation} \frac{1}{9} \end{equation}\)	(d) \(\begin{equation} \frac{2}{9} \end{equation}\)

(iv) The probability of distributing both milk and white chocolates is

(a) \(\begin{equation} \frac{3}{17} \end{equation}\)	(b) \(\begin{equation} \frac{5}{9} \end{equation}\)
(c) \(\begin{equation} \frac{1}{3} \end{equation}\)	(d) \(\begin{equation} \frac{1}{27} \end{equation}\)

(v) The probability of distributing all the chocolates is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{3}{4} \end{equation}\)

4)

Three persons toss 3 coins simultaneously and note the outcomes. Then, they ask few questions to one another. Help them in finding the answers of the following questions.

(i) The probability of getting atmost one tail is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{1}{4} \end{equation}\)

(ii) The probability of getting exactly 1 head is

(a) \(\begin{equation} \frac{1}{2} \end{equation}\)	(b) \(\begin{equation} \frac{1}{4} \end{equation}\)
(c) \(\begin{equation} \frac{1}{8} \end{equation}\)	(d) \(\begin{equation} \frac{3}{8} \end{equation}\)

(iii) The probability of getting exactly 3 tails is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{4} \end{equation}\)	(d) \(\begin{equation} \frac{1}{8} \end{equation}\)

(iv) The probability of getting atmost 3 heads is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{1}{8} \end{equation}\)

(v) The probability of getting atleast two heads is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{1}{4} \end{equation}\)

5)

Prateek goes to a toy shop to purchase a building block kit for his son. He found that the kit contains 120 blocks, of which 40 are red, 25 are blue, 30 are green and the rest are yellow. His son picks up a block at random. Find the probability that the block is

(i) of red colour

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{1}{3} \end{equation}\)

(ii) not of yellow colour

(a) \(\begin{equation} \frac{1}{6} \end{equation}\)	(b) \(\begin{equation} \frac{1}{4} \end{equation}\)
(c) \(\begin{equation} \frac{19}{24} \end{equation}\)	(d) \(\begin{equation} \frac{19}{25} \end{equation}\)

(iii) of green colour

(a) \(\begin{equation} \frac{1}{8} \end{equation}\)	(b) \(\begin{equation} \frac{1}{10} \end{equation}\)
(c) \(\begin{equation} \frac{1}{4} \end{equation}\)	(d) \(\begin{equation} \frac{1}{12} \end{equation}\)

(iv) of yellow colour

(a) \(\begin{equation} \frac{15}{118} \end{equation}\)	(b) \(\begin{equation} \frac{5}{24} \end{equation}\)
(c) \(\begin{equation} \frac{17}{24} \end{equation}\)	(d) \(\begin{equation} \frac{19}{50} \end{equation}\)

(v) not of blue colour

(a) \(\begin{equation} \frac{1}{8} \end{equation}\)	(b) \(\begin{equation} \frac{19}{24} \end{equation}\)
(c) \(\begin{equation} \frac{19}{31} \end{equation}\)	(d) \(\begin{equation} \frac{16}{55} \end{equation}\)

CBSE 10th Standard Maths Subject Probability Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)

In a play zone, Nishtha is playing claw crane game which consists of 58 teddy bears, 42 pokemons, 36 tigers and 64 monkeys. Nishtha picks a puppet at random. Now, find the probability of getting

(i) a tiger

(a) \(\begin{equation} \frac{3}{50} \end{equation}\)	(b) \(\begin{equation} \frac{9}{50} \end{equation}\)
(c) \(\begin{equation} \frac{1}{25} \end{equation}\)	(d) \(\begin{equation} \frac{27}{50} \end{equation}\)

(ii) a monkey

(a) \(\begin{equation} \frac{8}{25} \end{equation}\)	(b) \(\begin{equation} \frac{4}{25} \end{equation}\)
(c) \(\begin{equation} \frac{16}{25} \end{equation}\)	(d) \(\begin{equation} \frac{1}{5} \end{equation}\)

(iii) a teddy bear

(a) \(\begin{equation} \frac{41}{50} \end{equation}\)	(b) \(\begin{equation} \frac{29}{50} \end{equation}\)
(c) \(\begin{equation} \frac{29}{100} \end{equation}\)	(d) \(\begin{equation} \frac{41}{100} \end{equation}\)

(iv) not a monkey

(a) \(\begin{equation} \frac{1}{25} \end{equation}\)	(b) \(\begin{equation} \frac{8}{25} \end{equation}\)
(c) \(\begin{equation} \frac{13}{25} \end{equation}\)	(d) \(\begin{equation} \frac{17}{25} \end{equation}\)

(v) not a pokemon

(a) \(\begin{equation} \frac{27}{100} \end{equation}\)	(b) \(\begin{equation} \frac{43}{100} \end{equation}\)
(c) \(\begin{equation} \frac{61}{100} \end{equation}\)	(d) \(\begin{equation} \frac{79}{100} \end{equation}\)

2)

Rohit wants to distribute chocolates in his class on his birthday. The chocolates are of three types: Milk chocolate, White chocolate and Dark chocolate. If the total number of students in the class is 54 and everyone gets a chocolate, then answer the following questions.

(i) If the probability of distributing milk chocolates is 1/3, then the number of milk chocolates Rohit has, is

(a) 18	(b) 20
(c) 22	(d) 30

(ii) If the probability of distributing dark chocolates is 4/9, then the number of dark chocolates Rohit has, is

(a) 18	(b) 25
(c) 24	(d) 36

(iii) The probability of distributing white chocolates is

(a) \(\begin{equation} \frac{11}{27} \end{equation}\)	(b)\(\begin{equation} \frac{8}{21} \end{equation}\)
(c) \(\begin{equation} \frac{1}{9} \end{equation}\)	(d) \(\begin{equation} \frac{2}{9} \end{equation}\)

(iv) The probability of distributing both milk and white chocolates is

(a) \(\begin{equation} \frac{3}{17} \end{equation}\)	(b) \(\begin{equation} \frac{5}{9} \end{equation}\)
(c) \(\begin{equation} \frac{1}{3} \end{equation}\)	(d) \(\begin{equation} \frac{1}{27} \end{equation}\)

(v) The probability of distributing all the chocolates is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{3}{4} \end{equation}\)

3)

In a party, some children decided to play musical chair game. In the game the person playing the music has been advised to stop the music at any time in the interval of 3 mins after he start the music in each turn. On the basis of the given information, answer the following questions.
(i) What is the probability that the music will stop within first 30 sees after starting?

(a) \(\begin{equation} \frac{1}{6} \end{equation}\)	(b) \(\begin{equation} \frac{1}{5} \end{equation}\)
(c) \(\begin{equation} \frac{1}{4} \end{equation}\)	(d) \(\begin{equation} \frac{1}{3} \end{equation}\)

(ii) The probability that the music will stop within 45 sees after starting is

(a) \(\begin{equation} \frac{1}{4} \end{equation}\)	(b) \(\begin{equation} \frac{1}{5} \end{equation}\)
(c) \(\begin{equation} \frac{1}{6} \end{equation}\)	(d) \(\begin{equation} \frac{1}{8} \end{equation}\)

(iii) The probability that the music will stop after 2 mins after starting is

(a) \(\begin{equation} \frac{1}{8} \end{equation}\)	(b) \(\begin{equation} \frac{1}{5} \end{equation}\)
(c) \(\begin{equation} \frac{1}{4} \end{equation}\)	(d) \(\begin{equation} \frac{1}{3} \end{equation}\)

(iv) The probability that the music will not stop within first 60 sees after starting is

(a) \(\begin{equation} \frac{1}{3} \end{equation}\)	(b) \(\begin{equation} \frac{2}{3} \end{equation}\)
(c) \(\begin{equation} \frac{4}{5} \end{equation}\)	(d) \(\begin{equation} \frac{8}{9} \end{equation}\)

(v) The probability that the music will stop within first 82 sees after starting is

(a) \(\begin{equation} \frac{11}{30} \end{equation}\)	(b) \(\begin{equation} \frac{41}{90} \end{equation}\)
(c) \(\begin{equation} \frac{31}{35} \end{equation}\)	(d) \(\begin{equation} \frac{41}{93} \end{equation}\)

4)

Three persons toss 3 coins simultaneously and note the outcomes. Then, they ask few questions to one another. Help them in finding the answers of the following questions.

(i) The probability of getting atmost one tail is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{1}{4} \end{equation}\)

(ii) The probability of getting exactly 1 head is

(a) \(\begin{equation} \frac{1}{2} \end{equation}\)	(b) \(\begin{equation} \frac{1}{4} \end{equation}\)
(c) \(\begin{equation} \frac{1}{8} \end{equation}\)	(d) \(\begin{equation} \frac{3}{8} \end{equation}\)

(iii) The probability of getting exactly 3 tails is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{4} \end{equation}\)	(d) \(\begin{equation} \frac{1}{8} \end{equation}\)

(iv) The probability of getting atmost 3 heads is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{1}{8} \end{equation}\)

(v) The probability of getting atleast two heads is

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{1}{4} \end{equation}\)

5)

Prateek goes to a toy shop to purchase a building block kit for his son. He found that the kit contains 120 blocks, of which 40 are red, 25 are blue, 30 are green and the rest are yellow. His son picks up a block at random. Find the probability that the block is

(i) of red colour

(a) 0	(b) 1
(c) \(\begin{equation} \frac{1}{2} \end{equation}\)	(d) \(\begin{equation} \frac{1}{3} \end{equation}\)

(ii) not of yellow colour

(a) \(\begin{equation} \frac{1}{6} \end{equation}\)	(b) \(\begin{equation} \frac{1}{4} \end{equation}\)
(c) \(\begin{equation} \frac{19}{24} \end{equation}\)	(d) \(\begin{equation} \frac{19}{25} \end{equation}\)

(iii) of green colour

(a) \(\begin{equation} \frac{1}{8} \end{equation}\)	(b) \(\begin{equation} \frac{1}{10} \end{equation}\)
(c) \(\begin{equation} \frac{1}{4} \end{equation}\)	(d) \(\begin{equation} \frac{1}{12} \end{equation}\)

(iv) of yellow colour

(a) \(\begin{equation} \frac{15}{118} \end{equation}\)	(b) \(\begin{equation} \frac{5}{24} \end{equation}\)
(c) \(\begin{equation} \frac{17}{24} \end{equation}\)	(d) \(\begin{equation} \frac{19}{50} \end{equation}\)

(v) not of blue colour

(a) \(\begin{equation} \frac{1}{8} \end{equation}\)	(b) \(\begin{equation} \frac{19}{24} \end{equation}\)
(c) \(\begin{equation} \frac{19}{31} \end{equation}\)	(d) \(\begin{equation} \frac{16}{55} \end{equation}\)

CBSE 10th Standard Maths Subject Statistics Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
An agency has decided to install customised playground equipments at various colony parks. For that they decided to study the age-group of children playing in a park of the particular colony. The classification of children according to their ages, playing in a park is shown in the following table

Age group of children (in years) 6-8 8-10 10-12 12-14 14-16

Number of children 43 58 70 42 27

Based on the above information, answer the following questions.
(i) The maximum number of children are of the age-group

(a) 12-14 (b) 10-12 (c) 14-16 (d) 8-10

(ii) The lower limit of the modal class is

(a) 10 (b) 12 (c) 14 (d) 8

(iii) Frequency of the class succeeding the modal class is

(a) 58 (b) 70 (c) 42 (d) 27

(iv) The mode of the ages of children playing in the park is

(a) 9 years (b) 8 years (c) 11.5 years (d) 10.6 years

(v) If mean and mode of the ages of children playing in the park are same, then median will be equal to

(a) Mean (b) Mode

(c) Both (a) and (b) (d) Neither (a) nor (b)

2)

On a particular day, National Highway Authority ofIndia (NHAI) checked the toll tax collection of a particular toll plaza in Rajasthan.

The following table shows the toll tax paid by drivers and the number of vehicles on that particular day.

Toll tax (in Rs)	30-40	40-50	50-60	60-70	70-80
Number of vehicles	80	110	120	70	40

Based on the above information, answer the following questions.
(i) If A is taken as assumed mean, then the possible value of A is

(a) 32

(b) 42

(c) 85

(d) 55

(ii) If x_i's denotes the class marks and f_i's denotes the deviation of assumed mean (A) from x_i's, then the minimum value of |d_i| is

(a) -200

(b) -100

(c) 0

(d) 100

(iii) The mean of toll tax received. by NHAI by assumed mean method is

(a) Rs 52

(b) Rs 52.14

(c) Rs 52.50

(d) Rs 53.50

(iv) The mean of toll tax received by NHAI by direct method is

(a) equal to the mean of toll tax received by NHAI by assumed mean method

(b) greater than the mean of toll tax received by NHAI by assumed mean method

(c) less than the mean of toll tax received by NHAI by assumed mean method

(d) none of these

(v) The average toll tax received by NHAI in a day, from that particular toll plaza, is

(a) Rs 21000

(b) Rs 21900

(c) Rs 30000

(d) none of these

3)
Transport department of a city wants to buy some Electric buses for the city. For which they wants to analyse the distance travelled by existing public transport buses in a day.

The following data shows the distance travelled by 60 existing public transport buses in a day.

Daily distance travelled (in km) 200-209 210-219 220-229 230-239 240-249

Number of buses 4 14 26 10 6

Based on the above information, answer the following questions.
(i) The upper limit of a class and lower limit of its succeeding class is differ by

(a) 9 (b) 1 (c) 10 (d) none of these

(ii) The median class is

(a) 229.5-239.5 (b) 230-239 (c) 220-229 (d) 219.5-229.5

(iii) The cumulative frequency of the class preceding the median class is

(a) 14 (b) 18 (c) 26 (d) 10

(iv) The median of the distance travelled is

(a) 222 km (b) 225 km (c) 223 km (d) none of these

(v) If the mode of the distance travelled is 223.78 km, then mean of the distance travelled by the bus is

(a) 225 km (b) 220 km (c) 230.29 km (d) 224.29 km
4)
An electric scooter manufacturing company wants to declare the mileage of their electric scooters. For this, they recorded the mileage (km/ charge) of 50 scooters of the same model. Details of which are given in the following table.

Mileage (km/charge) 100-120 120-140 140-160 160-180

Number of scooters 7 12 18 13

Based on the above information, answer the following questions.
(i) The average mileage is

(a) 140 krn/charge (b) 150 krn/ charge (c) 130 krn/charge (d) 144.8 krn/charge

(ii) The modal value of the given data is

(a) 150 (b) 150.91 (c) 145.6 (d) 140.9

(ill) The median value of the given data is

(a) 140 (b) 146.67 (c) 130 (d) 136.6

(iv) Assumed mean method is useful in determining the

(a) Mean (b) Median (c) Mode (d) All of these

(v) The manufacturer can claim that the mileage for his scooter is

(a) 144 krn/charge (b) 155 krn/charge (c) 165 krn/charge (d) 175krn/charge
5)
Household income in India was drastically impacted due to the COVID-19 loekdown. Most of the companies decided to bring down the salaries of the employees by 50%.
The following table shows the salaries (in percent) received by 25 employees during loekdown.

Salaries received (in percent) 50-60 60-70 70-80 80-90

Number of employees 9 6 8 2

Based on the above information, answer the following questions.
(i) Total number of persons whose salary is reduced by more than 30%, is

(a) 10 (b) 20 (c) 25 (d) 15

(ii) Total number of persons whose salary is reduced by atmost 40%, is

(a) 15 (b) 10 (c) 16 (d) 8

(iii) The modal class is

(a) 50-60 (b) 60-70 (c) 70-80 (d) 80-90

(iv) The median class of the given data is

(a) 50-60 (b) 60-70 (c) 70-80 (d) 80-90

(v) The empirical relationship between mean, median and mode is

(a) 3 Median = Mode + 2 Mean (b) 3 Median = Mode - 2 Mean

(c) Median = 3 Mode - 2 Mean (d) Median = 3 Mode + 2 Mean

CBSE 10th Standard Maths Subject Statistics Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
As the demand for the products grew, a manufacturing company decided to hire more employees. For which they want to know the mean time required to complete the work for a worker. The following table shows the frequency distribution of the time required for each worker to complete a work.

Time (in hours) 15-19 20-24 25-29 30-34 35-39

Number of workers 10 15 12 8 5

Based on the above information, answer the following questions.
(i) The class mark of the class 25-29 is

(a) 17 (b) 22 (c) 27 (d) 32

(ii) If x_i's denotes the class marks and f_i's denotes the corresponding frequencies for the given data, then the value of \(\sum x_{i} f_{i}\) equals to

(a) 1200 (b) 1205 (c) 1260 (d) 1265

(iii) The mean time required to complete the work for a worker is

(a) 22 hrs (b) 23 hrs (c) 24 hrs (d) none of these

(iv) If a worker works for 8 hrs in a day, then approximate time required to complete the work for a worker is

(a) 3 days (b) 4 days (c) 5 days (d) 6 days

(v) The measure of central tendency is

(a) Mean (b) Median (c) Mode (d) All of these

2)

On a particular day, National Highway Authority ofIndia (NHAI) checked the toll tax collection of a particular toll plaza in Rajasthan.

The following table shows the toll tax paid by drivers and the number of vehicles on that particular day.

Toll tax (in Rs)	30-40	40-50	50-60	60-70	70-80
Number of vehicles	80	110	120	70	40

Based on the above information, answer the following questions.
(i) If A is taken as assumed mean, then the possible value of A is

(a) 32

(b) 42

(c) 85

(d) 55

(ii) If x_i's denotes the class marks and f_i's denotes the deviation of assumed mean (A) from x_i's, then the minimum value of |d_i| is

(a) -200

(b) -100

(c) 0

(d) 100

(iii) The mean of toll tax received. by NHAI by assumed mean method is

(a) Rs 52

(b) Rs 52.14

(c) Rs 52.50

(d) Rs 53.50

(iv) The mean of toll tax received by NHAI by direct method is

(a) equal to the mean of toll tax received by NHAI by assumed mean method

(b) greater than the mean of toll tax received by NHAI by assumed mean method

(c) less than the mean of toll tax received by NHAI by assumed mean method

(d) none of these

(v) The average toll tax received by NHAI in a day, from that particular toll plaza, is

(a) Rs 21000

(b) Rs 21900

(c) Rs 30000

(d) none of these

3)
Transport department of a city wants to buy some Electric buses for the city. For which they wants to analyse the distance travelled by existing public transport buses in a day.

The following data shows the distance travelled by 60 existing public transport buses in a day.

Daily distance travelled (in km) 200-209 210-219 220-229 230-239 240-249

Number of buses 4 14 26 10 6

Based on the above information, answer the following questions.
(i) The upper limit of a class and lower limit of its succeeding class is differ by

(a) 9 (b) 1 (c) 10 (d) none of these

(ii) The median class is

(a) 229.5-239.5 (b) 230-239 (c) 220-229 (d) 219.5-229.5

(iii) The cumulative frequency of the class preceding the median class is

(a) 14 (b) 18 (c) 26 (d) 10

(iv) The median of the distance travelled is

(a) 222 km (b) 225 km (c) 223 km (d) none of these

(v) If the mode of the distance travelled is 223.78 km, then mean of the distance travelled by the bus is

(a) 225 km (b) 220 km (c) 230.29 km (d) 224.29 km

4)

A group of 71 people visited to a museum on a certain day. The following table shows their ages.

Age (in years)	Number of persons
Less than 10	3
Less than 20	10
Less than 30	22
Less than 40	40
Less than 50	54
Less than 60	71

Based on the aboxe information, answer the following questions.
(i) If true class limits have been decided by making the classes of interval 10, then first class must be

(a) 5-15	(b) 0-10
(c) 10-20	(d) none of these

(ii) The median class for the given data will be

(a) 20-30

(b) 10-20

(c) 30-40

(d) 40-50

(iii) The cumulative frequency of class preceding the median class is

(a) 22

(b) 13

(c) 25

(d) 35

(iv) The median age of the persons visited the museum is

(a) 30 years

(b) 32.5 years

(c) 34 years

(d) 37.5 years

(v) If the price of a ticket for the age group 30-40 is Rs 30, then the total amount spent by this age group is

(a) Rs 360

(b) Rs 420

(c) Rs 540

(d) Rs 340

5)

An inspestor in an enforcement squad of electricity department visit to a locality of 100 families and record their monthly consumption of electricity, on the basis of family members, electronic items in the house and wastage of electricity, which is summarise in the following table.

Monthly Consumption (in kwh)	0-100	100-200	200-300	300-400	400-500	500-600	600-700	700-800	800-900	900-1000
Number of families	2	5	x	12	17	20	y	9	7	4

Based on the above information, answer the following questions.
(i) The value of x + y is

(a) 100

(b) 42

(c) 24

(d) 200

(ii) If the median of the above data is 525, then x is equal to

(a) 10

(b) 8

(c) 9

(d) none of these

(iii) What will be the upper limit of the modal class?

(a) 400

(c) 650

(b) 600

(d) 700

(iv) The average monthly consumption of a family of this locality is approximately

(a) 520 kwh

(b) 522 kwh

(c) 540 kwh

(d) none of these

(v) If A be the assumed mean, then A is always

(a) > (Actual mean)	(b) < (Actual Mean)
(c) = (Actual Mean)	(d) can't say

CBSE 10th Standard Maths Subject Surface Areas and Volumes Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
Arun a 10^th standard student makes a project on corona virus in science for an exhibition in his school. In this project, he picks a sphere which has volume 38808 cm³ and 11 cylindrical shapes, each of volume 1540 cm³ with length 10 cm.

Based on the above information, answer the following questions.
(i) Diameter of the base of the cylinder is

(a) 7 cm (b) 14 cm (c) 12 cm (d) 16 cm

(ii) Diameter of the sphere is

(a) 40 cm (b) 42 cm (c) 21 cm (d) 20 cm

(iii) Total volume of the shape formed is

(a) 85541 cm³ (b) 45738 cm³ (c) 24625 cm³ (d) 55748 cm³

(iv) Curved surface area of the one cylindrical shape is

(a) 850 cm² (b) 221 cm² (c) 440 cm² (d) 540 cm²

(v) Total area covered by cylindrical shapes on the surface of sphere is

(a) 1694 cm² (b) 1580 cm² (c) 1896 cm² (d) 1470 cm²
2)
Ajay is a Class X student. His class teacher Mrs Kiran arranged a historical trip to great Stupa of Sanchi. She explained that Stupa of Sanchi is great example of architecture in India. Its base part is cylindrical in shape. The dome of this stupa is hemispherical in shape, known as Anda. It also contains a cubical shape part called Hermika at the top. Path around Anda is known as Pradakshina Path.

Based on the above information, answer the following questions.
(i) Find the lateral surface area of the Hermika, if the side of cubical part is 8 m.

(a) 128 m² (b) 256 m² (c) 512 m² (d) 1024 m²

(ii) The diameter and height of the cylindrical base part are respectively 42 m and 12 m. If the volume of each brick used is 0.01 m³, then find the number of bricks used to make the cylindrical base.

(a) 1663200 (b) 1580500 (c) 1765000 (d) 1865000

(iii) If the diameter of the Anda is 42 m, then the volume of the Anda is

(a) 17475 m³ (b) 18605 m³ (c) 19404 m³ (d) 18650 m³

(iv) The radius of the Pradakshina path is 25 m. If Buddhist priest walks 14 rounds on this path, then find the distance covered by the priest.

(a) 1860 m (b) 3600 m (c) 2400 m (d) 2200 m

(v) The curved surface area of the Anda is

(a) 2856 m² (b) 2772 m² (c) 2473 m² (d) 2652 m²

3)

One day Rinku was going home from school, saw a carpenter working on wood. He found that he is carving out a cone of same height and same diameter from a cylinder. The height of the cylinder is 24 ern and base radius is 7 cm. While watching this, some questions came into Rinkus mind. Help Rinku to find the answer of the following questions.

(i) After carving out cone from the cylinder,

(a) Volume of the cylindrical wood will decrease.

(b) Height of the cylindrical wood will increase.

(c) Volume of cylindrical wood will increase.

(d) Radius of the cylindrical wood will decrease.

(ii) Find the slant height of the conical cavity so formed.

(a) 28 cm

(b) 38 cm

(c) 35 cm

(d) 25 cm

(iii) The curved surface area of the conical cavity so formed is

(a) 250 cm²

(b) 550 cm²

(c) 350 cm²

(d) 450 cm²

(iv) External curved surface area of the cylinder is

(a) 876 cm²

(b) 1250 cm²

(c) 1056 cm²

(d) 1025 cm²

(v) Volume of conical cavity is

(a) 1232 cm³

(b) 1248 cm³

(c) 1380 cm³

(d) 999 cm³

4)
A carpenter used to make and sell different kinds of wooden pen stands like rectangular, cuboidal, cylindrical, conical. Aarav went to his shop and asked him to make a pen stand as explained below. Pen stand must be of the cuboidal shape with three conical depressions, which can hold 3 pens. The dimensions of the cuboidal part must be 20 cm x 15 cm x 5 cm and the ffrlog radius and depth of each conical depression must be 0.6 cm and 2.1 cm respectively.

Based on the above information, answer the following questions.
(i) The volume of the cuboidal part is

(a) 1250 cm³ (b) 1500 cm³ (c) 1625 cm³ (d) 1500 cm³

(ii) Total volume of conical depressions is

(a) 2.508 cm³ (b) 1.5 cm³ (c) 2.376 cm³ (d) 3.6 cm³

(iii) Volume of the wood used in the entire stand is

(a) 631.31 cm³ (b) 3564 cm³ (c) 1502.376 cm³ (d) 1497.624 cm³

(iv) Total surface area of cone of radius r is given by

\((a) \pi r l+\pi r^{2}\) \((b) 2 \pi r l+\pi r^{2}\) \((c) \pi r^{2} l+\pi r^{2}\) \((d) \pi r l+2 \pi r^{3}\)

(v) If the cost of wood used is Rs 5 per cm³, then the total cost of making the pen stand is

(a) Rs 8450.50 (b) Rs 7480 (c) Rs 9962.14 (d) Rs 7488.12

5)

Meera and Dhara have 12 and 8 coins respectively each of radius 3.5 cm and thickness 0.5 cm. They place their coins one above the other to form solid cylinders .

Based on the above information, answer the following questions.
(i) Curved surface area of the cylinder made by Meera is

(a) 144 cm²

(b) 132 cm²

(c) 154 cm²

(d) 142 cm²

(ii) The ratio of curved surface area of the cylinders made by Meera and Dhara is

(a) 2: 5

(b) 3: 2

(c) 1: 2

(d) 2: 7

(iii) The volume of the cylinder made by Dhara is

(a) 154 cm³

(b) 144 cm³

(c) 132 cm³

(d) 142 cm³

(iv) The ratio of the volume of the cylinders made by Meera and Dhara is

(a) 1:2

(b) 2: 5

(c) 3: 2

(d) 4: 3

(v) When two coins are shifted from Meeras cylinder to Dhara's cylinder, then

(a) Volume of two cylinder become equal

(b) Volume of Meera's cylinder> Volume of Dharas cylinder

(c) Volume of Dhara's cylinder> Volume of Meeras cylinder

(d) None of these

CBSE 10th Standard Maths Subject Surface Areas and Volumes Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
Ajay is a Class X student. His class teacher Mrs Kiran arranged a historical trip to great Stupa of Sanchi. She explained that Stupa of Sanchi is great example of architecture in India. Its base part is cylindrical in shape. The dome of this stupa is hemispherical in shape, known as Anda. It also contains a cubical shape part called Hermika at the top. Path around Anda is known as Pradakshina Path.

Based on the above information, answer the following questions.
(i) Find the lateral surface area of the Hermika, if the side of cubical part is 8 m.

(a) 128 m² (b) 256 m² (c) 512 m² (d) 1024 m²

(ii) The diameter and height of the cylindrical base part are respectively 42 m and 12 m. If the volume of each brick used is 0.01 m³, then find the number of bricks used to make the cylindrical base.

(a) 1663200 (b) 1580500 (c) 1765000 (d) 1865000

(iii) If the diameter of the Anda is 42 m, then the volume of the Anda is

(a) 17475 m³ (b) 18605 m³ (c) 19404 m³ (d) 18650 m³

(iv) The radius of the Pradakshina path is 25 m. If Buddhist priest walks 14 rounds on this path, then find the distance covered by the priest.

(a) 1860 m (b) 3600 m (c) 2400 m (d) 2200 m

(v) The curved surface area of the Anda is

(a) 2856 m² (b) 2772 m² (c) 2473 m² (d) 2652 m²

2)

One day Rinku was going home from school, saw a carpenter working on wood. He found that he is carving out a cone of same height and same diameter from a cylinder. The height of the cylinder is 24 ern and base radius is 7 cm. While watching this, some questions came into Rinkus mind. Help Rinku to find the answer of the following questions.

(i) After carving out cone from the cylinder,

(a) Volume of the cylindrical wood will decrease.

(b) Height of the cylindrical wood will increase.

(c) Volume of cylindrical wood will increase.

(d) Radius of the cylindrical wood will decrease.

(ii) Find the slant height of the conical cavity so formed.

(a) 28 cm

(b) 38 cm

(c) 35 cm

(d) 25 cm

(iii) The curved surface area of the conical cavity so formed is

(a) 250 cm²

(b) 550 cm²

(c) 350 cm²

(d) 450 cm²

(iv) External curved surface area of the cylinder is

(a) 876 cm²

(b) 1250 cm²

(c) 1056 cm²

(d) 1025 cm²

(v) Volume of conical cavity is

(a) 1232 cm³

(b) 1248 cm³

(c) 1380 cm³

(d) 999 cm³

3)
To make the learning process more interesting, creative and innovative, Amayras class teacher brings clay in the classroom, to teach the topic - Surface Areas and Volumes. With clay, she forms a cylinder of radius 6 ern and height 8 cm. Then she moulds the cylinder into a sphere and asks some questions to students.

(i) The radius of the sphere so formed is

(a) 4 cm (b) 6 cm (c) 7 cm (d) 8 cm

(ii) The volume of the sphere so formed is

(a) 905.14 cm³ (b) 903.27 cm³ (c) 1296.5 cm³ (d) 1156.63 cm³

(iii) Find the ratio of the volume of sphere to the volume of cylinder.

(a) 2:1 (b) 1:2 (c) 1:1 (d) 3: 1

(iv) Total surface area of the cylinder is

(a) 528 cm² (b) 756 cm² (c) 625 cm² (d) 636 cm²

(v) During the conversion of a solid from one shape to another the volume of new shape will

(a) be increase (b) be decrease (c) remain unaltered (d) be double
4)
A carpenter used to make and sell different kinds of wooden pen stands like rectangular, cuboidal, cylindrical, conical. Aarav went to his shop and asked him to make a pen stand as explained below. Pen stand must be of the cuboidal shape with three conical depressions, which can hold 3 pens. The dimensions of the cuboidal part must be 20 cm x 15 cm x 5 cm and the ffrlog radius and depth of each conical depression must be 0.6 cm and 2.1 cm respectively.

Based on the above information, answer the following questions.
(i) The volume of the cuboidal part is

(a) 1250 cm³ (b) 1500 cm³ (c) 1625 cm³ (d) 1500 cm³

(ii) Total volume of conical depressions is

(a) 2.508 cm³ (b) 1.5 cm³ (c) 2.376 cm³ (d) 3.6 cm³

(iii) Volume of the wood used in the entire stand is

(a) 631.31 cm³ (b) 3564 cm³ (c) 1502.376 cm³ (d) 1497.624 cm³

(iv) Total surface area of cone of radius r is given by

\((a) \pi r l+\pi r^{2}\) \((b) 2 \pi r l+\pi r^{2}\) \((c) \pi r^{2} l+\pi r^{2}\) \((d) \pi r l+2 \pi r^{3}\)

(v) If the cost of wood used is Rs 5 per cm³, then the total cost of making the pen stand is

(a) Rs 8450.50 (b) Rs 7480 (c) Rs 9962.14 (d) Rs 7488.12

5)

Meera and Dhara have 12 and 8 coins respectively each of radius 3.5 cm and thickness 0.5 cm. They place their coins one above the other to form solid cylinders .

Based on the above information, answer the following questions.
(i) Curved surface area of the cylinder made by Meera is

(a) 144 cm²

(b) 132 cm²

(c) 154 cm²

(d) 142 cm²

(ii) The ratio of curved surface area of the cylinders made by Meera and Dhara is

(a) 2: 5

(b) 3: 2

(c) 1: 2

(d) 2: 7

(iii) The volume of the cylinder made by Dhara is

(a) 154 cm³

(b) 144 cm³

(c) 132 cm³

(d) 142 cm³

(iv) The ratio of the volume of the cylinders made by Meera and Dhara is

(a) 1:2

(b) 2: 5

(c) 3: 2

(d) 4: 3

(v) When two coins are shifted from Meeras cylinder to Dhara's cylinder, then

(a) Volume of two cylinder become equal

(b) Volume of Meera's cylinder> Volume of Dharas cylinder

(c) Volume of Dhara's cylinder> Volume of Meeras cylinder

(d) None of these

CBSE 10th Standard Maths Subject Areas Related to Circles Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)

Principle of a school decided to give badges to students who are chosen for the post of Head boy, Head girl, Prefect and Vice Prefect. Badges are circular in shape with two colour area, red and silver, as shown in figure. The diameter of the region representing red colour is 22 cm and silver colour is filled in 10.5 ern wide ring. Based on the above information, answer the following questions.

(i) The radius of circle representing the red region is

(a) 9 cm

(b) 10 cm

(c) 11 cm

(d) 12 cm

(ii) Find the area of the red region.

(a) 380.28 cm²

(b) 382.28 cm²

(c) 384.28 cm²

(d) 378.28 cm²

(iii) Find the radius of the circle formed by combining the red and silver region.

(a) 20.5 cm

(b) 21.5 cm

(c) 22.5 cm

(d) 23.5 cm

(iv) Find the area of the silver region.

(a) 172.50 cm²

(b) 1062.50 cm²

(c) 1172.50 cm²

(d) 1072.50 cm²

(v) Area of the circular path formed by two concentric circles of radii r₁ and r₂ (r₁ > r₂) =

(a) \(\pi\)(\({r}_{1}^{2}\) + \({r}_{2}^{2}\)) sq. units	(b) \(\pi\)(\({r}_{1}^{2}\) - \({r}_{2}^{2}\)) sq. units
(c) 2 \(\pi\)(\({r}_{1}^{2}\) + \({r}_{2}^{2}\)) sq. units	(d) 2 \(\pi\)(\({r}_{1}^{2}\) - \({r}_{2}^{2}\)) sq. units

2)
Mr Ramanand purchased a plot QRUT to build his house. He leave space of two congruent semicircles for gardening and a rectangular area of breadth 3 em for car parking.

Based on the above information, answer the following questions.
(i) Area of square PQRS is

(a) 700 cm² (b) 729 cm² (c) 732 cm² (d) 735 cm²

(ii) Area of rectangle left for car parking is

(a) 64 cm² (b) 76 cm² (c) 81 cm² (d) 100 cm²

(iii) Radius of semi-circle is

(a) 6.75 cm (b) 7 cm (c) 7.75 cm (d) 8.75 cm

(iv) Area of a semi-circle is

(a) 61.59 cm² (b) 66.29 cm² (c) 70.36 cm² (d) 71.59 cm²

(v) Find the area of the shaded region

(a) 660.82 cm² (b) 666.82 cm² (c) 669.89 cm² (d) 700 cm²
3)
Makar Sankranti is a fun and delightful occasion. Like many other festivals, the kite flying competition also has a historical and cultural significance attached to it. The following figure shows a kite in which BCD is the shape of quadrant of a circle of radius 42 cm, ABCD is a square and \(\Delta\)CEF is an isosceles right angled triangle whose equal sides are 7 cm long.

Based on the above information, answer the following questions.
(i) Find the area of the square

(a) 1700 cm² (b) 1764 cm² (c) 1800 cm² (d) 1864 cm²

(ii) Area of quadrant BCD is

(a) 1290 cm² (b) 1380 cm² (c) 1386 cm² (d) 1390 cm²

(iii) Find the area of \(\Delta\)CEF.

(a) 24.5 cm² (b) 25 cm² (c) 25.5 cm² (d) 26 cm²

(iv) Area of the shaded portion is

(a) 1377 cm² (b) 1390 cm² (c) 1400 cm² (d) 1410.5 cm²

(v) Area of the unshaded portion is

(a) 370 cm² (b) 378 cm² (c) 380 cm² (d) 384 cm²

4)

Gayatri have a triangular shaped grass field. At the three corners of the field, a cow, a buffalo and a horse are tied separately to the pegs by means of ropes of3.5 m each to graze in the field, as shown in the figure. Sides of the triangular field are 25 m, 24 m and 7 m. Based on the above information, answer the following questions.

(i) Area of triangular field is

(a) 82 m²

(b) 84 m²

(c) 86 m²

(d) 88 m²

(ii) Area of the region grazed by the cow is

\((a) \frac{\angle A}{360^{\circ}} \times \pi \times(3.5)^{2}\)

\((b) \frac{\angle B}{360^{\circ}} \times \pi \times(24)^{2}\)

\((c) \frac{\angle C}{360^{\circ}} \times \pi \times(3.5)^{2}\)

(d) None of these

(iii) Area of region grazed by the buffalo and the horse is

\((a) \frac{(\angle A+\angle C)}{360^{\circ}} \times \pi \times(5.5)^{2}\)	\((b) \frac{(\angle B+\angle C)}{360^{\circ}} \times \pi \times(5.6)^{2}\)
\((c) \frac{(\angle A+\angle C)}{360^{\circ}} \times \pi \times(3.5)^{2}\)	\((d) \frac{(\angle B+\angle C)}{360^{\circ}} \times \pi \times(3.5)^{2}\)

(iv) Total area grazed by the cow, the buffalo and the horse is

(a) 16.25 m²

(b) 17.3 m²

(c) 18.25 m²

(d) 19.25 m²

(v) Find the area of the field that cannot be grazed.

(a) 60.75 m²

(b) 64.75 m²

(c) 68 m²

(d) 69.75 m²

5)
To find the polluted region in different areas of Dwarka (a part of Delhi represented by the circle given below) a survey was conducted by the students of class X. It was found that the shaded region is the polluted region, where O is the centre of the circle.

Based on the above information, answer the following questions.
(i) Find the radius of the circle

(a) 12.5 cm (b) 13.5 cm (c) 15 cm (d) 16.5 cm

(ii) Find the area of the circle.

(a) 481.7 cm² (b) 490 cm² (c) 491.07 cm² (d) 495.6 cm²

(Hi) If D lies at the middle of arc BC, then area of region COD is

(a) 121 cm² (b) 122.76 cm² (c) 126 cm² (d) 129.8 cm²

(iv) Area of the \(\Delta\)BAC is

(a) 77 cm² (b) 79 cm² (c) 81 cm² (d) 84 cm²

(v) Find .the area of the polluted region.

(a) 280.31 cm² (b) 284.31 cm² (c) 285.31 cm² (d) 240.31 cm²

CBSE 10th Standard Maths Subject Areas Related to Circles Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)

Principle of a school decided to give badges to students who are chosen for the post of Head boy, Head girl, Prefect and Vice Prefect. Badges are circular in shape with two colour area, red and silver, as shown in figure. The diameter of the region representing red colour is 22 cm and silver colour is filled in 10.5 ern wide ring. Based on the above information, answer the following questions.

(i) The radius of circle representing the red region is

(a) 9 cm

(b) 10 cm

(c) 11 cm

(d) 12 cm

(ii) Find the area of the red region.

(a) 380.28 cm²

(b) 382.28 cm²

(c) 384.28 cm²

(d) 378.28 cm²

(iii) Find the radius of the circle formed by combining the red and silver region.

(a) 20.5 cm

(b) 21.5 cm

(c) 22.5 cm

(d) 23.5 cm

(iv) Find the area of the silver region.

(a) 172.50 cm²

(b) 1062.50 cm²

(c) 1172.50 cm²

(d) 1072.50 cm²

(v) Area of the circular path formed by two concentric circles of radii r₁ and r₂ (r₁ > r₂) =

(a) \(\pi\)(\({r}_{1}^{2}\) + \({r}_{2}^{2}\)) sq. units	(b) \(\pi\)(\({r}_{1}^{2}\) - \({r}_{2}^{2}\)) sq. units
(c) 2 \(\pi\)(\({r}_{1}^{2}\) + \({r}_{2}^{2}\)) sq. units	(d) 2 \(\pi\)(\({r}_{1}^{2}\) - \({r}_{2}^{2}\)) sq. units

2)
While doing dusting a maid found a button whose upper face is of black colour, as shown in the figure. The diameter of each of the smaller identical circles is 1/4 of the diameter of the larger circle whose radius is 16 cm.

Based on the above information, answer the following questions.
(i) The area of each of the smaller circle is

(a) 40.28 cm² (b) 46.39 cm² (c) 50.28 cm² (d) 52.3 cm²

(ii) The area of the larger circle is

(a) 804.57 cm² (b) 704.57 cm² (c) 855.57 cm² (d) 990.57 cm²

(iii) The area of the black colour region is

(a) 600.45 cm² (b) 603.45 cm² (c) 610.45 cm² (d) 623.45 cm²

(iv) The area of quadrant of a smaller circle is

(a) 11.57 cm² (b) 13.68 cm² (c) 12 cm² (d) 12.57 cm²

(v) If two concentric circles are of radii 2 cm and 5 cm, then the area between them is

(a) 60 cm² (b) 63 cm² (c) 66 cm² (d) 68 cm²
3)
Mr Ramanand purchased a plot QRUT to build his house. He leave space of two congruent semicircles for gardening and a rectangular area of breadth 3 em for car parking.

Based on the above information, answer the following questions.
(i) Area of square PQRS is

(a) 700 cm² (b) 729 cm² (c) 732 cm² (d) 735 cm²

(ii) Area of rectangle left for car parking is

(a) 64 cm² (b) 76 cm² (c) 81 cm² (d) 100 cm²

(iii) Radius of semi-circle is

(a) 6.75 cm (b) 7 cm (c) 7.75 cm (d) 8.75 cm

(iv) Area of a semi-circle is

(a) 61.59 cm² (b) 66.29 cm² (c) 70.36 cm² (d) 71.59 cm²

(v) Find the area of the shaded region

(a) 660.82 cm² (b) 666.82 cm² (c) 669.89 cm² (d) 700 cm²
4)
Makar Sankranti is a fun and delightful occasion. Like many other festivals, the kite flying competition also has a historical and cultural significance attached to it. The following figure shows a kite in which BCD is the shape of quadrant of a circle of radius 42 cm, ABCD is a square and \(\Delta\)CEF is an isosceles right angled triangle whose equal sides are 7 cm long.

Based on the above information, answer the following questions.
(i) Find the area of the square

(a) 1700 cm² (b) 1764 cm² (c) 1800 cm² (d) 1864 cm²

(ii) Area of quadrant BCD is

(a) 1290 cm² (b) 1380 cm² (c) 1386 cm² (d) 1390 cm²

(iii) Find the area of \(\Delta\)CEF.

(a) 24.5 cm² (b) 25 cm² (c) 25.5 cm² (d) 26 cm²

(iv) Area of the shaded portion is

(a) 1377 cm² (b) 1390 cm² (c) 1400 cm² (d) 1410.5 cm²

(v) Area of the unshaded portion is

(a) 370 cm² (b) 378 cm² (c) 380 cm² (d) 384 cm²
5)
A farmer has a rectangular field oflength 30 m and breadth 15 m. By the farmer a pit of diameter 7 m is dug 12 m deep for rain water harvesting. The earth taken out is spread in the field.

Based on the above information, answer the following questions.
(I) Find the volume of the earth taken out.

(a) 460 m³ (b) 462 m³ (c) 465 m³ (d) 468 m³

(ii) The area of the rectangular field is

(a) 420 m² (b) 430 m² (c) 440 m² (d) 450m²

(iii) Find'the area of the top of the pit.

(a) 38.5 m² (b) 40.5 m² (c) 41.5 m² (d) None of these

(iv) The area of the remaining field is

(a) 402.3 m² (b) 405 m² (c) 410 m² (d) 411.5 m²

(v) Find the level rise in the field

(a) 0.5 m (b) 3 m (c) 1.12 m (d) 2.12 m

CBSE 10th Standard Maths Subject Some Applications of Trigonometry Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
There are two temples on each bank of a river. One temple is 50 m high. A man, who is standing on the top of 50 m high temple, observed from the top that angle of depression of the top and foot of other temple are 30° and 60° respectively. (Take \(\sqrt{3}\) = 1.73)

Based on the above information, answer the following questions.
(i) Measure of \(\angle\)ADF is equal to

(a) 45° (b) 60° (c) 30° (d) 90°

(ii) Measure of \(\angle\)ACB is equal to

(a) 45° (b) 60° (c) 30° (d) 90°

(iii) Width of the river is

(a) 28.90 m (b) 26.75 m (c) 25 m (d) 27 m

(iv) Height of the other temple is

(a) 32.5 m (b) 35 m (c) 33.33 m (d) 40 m

(v) Angle of depression is always

(a) reflex angle (b) straight

(c) an obtuse angle (d) an acute angle
2)
A circus artist is climbing through a 15 m long rope which is highly stretched and tied from the top of a vertical pole to the ground as shown below. Based on the above information, answer the following questions.

(i) Find the height of the pole, if angle made by rope to the ground level is 45°.

\((a) 15 \mathrm{~m}\) \((b) 15 \sqrt{2} \mathrm{~m}\)

\((c) \frac{15}{\sqrt{3}} \mathrm{~m}\) \((d) \frac{15}{\sqrt{2}} \mathrm{~m}\)

(ii) If the angle made by the rope to the ground level is 45°, then find the distance between artist and pole at ground level.

\((a) \frac{15}{\sqrt{2}} \mathrm{~m}\) \((b) 15 \sqrt{2} \mathrm{~m}\) \((c) 15 \mathrm{~m}\) \((d) {15}{\sqrt{3}} \mathrm{~m}\)

(iii) Find the height of the pole if the angle made by the rope to the ground level is 30°.

(a) 2.5 m (b) 5 m (c) 7.5 m (d) 10 m

(iv) If the angle made by the rope to the ground level is 30° and 3 m rope is broken, then find the height of the pole

(a) 2m (b) 4m (c) 5m (d) 6m

(v) Which mathematical concept is used here?

(a) Similar Triangles (b) Pythagoras Theorem

(c) Application of Trigonometry (d) None of these
3)
An electrician has to repair an electric fault on the pole of height of8 m. He needs to reach a point 2 m below the top of the pole to undertake the repair work.

Based on the above information, answer the following questions.
(i) Length of BD is

(a) 10 m (b) 6 m (c) 4 m (d) 4 m

(ii) What should be the length of ladder, so that it makes an angle of 60° with the ground?

\((a) 4\sqrt{3} {~m}\) \((b) 2\sqrt{3} {~m}\) \((c) 3\sqrt{3} {~m}\) \((d) 5\sqrt{3} {~m}\)

(iii) The distance between the foot ofladder and pole is

\((a) 6\sqrt{3} {~m}\) \((b) 4\sqrt{3} {~m}\) \((c) 3\sqrt{3} {~m}\) \((d) 2\sqrt{3} {~m}\)

(iv) What will be the measure of \(\angle\)BCD when BD and CD are equal?

(a) 30° (b) 45° (c) 60° (d) 75°

(v) Find the measure of \(\angle\)DBC.

(a) 15° (b) 60° (c) 30° (d) 45°
4)
A boy is standing on the top of light house. He observed that boat P and boat Q are approaching to light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. He also knows that height of the light house is 100 m.

Based on the above information, answer the following questions.
(i) Measure of \(\angle\)ACD is equal to

(a) 30° (b) 45° (c) 60° (d) 90°

(ii) If \(\angle\)YAB = 30°, then \(\angle\)ABD is also 30°, Why?

(a) vertically opposite angles (b) alternate interior angles

(c) alternate exterior angles (d) corresponding angles

(iii) Length of CD is equal to

(a) 90 m (b) 60 m (c) 100 m (d) 80 m

(iv) Length of BD is equal to

(a) 50 m (b) 100 m (c) 100\(\sqrt{2}\) m (d) 100\(\sqrt{3}\) m

(v) Length of AC is equal to

(a)100\(\sqrt{2}\) m (b) 100\(\sqrt{3}\) m (c) 50 m (d) 100 m
5)
Teewan, Arun and Pankaj were celebrating the festival of Diwali in open ground with firecrackers. There is a pedestal in the ground. All of sudden Teewan stands on pedestal and release sky lantern from the top of pedestal.

Based on the above information answer the following questions. (Take \(\sqrt{3}\) = J .73)
(i) Which one is a pair of angle of depression?

\((a) (\angle x, \angle y)\) \((b) (\angle y, \angle z)\) \((c) (\angle z, \angle t)\) \((d) (\angle r, \angle q)\)

(ii) If the position of Pankaj is 25 m away from the base of pedestal and Zr = 30°, then find the height of pedestal.

(a) 14.45m (b) 15.5m (c) 16.36m (d) 17.36m

(iii) If the height of pedestal is 30 m, \(\angle\)t = 45° and \(\angle\)z = 30°, then the horizontal distance between Arun and Pankaj is

(a) 24.5 m (b) 19.5 m (c) 20 m (d) 21.9 m

(iv) If the vertical height of sky lantern from the top of pedestal is 12 m and \(\angle\)y = 30°, then distance between Teewan and sky lantern is

(a) 20 m (b) 16.97 m (c) 24 m (d) 19.86 m

(v) If \(\angle\)q = 60° and position of Arun is 15 m away from the base of pedestal, then find the height of pedestal.

(a) 16.25 m (b) 25 m (c) 25.95 m (d) 26 m

CBSE 10th Standard Maths Subject Some Applications of Trigonometry Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
There are two temples on each bank of a river. One temple is 50 m high. A man, who is standing on the top of 50 m high temple, observed from the top that angle of depression of the top and foot of other temple are 30° and 60° respectively. (Take \(\sqrt{3}\) = 1.73)

Based on the above information, answer the following questions.
(i) Measure of \(\angle\)ADF is equal to

(a) 45° (b) 60° (c) 30° (d) 90°

(ii) Measure of \(\angle\)ACB is equal to

(a) 45° (b) 60° (c) 30° (d) 90°

(iii) Width of the river is

(a) 28.90 m (b) 26.75 m (c) 25 m (d) 27 m

(iv) Height of the other temple is

(a) 32.5 m (b) 35 m (c) 33.33 m (d) 40 m

(v) Angle of depression is always

(a) reflex angle (b) straight

(c) an obtuse angle (d) an acute angle
2)
There are two windows in a house. First window is at the height of 2 m above the ground and other window is 4 m vertically above the lower window. Ankit and Radha are sitting inside the two windows at points G and F respectively. At an instant, the angles of elevation of a balloon from these windows are observed to be 60° and 30° as shown below

Based on the above information, answer the following questions.
(i) Who is more closer to the balloon?

(a) Ankit (b) Radha

(c) Both are at equal distance (d) Can't be determined

(ii) Value of DF is equal to

\((a) \frac{h}{\sqrt{3}} \mathrm{~m}\) \((b) h \sqrt{3} \mathrm{~m}\) \((c) \frac{h}{2} \mathrm{~m}\) \((d) 2 h \mathrm{~m}\)

(iii) Value of h is

(a) 2 (b) 3 (c) 4 (d) 5

(iv) Height of the balloon from the ground is

(a) 4 m (b) 6 m (c) 8 m (d) 10 m

(v) If the balloon is moving towards the building, then both angle of elevation will

(a) remain same (b) increases (c) decreases (d) can't be determined
3)
A circus artist is climbing through a 15 m long rope which is highly stretched and tied from the top of a vertical pole to the ground as shown below. Based on the above information, answer the following questions.

(i) Find the height of the pole, if angle made by rope to the ground level is 45°.

\((a) 15 \mathrm{~m}\) \((b) 15 \sqrt{2} \mathrm{~m}\)

\((c) \frac{15}{\sqrt{3}} \mathrm{~m}\) \((d) \frac{15}{\sqrt{2}} \mathrm{~m}\)

(ii) If the angle made by the rope to the ground level is 45°, then find the distance between artist and pole at ground level.

\((a) \frac{15}{\sqrt{2}} \mathrm{~m}\) \((b) 15 \sqrt{2} \mathrm{~m}\) \((c) 15 \mathrm{~m}\) \((d) {15}{\sqrt{3}} \mathrm{~m}\)

(iii) Find the height of the pole if the angle made by the rope to the ground level is 30°.

(a) 2.5 m (b) 5 m (c) 7.5 m (d) 10 m

(iv) If the angle made by the rope to the ground level is 30° and 3 m rope is broken, then find the height of the pole

(a) 2m (b) 4m (c) 5m (d) 6m

(v) Which mathematical concept is used here?

(a) Similar Triangles (b) Pythagoras Theorem

(c) Application of Trigonometry (d) None of these
4)
There is fire incident in the house. The house door is locked so, the fireman is trying to enter the house from the window. He places the ladder against the wall such that its top reaches the window as shown in the figure .

Based on. the above information, answer the following questions.
(i) If window is 6 m above the ground and angle made by the foot ofladder to the ground is 30°, then length of the ladder is

(a) 8m (b) 10m (c) 12m (d) 14m

(ii) If fireman place the ladder 5 m away from the wall and angle of elevation is observed to be 30°, then length of the ladder is

(a) 5 m \((b) \frac{10}{\sqrt{3}} \mathrm{~m}\) \((c) \frac{15}{\sqrt{2}} \mathrm{~m}\) (d) 20 m

(iii) If fireman places the ladder 2.5 m away from the wall and angle of elevation is observed to be 60°, then find the height of the window. (Take \(\sqrt{3}\) = 1.73)

(a) 4.325 m (b) 5.5 m (c) 6.3 m (d) 2.5 m

(iv) If the height of the window is 8 m above the ground and angle of elevation is observed to be 45°, then horizontal distance between the foot of ladder and wall is

(a) 2 m (b) 4 m (c) 6 m (d) 8 m

(v) If the fireman gets a 9 m long ladder and window is at 6 m height, then how far should the ladder be placed?

(a) 5 m (b) 3\(\sqrt{5}\)m (c) 3 m (d) 4 m

5)

Rohit is standing at the top of the building observes a car at an angle of 30°, which is approaching the foot of the building with a uniform speed. 6 seconds later, angle of depression of car formed to be 60°, whose distance at that instant from the building is 25 m.

Based on the above information, answer the following questions.
(i) Height of the building is

\((a) 25\sqrt{2} {~m}\)

(b) 50 m

\((a) 25\sqrt{3} {~m}\)

(d) 25 m

(ii) Distance between two positions of the car is

(a) 40 m

(b) 50 m

(c) 60 m

(d) 75 m

(iii) Total time taken by the car to reach the foot of the building from starting point is

(a) 4 sec.

(b) 3 sec.

(c) 6 sec.

(d) 9 sec.

(iv) The distance of the observer from the car when it makes an angle of 60° is

(a) 25 m

(b) 45 m

(c) 50 m

(d) 75 m

(v) The angle of elevation increases

(a) when point of observation moves towards the object

(b) when point of observation moves away from the object

(c) when object moves away from the observer

(d) None of these

CBSE 10th Standard Maths Subject Circles Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
In a park, four poles are standing at positions A, B, C and D around the fountain such that the cloth joining the poles AB, BC, CD and DA touches the fountain at P, Q, Rand S respectively as shown in the figure.

Based on the above information, answer the following questions.
(i) If 0 is the centre of the circular fountain, then \(\angle\)OSA =

(a) 60° (b) 90°

(c) 45° (d) None of these

(ii) Which of the following is correct?

(a) AS = AP (b) BP= BQ (c) CQ = CR (d) All of these

(iii) If DR = 7 cm and AD = 11 ern, then AP =

(a) 4 cm (b) 18 cm (c) 7 cm (d) 11 cm

(iv) If O is the centre of the fountain, with \(\angle\)QCR = 60°, then \(\angle\)QOR

(a) 60° (b) 120° (c) 90° (d) 30°

(v) Which of the following is correct?

(a) AB + BC = CD + DA (b) AB + AD = BC + CD

(c) AB + CD = AD + BC (d) All of these
2)
Smita always finds it confusing with the concepts of tangent and secant of a circle. But this time she has determined herself to get concepts easier. So, she started listing down the differences between tangent and secant of a circle along with their relation. Here, some points in question form are listed by Smita in her notes. Try answering them to clear your concepts also.

(i) A line that intersects a circle exactly at two points is called

(a) Secant (b) Tangent (c) Chord (d) Both (a) and (b)

(ii) Number of tangents that can be drawn on a circle is

(a) 1 (b) 0 (c) 2 (d) Infinite

(iii) Number of tangents that can be drawn to a circle from a point not on it, is

(a) 1 (b) 2 (c) 0 (d) Infinite

(iv) Number of secants that can be drawn to a circle from a point on it is

(a) Infinite (b) 1 (c) 2 (d) 0

(v) A line that touches a circle at only one point is called

(a) Secant (b) Chord (c) Tangent (d) Diameter
3)
In a maths class, the teacher draws two circles that touch each other externally at point K with centres A and B and radii 5 em and 4 em respectively as shown in the figure.

Based on the above information, answer the following questions.
(i) The value of PA =

(a) 12 cm (b) 5 cm (c) 13 cm (d) Can't be determined

(ii) The value of BQ =

(a) 4 cm (b) 5 cm (c) 6 cm (d) None of these

(iii) The value of PK =

(a) 13 cm (b) 15 cm (c) 16 cm (d) 18 cm

(iv) The value of QY =

(a) 2 cm (b) 5 cm (c) 1 cm (d) 3 cm

(v) Which of the following is true?

(a) PS²=PA.PK (b) TQ²=QB.QK (c) PS²=PX.PK (d) TQ² = QA.QB
4)
In an online test, Ishita comes across the statement - If a tangent is drawn to a circle from an external point, then the square of length of tangent drawn is equal to difference of squares of distance of the tangent from the centre of circle and radius of the circle.

Help Ishita, in answering the following questions based on the above statement.
(i) If AB is a tangent to a circle with centre O at B such that AB = 10 cm and OB = 5 cm, then OA =

\((a) 3 \sqrt{5} \mathrm{~cm}\) \((b) 5 \sqrt{5} \mathrm{~cm}\) \((c) 4 \sqrt{5} \mathrm{~cm}\) \((d) 6 \sqrt{5} \mathrm{~cm}\)

(ii) In the adjoining figure, radius of the circle is

(a) 8 cm (b) 7 cm (c) 9 cm (d) 10 cm

(iii) In the adjoining figure, length of tangent AP is

(a) 12 cm (b) 24 cm (c) 30 cm (d) None of these

(iv) PT is a tangent to a circle with centre 0 and diameter = 40 cm. If PT = 21 cm, then OP =

(a) 33 cm (b) 29 cm (c) 37 cm (d) None of these

(v) In the adjoining figure, the length of the tangent is

(a) 15 cm (b) 9 cm (c) 8 cm (d) 10 cm
5)
Following are questions of section-A in assessment test on circle that Eswar attend last month in school. He scored 5 out of 5 in this section. Answer the questions and check your score if 1 mark is allotted to each question.

(i) If two tangents AB and CDdrawn to a circle with centre 0 at P and Q respectively, are parallel to each other, then which of the following is correct?

(a) \(\angle\)POQ = 180° (b) PQ is a diameter

(c) \(\angle\)APQ = \(\angle\)PQD = 90° (d) All of these

(ii) If I is a tangent to the circle with centre 0 and line m is passing through 0 intersects the tangent I at point of contact, then

(a) I || m (b) l \(\perp\)m

(c) line I and line m intersects and makes an angle of 60° (d) can't be determined

(iii) Number of tangents that can be drawn to a circle from a point inside it, is

(a) 1 (b) 2 (c) infinite (d) 0

(iv) Which of the following is true?

(a) PQ is a tangent to both the circles (b) Two circles are concentric

(c) PQ is a tangent to bigger circle only (d) PQ is a tangent to smaller circle only

(v) A parallelogram circumscribing a circle is called a

(a) rhombus (b) rectangle

(c) square (d) none of these

CBSE 10th Standard Maths Subject Circles Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
Smita always finds it confusing with the concepts of tangent and secant of a circle. But this time she has determined herself to get concepts easier. So, she started listing down the differences between tangent and secant of a circle along with their relation. Here, some points in question form are listed by Smita in her notes. Try answering them to clear your concepts also.

(i) A line that intersects a circle exactly at two points is called

(a) Secant (b) Tangent (c) Chord (d) Both (a) and (b)

(ii) Number of tangents that can be drawn on a circle is

(a) 1 (b) 0 (c) 2 (d) Infinite

(iii) Number of tangents that can be drawn to a circle from a point not on it, is

(a) 1 (b) 2 (c) 0 (d) Infinite

(iv) Number of secants that can be drawn to a circle from a point on it is

(a) Infinite (b) 1 (c) 2 (d) 0

(v) A line that touches a circle at only one point is called

(a) Secant (b) Chord (c) Tangent (d) Diameter
2)
A backyard is in the shape of a triangle with right angle at B, AB = 6 m and BC = 8 m. A pit was dig inside it such that it touches the walls AC, BC and AB at P, Q and R respectively such that AP = x m.

Based on the above information, answer the following questions.
(i) The value of AR =

(a) 2x m (b) x/2 m (c) x m (d) 3x m

(ii) The value of BQ =

(a) 2x m (b) (6-x) m (c) (2 - x) cm (d) 4x m

(iii) The value of CQ =

(a) (4+x)m (b) (10 - x) m (c) (2+x)m (d) both (b) and (c)

(iv) Which of the following is correct?

(a) Quadrilateral AROP is a square. (b) Quadrilateral BROQ is a square.

(c) Quadrilateral CQOP is a square. (d) None of these

(v) Radius of the pit is

(a) 2 cm (b) 3 cm (c) 4 cm (d) 5 cm
3)
In a maths class, the teacher draws two circles that touch each other externally at point K with centres A and B and radii 5 em and 4 em respectively as shown in the figure.

Based on the above information, answer the following questions.
(i) The value of PA =

(a) 12 cm (b) 5 cm (c) 13 cm (d) Can't be determined

(ii) The value of BQ =

(a) 4 cm (b) 5 cm (c) 6 cm (d) None of these

(iii) The value of PK =

(a) 13 cm (b) 15 cm (c) 16 cm (d) 18 cm

(iv) The value of QY =

(a) 2 cm (b) 5 cm (c) 1 cm (d) 3 cm

(v) Which of the following is true?

(a) PS²=PA.PK (b) TQ²=QB.QK (c) PS²=PX.PK (d) TQ² = QA.QB
4)
Prem did an activity on tangents drawn to a circle from an external point using 2 straws and a nail for maths project as shown in figure.

Based on the above information, answer the following questions.
(i) Number of tangents that can be drawn to a circle from an external point is

(a) 1 (b) 2 (c) infinite (d) any number depending on radius of circle

(ii) On the basis of which of the following congruency criterion,\(\Delta \mathrm{OAP} \cong \Delta \mathrm{OBP} ?\)

(a) ASA (b) SAS (c) RHS (d) SSS

(iii) If \(\angle\)AOB = 150°, then \(\angle\)APB =

(a) 75° (b) 30° (c) 60° (d) 100°

(iv) If \(\angle\)APB = 40°, then \(\angle\)BAO =

(a) 40° (b) 30° (c) 50° (d) 20°

(v) If \(\angle\)ABO = 45°, then which of the following is correct option?

(a) \(A P \perp B P\) (b) PAOB is square (c) \(\angle\)AOB = 90° (d) All of these
5)
In an online test, Ishita comes across the statement - If a tangent is drawn to a circle from an external point, then the square of length of tangent drawn is equal to difference of squares of distance of the tangent from the centre of circle and radius of the circle.

Help Ishita, in answering the following questions based on the above statement.
(i) If AB is a tangent to a circle with centre O at B such that AB = 10 cm and OB = 5 cm, then OA =

\((a) 3 \sqrt{5} \mathrm{~cm}\) \((b) 5 \sqrt{5} \mathrm{~cm}\) \((c) 4 \sqrt{5} \mathrm{~cm}\) \((d) 6 \sqrt{5} \mathrm{~cm}\)

(ii) In the adjoining figure, radius of the circle is

(a) 8 cm (b) 7 cm (c) 9 cm (d) 10 cm

(iii) In the adjoining figure, length of tangent AP is

(a) 12 cm (b) 24 cm (c) 30 cm (d) None of these

(iv) PT is a tangent to a circle with centre 0 and diameter = 40 cm. If PT = 21 cm, then OP =

(a) 33 cm (b) 29 cm (c) 37 cm (d) None of these

(v) In the adjoining figure, the length of the tangent is

(a) 15 cm (b) 9 cm (c) 8 cm (d) 10 cm

CBSE 10th Standard Maths Subject Introduction to Trigonometry Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
Three friends - Anshu, Vijay and Vishal are playing hide and seek in a park. Anshu and Vijay hide in the shrubs and Vishal have to find both of them. If the positions of three friends are at A, Band C respectively as shown in the figure and forms a right angled triangle such that AB = 9 m, BC = 3\(\sqrt{3}\) m and \(\angle\)B = 90°, then answer the following questions.

(i) The measure of \(\angle\)A is

(a) 30° (b) 45° (c) 60° (d) None of these

(ii) The measure of \(\angle\)C is

(a) 30° (b) 45° (c) 60° (d) None of these

(iii) The length of AC is

\((a) 2 \sqrt{3} \mathrm{~m}\) \((b) \sqrt{3} \mathrm{~m}\) \((c) 4 \sqrt{3} \mathrm{~m}\) \((d) 6 \sqrt{3} \mathrm{~m}\)

(iv) cos2A =

(a) 0 \((b) \frac{1}{2}\) \((c) \frac{1}{\sqrt{2}}\) \((d) \frac{\sqrt{3}}{2}\)

(v) sin \(\left(\frac{C}{2}\right)\) =

(a) 0 \((b) \frac{1}{2}\) \((c) \frac{1}{\sqrt{2}}\) \((d) \frac{\sqrt{3}}{2}\)
2)
Two aeroplanes leave an airport, one after the other. After moving on runway, one flies due North and other flies due South. The speed of two aeroplanes is 400 km/hr and 500 km/hr respectively. Considering PQ as runway and A and B are any two points in the path followed by two planes, then answer the following questions.

(i) Find \(\tan \theta ; \text { if } \angle A P Q=\theta\)

\((a) \frac{1}{2}\) \((b) \frac{1}{\sqrt{2}}\) \((c) \frac{\sqrt{3}}{2}\) \((d) \frac{3}{4}\)

(ii) Find cot B

\((a) \frac{3}{4}\) \((b) \frac{15}{4}\) \((c) \frac{3}{8}\) \((d) \frac{15}{8}\)

(iii) Find tanA.

\((a) 2\) \((b) \sqrt{2}\) \((c) \frac{4}{3}\) \((d) \frac{2}{\sqrt{3}}\)

(iv) Find secA.

\((a) 1\) \((b) \frac{2}{3}\) \((c) \frac{4}{3}\) \((d) \frac{5}{3}\)

(v) Find cosecB.

\((a) \frac{17}{8}\) \((b) \frac{12}{5}\) \((c) \frac{5}{12}\) \((d) \frac{8}{17}\)
3)
Anita, a student of class 10^th, has to made a project on 'Introduction to Trigonometry' She decides to make a bird house which is triangular in shape. She uses cardboard to make the bird house as shown in the figure. Considering the front side of bird house as right angled triangle PQR, right angled at R, answer the following questions.

(i) If \(\angle P Q R=\theta, \text { then } \cos \theta=\)

\((a) \frac{12}{5}\) \((b) \frac{5}{12}\) \((c) \frac{12}{13}\) \((d) \frac{13}{12}\)

(ii) The value of sec \(\theta\) =

\((a) \frac{5}{12}\) \((b) \frac{12}{5}\) \((c) \frac{13}{12}\) \((d) \frac{12}{13}\)

(iii) The value of \(\frac{\tan \theta}{1+\tan ^{2} \theta}=\)

\((a) \frac{5}{12}\) \((b) \frac{12}{5}\) \((c) \frac{60}{169}\) \((d) \frac{169}{60}\)

(iv) The value of \(\cot ^{2} \theta-\operatorname{cosec}^{2} \theta=\)

(a) -1 (b) 0 (c) 1 (d) 2

(v) The value of \(\sin ^{2} \theta+\cos ^{2} \theta=\)

(a) 0 (b) 1 (c) -1 (d) 2
4)
Ritu's daughter is feeling so hungry and so thought to eat something. She looked into the fridge and found some bread pieces. She decided to make a sandwich. She cut the piece of bread diagonally and found that it forms a
righ.t angled triangle with sides 4 cm, 4\(\sqrt{3}\) cm and 8 cm.

On the basis of above information, answer the following questions.
(i) The value of \(\angle\)M =

(a) 30° (b) 60° (c) 45° (d) None of these

(ii) The value of \(\angle\)K =

(a) 45° (b) 30 ° (c) 60° (d) None of these

(iii) Find the value of tanM.

\((a) \sqrt{3}\) \((b) \frac{1}{\sqrt{3}}\) (c) 1 (d) None of these

(iv) sec²M - 1 =

(a) tanM (b) tan2M (c) tan²M (d) None of these

(v) The value of \(\frac{\tan ^{2} 45^{\circ}-1}{\tan ^{2} 45^{\circ}+1}\) is

(a) 0 (b) 1 (c) 2 (d) -1
5)
Aanya and her father go to meet her friend Juhi for a party. When they reached to [uhi's place, Aanya saw the roof of the house, which is triangular in shape. If she imagined the dimensions of the roof as given in the figure, then answer the following questions.

(i) If D is the mid point of AC, then BD =

(a) 2m (b) 3m (c) 4m (d) 6m

(ii) Measure of \(\angle\)A =

(a) 30° (b) 60° (c) 45° (d) None of these

(iii) Measure of \(\angle\)C =

(a) 30° (b) 60° (c) 45° (d) None of these

(iv) Find the value of sinA + cosC.

(a) 0 (b) 1 (c) \(\frac{1}{2}\) (d) \(\sqrt{2}\)

(v) Find the value of tan²C + tan² A.

(a) 0 (b) 1 (c) 2 (d) \(\frac{1}{2}\)

CBSE 10th Standard Maths Subject Introduction to Trigonometry Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
Three friends - Anshu, Vijay and Vishal are playing hide and seek in a park. Anshu and Vijay hide in the shrubs and Vishal have to find both of them. If the positions of three friends are at A, Band C respectively as shown in the figure and forms a right angled triangle such that AB = 9 m, BC = 3\(\sqrt{3}\) m and \(\angle\)B = 90°, then answer the following questions.

(i) The measure of \(\angle\)A is

(a) 30° (b) 45° (c) 60° (d) None of these

(ii) The measure of \(\angle\)C is

(a) 30° (b) 45° (c) 60° (d) None of these

(iii) The length of AC is

\((a) 2 \sqrt{3} \mathrm{~m}\) \((b) \sqrt{3} \mathrm{~m}\) \((c) 4 \sqrt{3} \mathrm{~m}\) \((d) 6 \sqrt{3} \mathrm{~m}\)

(iv) cos2A =

(a) 0 \((b) \frac{1}{2}\) \((c) \frac{1}{\sqrt{2}}\) \((d) \frac{\sqrt{3}}{2}\)

(v) sin \(\left(\frac{C}{2}\right)\) =

(a) 0 \((b) \frac{1}{2}\) \((c) \frac{1}{\sqrt{2}}\) \((d) \frac{\sqrt{3}}{2}\)
2)
Two aeroplanes leave an airport, one after the other. After moving on runway, one flies due North and other flies due South. The speed of two aeroplanes is 400 km/hr and 500 km/hr respectively. Considering PQ as runway and A and B are any two points in the path followed by two planes, then answer the following questions.

(i) Find \(\tan \theta ; \text { if } \angle A P Q=\theta\)

\((a) \frac{1}{2}\) \((b) \frac{1}{\sqrt{2}}\) \((c) \frac{\sqrt{3}}{2}\) \((d) \frac{3}{4}\)

(ii) Find cot B

\((a) \frac{3}{4}\) \((b) \frac{15}{4}\) \((c) \frac{3}{8}\) \((d) \frac{15}{8}\)

(iii) Find tanA.

\((a) 2\) \((b) \sqrt{2}\) \((c) \frac{4}{3}\) \((d) \frac{2}{\sqrt{3}}\)

(iv) Find secA.

\((a) 1\) \((b) \frac{2}{3}\) \((c) \frac{4}{3}\) \((d) \frac{5}{3}\)

(v) Find cosecB.

\((a) \frac{17}{8}\) \((b) \frac{12}{5}\) \((c) \frac{5}{12}\) \((d) \frac{8}{17}\)
3)
Anita, a student of class 10^th, has to made a project on 'Introduction to Trigonometry' She decides to make a bird house which is triangular in shape. She uses cardboard to make the bird house as shown in the figure. Considering the front side of bird house as right angled triangle PQR, right angled at R, answer the following questions.

(i) If \(\angle P Q R=\theta, \text { then } \cos \theta=\)

\((a) \frac{12}{5}\) \((b) \frac{5}{12}\) \((c) \frac{12}{13}\) \((d) \frac{13}{12}\)

(ii) The value of sec \(\theta\) =

\((a) \frac{5}{12}\) \((b) \frac{12}{5}\) \((c) \frac{13}{12}\) \((d) \frac{12}{13}\)

(iii) The value of \(\frac{\tan \theta}{1+\tan ^{2} \theta}=\)

\((a) \frac{5}{12}\) \((b) \frac{12}{5}\) \((c) \frac{60}{169}\) \((d) \frac{169}{60}\)

(iv) The value of \(\cot ^{2} \theta-\operatorname{cosec}^{2} \theta=\)

(a) -1 (b) 0 (c) 1 (d) 2

(v) The value of \(\sin ^{2} \theta+\cos ^{2} \theta=\)

(a) 0 (b) 1 (c) -1 (d) 2
4)
Ritu's daughter is feeling so hungry and so thought to eat something. She looked into the fridge and found some bread pieces. She decided to make a sandwich. She cut the piece of bread diagonally and found that it forms a
righ.t angled triangle with sides 4 cm, 4\(\sqrt{3}\) cm and 8 cm.

On the basis of above information, answer the following questions.
(i) The value of \(\angle\)M =

(a) 30° (b) 60° (c) 45° (d) None of these

(ii) The value of \(\angle\)K =

(a) 45° (b) 30 ° (c) 60° (d) None of these

(iii) Find the value of tanM.

\((a) \sqrt{3}\) \((b) \frac{1}{\sqrt{3}}\) (c) 1 (d) None of these

(iv) sec²M - 1 =

(a) tanM (b) tan2M (c) tan²M (d) None of these

(v) The value of \(\frac{\tan ^{2} 45^{\circ}-1}{\tan ^{2} 45^{\circ}+1}\) is

(a) 0 (b) 1 (c) 2 (d) -1
5)
Aanya and her father go to meet her friend Juhi for a party. When they reached to [uhi's place, Aanya saw the roof of the house, which is triangular in shape. If she imagined the dimensions of the roof as given in the figure, then answer the following questions.

(i) If D is the mid point of AC, then BD =

(a) 2m (b) 3m (c) 4m (d) 6m

(ii) Measure of \(\angle\)A =

(a) 30° (b) 60° (c) 45° (d) None of these

(iii) Measure of \(\angle\)C =

(a) 30° (b) 60° (c) 45° (d) None of these

(iv) Find the value of sinA + cosC.

(a) 0 (b) 1 (c) \(\frac{1}{2}\) (d) \(\sqrt{2}\)

(v) Find the value of tan²C + tan² A.

(a) 0 (b) 1 (c) 2 (d) \(\frac{1}{2}\)

CBSE 10th Standard Maths Subject Coordinate Geometry Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
Alia and Shagun are friends living on the same street in Patel Nagar. Shaguns house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point 0, i.e., the origin, Alia's house is at A. Shaguns house is at B and library is at C. Based on the above information, answer the following questions.

(i) How far is Alia's house from Shaguns house?

(a) 3 units (b) 4 units (c) 5 units (d) 2 units

(ii) How far is the library from Shaguns house?

(a) 3 units (b) 2 units (c) 5 units (d) 4 units

(iii) How far is the library from Alia's house?

(a) 2 units (b) 3 units (c) 4 units (d) (d) None of these

(iv) Which of the following is true?

(a) ABC forms a scalene triangle (b) ABC forms an isosceles triangle

(c) ABC forms an equilateral triangle (d) None of these

(v) How far is the school from Alia's house than Shaguns house?

(a) \(\sqrt(13)\) units (b) \(\sqrt(5)\) units (c) (\(\sqrt(13)\) + \(\sqrt(5)\) )units (d) (\(\sqrt(13)\) - \(\sqrt(5)\) ) units
2)
Satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is situated at the point of intersection of x and y-axes. If we go 2 em east and 3 em north from the house, then we reach to a Grocery store. If we go 4 em west and 6 em south from the house, then we reach to a Electrician's shop. If we go 6 em east and 8 em south from the house, then we reach to a food cart. If we go 6 em west and 8 em north from the house, then we reach to a bus stand.

Based on the above information, answer the following questions.
(i) The distance between grocery store and food cart is

(a) 12 cm (b) 15 cm (c) 18 cm (d) none of these

(ii) The distance of the bus stand from the house is

(a) 5 cm (b) 10 cm (c) 12 cm (d) 15 cm

(iii) If the grocery store and electrician's shop lie on a line, the ratio of distance of house from grocery store to that from electrician's shop, is

(a) 3.2 (b) 2.3 (c) 1.2 (d) 2.1

(iv) The ratio of distances of house from bus stand to food cart is

(a) 1.2 (b) 2.1 (c) 1.1 (d) none of these

(v) The coordinates of positions of bus stand, grocery store, food cart and electrician's shop form a

(a) rectangle (b) parallelogram (c) square (d) none of these

3)

To raise social awareness about hazards of smoking, a school decided to start 'No smoking' campaign. 10 students are asked to prepare campaign banners in the shape of a triangle. The vertices of one of the triangle are P( -3,4), Q(3, 4) and R(-2, -1).

Based on the above information, answer the following questions.
(i) The coordinates of centroid of \(\Delta\)PQR are

\((a) \left(\frac{2}{3}, \frac{7}{3}\right)^{n}\)

\((b) \left(\frac{1}{3}, \frac{1}{3}\right)\)

\((c) \left(\frac{-2}{3}, \frac{7}{3}\right)\)

\((d) \left(\frac{7}{3}, \frac{2}{3}\right)\)

(ii) If S be the mid-point of line joining P and Q, then coordinates of S are

(a) (4,0)

(b) (2,0)

(c) (0,2)

(d) (0,4)

(iii) If T be the mid-point of line joining Rand Q, then coordinates of T are

\((a) \left(\frac{1}{2}, \frac{1}{2}\right)\)

\((b) \left(\frac{3}{2}, \frac{1}{2}\right)\)

\((c) \left(\frac{1}{2}, \frac{3}{2}\right)\)

(d) none of these

(iv) If Ube the mid-point of line joining Rand P, then coordinates of U are

\((a) \left(-\frac{5}{2}, \frac{3}{2}\right)\)

\((b) \left(\frac{3}{2},-\frac{5}{2}\right)\)

\((c) \left(\frac{3}{2}, \frac{5}{2}\right)\)

\((d) \left(\frac{5}{2}, \frac{3}{2}\right)\)

(v) The coordinates of centroid of \(\Delta\)STU are

\((a) \left(\frac{2}{3}, \frac{7}{3}\right)\)

\((b) \left(\frac{1}{3}, \frac{1}{3}\right)\)

\((c) \left(-\frac{2}{3}, \frac{7}{3}\right)\)

\((d) \left(\frac{7}{3}, \frac{2}{3}\right)\)

4)
There are two routes to travel from source A to destination B by bus. First bus reaches at B via point C and second bus reaches from A to B directly. The position of A, Band C are represented in the following graph:

Based on the above information, answer the following questions.
(i) The distance between A and B is

(a) 13 km (b) 26 km (c) \(\sqrt{13}\)km (d) none of these

(ii) The distance between A and Cis

(a) 5 km (b) 2 km (c) \(\sqrt{5}\)km (d) \(5\sqrt{2}\) km

(iii) If it is assumed that both buses have same speed, then by which bus do you want to travel from A to B?

(a) Firstbus (b) Secondbus (c) Any of them (d) None of these

(iv) If the fare for first bus is Rs10/km, then what will be the fare for total journey by that bus?

(a) Rs 83 (b) Rs 38 (c) Rs 45 (d) none of these

(v) If the fare for second bus is Rs 15/km, then what will be the fare to reach to the destination by this bus?

(a) Rs 105 (b) Rs 108 (c) Rs 110 (d) Rs 115
5)
In an examination hall, students are seated at a distance of 2 m from each other, to maintain the social distance due to CORONA virus pandemic. Let three students sit at points A, Band C whose coordinates are (4, -3), (7,3) and (8, 5) respectively.

Based on the above information, answer the following questions.
(i) The distance between A and C is

(a) \(\sqrt{5}\) units (b) \(4\sqrt{5}\) units (c) \(3\sqrt{5}\) units (d) none of these

(ii) If an invigilator at the point I, lying on the straight line joining Band C such that it divides the distance between them in the ratio of 1 : 2. Then coordinates of I are

\((a) \left(\frac{22}{3}, \frac{11}{3}\right)\) \((b) \left(\frac{23}{3}, \frac{13}{3}\right)\) (c) (6,1) (d) (9,1)

(iii) The mid-point of the line segment joining A and C is

(a) (1.6) (b) (6.1) \(\text { (c) }\left(\frac{11}{2}, 0\right)\) (d) none of these

(iv) The ratio in which B divides the line segment joining A and C is

(a) 2:1 (b) 3:1 (c) 1:2 (d) none of these

(v) The points A, Band C lie on

(a) a straight line (b) an equilateral triangle

(c) a scalene triangle (d) an isosceles triangle

CBSE 10th Standard Maths Subject Coordinate Geometry Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
Alia and Shagun are friends living on the same street in Patel Nagar. Shaguns house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point 0, i.e., the origin, Alia's house is at A. Shaguns house is at B and library is at C. Based on the above information, answer the following questions.

(i) How far is Alia's house from Shaguns house?

(a) 3 units (b) 4 units (c) 5 units (d) 2 units

(ii) How far is the library from Shaguns house?

(a) 3 units (b) 2 units (c) 5 units (d) 4 units

(iii) How far is the library from Alia's house?

(a) 2 units (b) 3 units (c) 4 units (d) (d) None of these

(iv) Which of the following is true?

(a) ABC forms a scalene triangle (b) ABC forms an isosceles triangle

(c) ABC forms an equilateral triangle (d) None of these

(v) How far is the school from Alia's house than Shaguns house?

(a) \(\sqrt(13)\) units (b) \(\sqrt(5)\) units (c) (\(\sqrt(13)\) + \(\sqrt(5)\) )units (d) (\(\sqrt(13)\) - \(\sqrt(5)\) ) units
2)
A person is riding his bike on a straight road towards East from his college to city A and then to city B. At some point in between city A and city B, he suddenly realises that there is not enough petrol for the journey. Also, there is no petrol pump on the road between these two cities.

Based on the above information, answer the following questions.
(i) The value of y is equal to

(a) 2 (b) 3 (c) 4 (d) 5

(ii) The value of x is equal to

(a) 4 (b) 5 (c) 8 (d) 7

(iii) If M is any point exactly in between city A and city B, then coordinates of M are

(a) 3,3 (b) 4,4 (c) 5,5 (d) 6,6

(iv) The ratio in which A divides the line segment joining the points O and M is

(a) 1:2 (b) 2.1 (c) 3.2 (d) 2.3

(v) If the person analyse the petrol at the point M(the mid point of AB), then what should be his decision?

(a) Should he travel back to college (b) Should try his luck to move towards city B

(c) Should be travel back to city A (d) None of these
3)
Satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is situated at the point of intersection of x and y-axes. If we go 2 em east and 3 em north from the house, then we reach to a Grocery store. If we go 4 em west and 6 em south from the house, then we reach to a Electrician's shop. If we go 6 em east and 8 em south from the house, then we reach to a food cart. If we go 6 em west and 8 em north from the house, then we reach to a bus stand.

Based on the above information, answer the following questions.
(i) The distance between grocery store and food cart is

(a) 12 cm (b) 15 cm (c) 18 cm (d) none of these

(ii) The distance of the bus stand from the house is

(a) 5 cm (b) 10 cm (c) 12 cm (d) 15 cm

(iii) If the grocery store and electrician's shop lie on a line, the ratio of distance of house from grocery store to that from electrician's shop, is

(a) 3.2 (b) 2.3 (c) 1.2 (d) 2.1

(iv) The ratio of distances of house from bus stand to food cart is

(a) 1.2 (b) 2.1 (c) 1.1 (d) none of these

(v) The coordinates of positions of bus stand, grocery store, food cart and electrician's shop form a

(a) rectangle (b) parallelogram (c) square (d) none of these
4)
A round clock is traced on a graph paper as shown below. The boundary intersect the coordinate axis at a distance of 4/3 units from origin.

Based on the above information, answer the following questions .
(i) Circle intersect the positive y-axis at

\(A\left(\frac{2}{3}, 0\right),\) \((b) \left(0, \frac{2}{3}\right)\) \((c) \left(0, \frac{4}{3}\right)\) \((d) \left(\frac{4}{3}, 0\right)\)

(ii) The centre of circle is the

(a) mid-point of points of intersection with x-axis (b) mid-point of points of intersection with y-axis

(c) both (a) and (b) (d) none of these

(iii) The radius of the circle is

\((a) \frac{4}{3} units\) \((b) \frac{3}{2} units\) \((c) \frac{2}{3} units\) \((d) \frac{3}{4} units\)

(iv) The area of the circle is

\((a) 16 \pi^{2} sq. units\) \((b) \frac{16}{9} \pi sq. units\) \((c) \frac{4}{9} \pi^{2} sq. units\) \((d) 4 \pi sq. units\)

(v) If \(\left(1, \frac{\sqrt{7}}{3}\right)\) is one of the ends of a diameter, then its other end is

\((a) \left(-1, \frac{\sqrt{7}}{3}\right)\) \((b) \left(1,-\frac{\sqrt{7}}{3}\right)\) \((c) \left(1, \frac{\sqrt{7}}{3}\right)\) \((d) \left(-1,-\frac{\sqrt{7}}{3}\right)\)

5)

To raise social awareness about hazards of smoking, a school decided to start 'No smoking' campaign. 10 students are asked to prepare campaign banners in the shape of a triangle. The vertices of one of the triangle are P( -3,4), Q(3, 4) and R(-2, -1).

Based on the above information, answer the following questions.
(i) The coordinates of centroid of \(\Delta\)PQR are

\((a) \left(\frac{2}{3}, \frac{7}{3}\right)^{n}\)

\((b) \left(\frac{1}{3}, \frac{1}{3}\right)\)

\((c) \left(\frac{-2}{3}, \frac{7}{3}\right)\)

\((d) \left(\frac{7}{3}, \frac{2}{3}\right)\)

(ii) If S be the mid-point of line joining P and Q, then coordinates of S are

(a) (4,0)

(b) (2,0)

(c) (0,2)

(d) (0,4)

(iii) If T be the mid-point of line joining Rand Q, then coordinates of T are

\((a) \left(\frac{1}{2}, \frac{1}{2}\right)\)

\((b) \left(\frac{3}{2}, \frac{1}{2}\right)\)

\((c) \left(\frac{1}{2}, \frac{3}{2}\right)\)

(d) none of these

(iv) If Ube the mid-point of line joining Rand P, then coordinates of U are

\((a) \left(-\frac{5}{2}, \frac{3}{2}\right)\)

\((b) \left(\frac{3}{2},-\frac{5}{2}\right)\)

\((c) \left(\frac{3}{2}, \frac{5}{2}\right)\)

\((d) \left(\frac{5}{2}, \frac{3}{2}\right)\)

(v) The coordinates of centroid of \(\Delta\)STU are

\((a) \left(\frac{2}{3}, \frac{7}{3}\right)\)

\((b) \left(\frac{1}{3}, \frac{1}{3}\right)\)

\((c) \left(-\frac{2}{3}, \frac{7}{3}\right)\)

\((d) \left(\frac{7}{3}, \frac{2}{3}\right)\)

CBSE 10th Standard Maths Subject Triangles Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
An aeroplane leaves an airport and flies due north at a speed of 1200km /hr. At the same time, another aeroplane leaves the same station and flies due west at the speed of 1500 km/hr as shown below. After \(1 \frac{1}{2}\) hr both the aeroplanes reaches at point P and Q respectively.

(i) Distance travelled by aeroplane towards north after \(1 \frac{1}{2}\) hr is

(a) 1800 km (b) 1500 km (c) 1400km (d) 1350 km

(ii) Distance travelled by aeroplane towards west after \(1 \frac{1}{2}\) hr is

(a) 1600 km (b) 1800 km (c) 2250km (d) 2400 km

(iii) In the given figure,\(\angle\)POQ is

(a) 70° (b) 90° (c) 80° (d) 100°

(iv) Distance between aeroplanes after \(1 \frac{1}{2}\) hr is

\((a) 450 \sqrt{41} \mathrm{~km}\) \((b) 350 \sqrt{31} \mathrm{~km}\) \((c) 125 \sqrt{12} \mathrm{~km}\) \((d) 472 \sqrt{41} \mathrm{~km}\)

(v) Area of \(\Delta\)POQ is

(a) 185000km² (b) 179000km²

(c) 186000km² (d) 2025000 km²
2)
Meenal was trying to find the height of tower near his house. She is using the properties of similar triangles. The height of Meenal's house is 20 m. When Meenal's house casts a shadow of 10m long on the ground, at the same time, tower casts a shadow of 50 m long and Arun's house casts a shadow of 20 m long on the ground as shown below.

Based on the above information, answer the following questions.
(i) What is the height of tower?

(a) 100 m (b) 50 m (c) 15 m (d) 45 m

(ii) What will be the length of shadow of tower when Meenal's house casts a shadow of 15 m?

(a) 45 m (b) 70 m (c) 75 m (d) 72 m

(iii) Height of Aruns house is

(a) 80 m (b) 75 m (c) 60 m (d) 40 m

(iv) If tower casts a shadow of 40 rn, then find the length of shadow of Arun's house

(a) 18 m (b) 17 m (c) 16 m (d) 14 m

(v) If tower casts a shadow of 40 m, then what will be the length of shadow of Meenal's house?

(a) 7 m (b) 9 m (c) 4 m (d) 8 m
3)
Minister of a state went to city Q from city P. There is a route via city R such that PR \(\perp\)RQ. PR = 2x km and RQ = 2(x + 7) km. He noticed that there is a proposal to construct a 26 km highway which directly connects the two cities P and Q.

Based on the above information, answer the following questions.
(i) Which concept can be used to get the value of x?

(a) Thales theorem (b) Pythagoras theorem

(c) Converse ofthales theorem (d) Converse of Pythagoras theorem

(ii) The value of x is

(a) 4 (b) 6 (c) 5 (d) 8

(iii) The value of PR is

(a) 10 km (b) 20 km (c) 15 km (d) 25 km

(iv) The value of RQ is

(a) 12 km (b) 24 km (c) 16 km (d) 20 km

(v) How much distance will be saved in reaching city Q after the construction of highway?

(a) 10 km (b) 9 km (c) 4 km (d) 8 km
4)
Class teacher draw the shape of quadrilateral on board. Ankit observed the shape and explored on his notebook in different ways as shown below.

Based on the above information, answer the following questions.
(i) In if ABCD is a trapezium with AB || CD, E and F are points on non-parallel sides AD and BC respectively such that EF || AB, then \(\frac{A E}{E D}=\)

(a) \(\frac{B E}{C D}\) (b) \(\frac{A B}{C D}\) (c) \(\frac{B F}{F C}\) (d) None of these

(ii) In if AB || CD, and DO = 3x - 19, OB = x - 5, OC = x - 3 and AO = 3, then the value of x can be

(a) 5 or 8 (b) 8 or 9 (c) 10 or 12 (d) 13 or 14

(iii) In if OD = 3x - 1, OB = 5x - 3, OC = 2x + 1 and AO = 6x - 5, then the value of x is

(a) 0 (b) 1 (c) 2 (d) 3

(iv) In \(\Delta\) ABC, if PQ || BC and AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, then AB + PQ is equal to

(a) 7.2 cm (b) 5.9 cm (c) 2.6 cm (d) 8.4 cm

(v) In \(\Delta\)DEF, if RS || EF, DR = 4x - 3, DS = 8x - 7, ER = 3x - 1 and FS = 5x - 3, then the value of x is

(a) 1 (b) 5.9 cm (c) 2.6 cm (d) 8.4 cm
5)
Two hotels are at the ground level on either side of a mountain. On moving a certain distance towards the top of the mountain two huts are situated as shown in the figure. The ratio between the distance from hotel B to hut-2 and that ofhut-2 to mountain top is 3: 7.

Based on the above information, answer the following questions.
(i) What is the ratio of the perimeters of the triangle formed by both hotels and mountain top to the triangle formed by both huts and mountain top?

(a) 5: 2 (b) 10: 7 (c) 7: 3 (d) 3: 10

(ii) The distance between the hotel A and hut-I is

(a) 2.5 miles (b) 29 miles (c) 4.29 miles (d) 1.5 miles

(iii) If the horizontal distance between the hut -1 and hut -2 is 8 miles, then the distance between the two hotels is

(a) 2.4 miles (b) 11.43 miles (c) 9 miles (d) 7 miles

(iv) If the distance from mountain top to hut-1 is 5 miles more than that of distance from hotel B to mountain top, then what is the distance between hut-2 and mountain top?

(a) 3.5 miles (b) 6 miles (c) 5.5 miles (d) 4 miles

(v) What is the ratio of areas of two parts formed in the complete figure?

(a) 53: 21 (b) 10: 41 (c) 51: 33 (d) 49:51

CBSE 10th Standard Maths Subject Triangles Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
In a classroom, students were playing with some pieces of cardboard as shown below.

All of a sudden, teacher entered into classroom. She told students to arrange all pieces. On seeing this beautiful image, she observed that \(\Delta\) ADH is right angled triangle, which contains.

(i) right triangles ABJ and IGH.
(ii) quadrilateral GFJI
(iii) squares JKLM and LCBK
(iv) rectangles MLEF and LCDE.
After observation, she ask certain questions to students. Help them to answer these questions.
(i) If an insect (small ant) walks 24 m from H to F, then walks 6 m to reach at M, then walks 4 m to reach at L and finally crossing K, reached at J. Find the distance between initial and final position of insect.

(a) 25m (b) 26m (c) 27m (d) 28m

(ii) If m, n and r are the sides of right triangle ABJ, then which of the following can be correct?

(a) m²+n²= r² (b) m²+n²+r²-=0

(c) m² + n² = 2r² (d) none of these

(iii) If \(\Delta\)ABJ ~ \(\Delta\)ADH, then which similarity criterion is used here?

(a) AA (b) SAS (c) AAS (d) SSS

(iv) If \(\angle\)ABJ = 90° and B, J are mid points of sides AD and AH respectively and BJ || DH, then which of the following option is false?

\((a) \triangle A B J \sim \triangle A D H\) \((b) 2 B J=D H\) \((c) A J^{2}=J B^{2}+A B^{2}\) \((d) \frac{A B}{B D}=\frac{A J}{A H}\)

(v) If \(\Delta\)PQR is right triangle with QM \(\perp\) PR, then which of the following is not correct?

\((a) \Delta P M Q \sim \Delta P Q R\)

\((b) Q R^{2}=P R^{2}-P Q^{2}\)

\((c) P R^{2}=P Q+Q R\)

\((d) \Delta P M Q \sim \Delta Q M R\)
2)
An aeroplane leaves an airport and flies due north at a speed of 1200km /hr. At the same time, another aeroplane leaves the same station and flies due west at the speed of 1500 km/hr as shown below. After \(1 \frac{1}{2}\) hr both the aeroplanes reaches at point P and Q respectively.

(i) Distance travelled by aeroplane towards north after \(1 \frac{1}{2}\) hr is

(a) 1800 km (b) 1500 km (c) 1400km (d) 1350 km

(ii) Distance travelled by aeroplane towards west after \(1 \frac{1}{2}\) hr is

(a) 1600 km (b) 1800 km (c) 2250km (d) 2400 km

(iii) In the given figure,\(\angle\)POQ is

(a) 70° (b) 90° (c) 80° (d) 100°

(iv) Distance between aeroplanes after \(1 \frac{1}{2}\) hr is

\((a) 450 \sqrt{41} \mathrm{~km}\) \((b) 350 \sqrt{31} \mathrm{~km}\) \((c) 125 \sqrt{12} \mathrm{~km}\) \((d) 472 \sqrt{41} \mathrm{~km}\)

(v) Area of \(\Delta\)POQ is

(a) 185000km² (b) 179000km²

(c) 186000km² (d) 2025000 km²
3)
Meenal was trying to find the height of tower near his house. She is using the properties of similar triangles. The height of Meenal's house is 20 m. When Meenal's house casts a shadow of 10m long on the ground, at the same time, tower casts a shadow of 50 m long and Arun's house casts a shadow of 20 m long on the ground as shown below.

Based on the above information, answer the following questions.
(i) What is the height of tower?

(a) 100 m (b) 50 m (c) 15 m (d) 45 m

(ii) What will be the length of shadow of tower when Meenal's house casts a shadow of 15 m?

(a) 45 m (b) 70 m (c) 75 m (d) 72 m

(iii) Height of Aruns house is

(a) 80 m (b) 75 m (c) 60 m (d) 40 m

(iv) If tower casts a shadow of 40 rn, then find the length of shadow of Arun's house

(a) 18 m (b) 17 m (c) 16 m (d) 14 m

(v) If tower casts a shadow of 40 m, then what will be the length of shadow of Meenal's house?

(a) 7 m (b) 9 m (c) 4 m (d) 8 m
4)
Minister of a state went to city Q from city P. There is a route via city R such that PR \(\perp\)RQ. PR = 2x km and RQ = 2(x + 7) km. He noticed that there is a proposal to construct a 26 km highway which directly connects the two cities P and Q.

Based on the above information, answer the following questions.
(i) Which concept can be used to get the value of x?

(a) Thales theorem (b) Pythagoras theorem

(c) Converse ofthales theorem (d) Converse of Pythagoras theorem

(ii) The value of x is

(a) 4 (b) 6 (c) 5 (d) 8

(iii) The value of PR is

(a) 10 km (b) 20 km (c) 15 km (d) 25 km

(iv) The value of RQ is

(a) 12 km (b) 24 km (c) 16 km (d) 20 km

(v) How much distance will be saved in reaching city Q after the construction of highway?

(a) 10 km (b) 9 km (c) 4 km (d) 8 km
5)
Class teacher draw the shape of quadrilateral on board. Ankit observed the shape and explored on his notebook in different ways as shown below.

Based on the above information, answer the following questions.
(i) In if ABCD is a trapezium with AB || CD, E and F are points on non-parallel sides AD and BC respectively such that EF || AB, then \(\frac{A E}{E D}=\)

(a) \(\frac{B E}{C D}\) (b) \(\frac{A B}{C D}\) (c) \(\frac{B F}{F C}\) (d) None of these

(ii) In if AB || CD, and DO = 3x - 19, OB = x - 5, OC = x - 3 and AO = 3, then the value of x can be

(a) 5 or 8 (b) 8 or 9 (c) 10 or 12 (d) 13 or 14

(iii) In if OD = 3x - 1, OB = 5x - 3, OC = 2x + 1 and AO = 6x - 5, then the value of x is

(a) 0 (b) 1 (c) 2 (d) 3

(iv) In \(\Delta\) ABC, if PQ || BC and AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, then AB + PQ is equal to

(a) 7.2 cm (b) 5.9 cm (c) 2.6 cm (d) 8.4 cm

(v) In \(\Delta\)DEF, if RS || EF, DR = 4x - 3, DS = 8x - 7, ER = 3x - 1 and FS = 5x - 3, then the value of x is

(a) 1 (b) 5.9 cm (c) 2.6 cm (d) 8.4 cm

CBSE 10th Standard Maths Subject Arithmetic Progressions Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
In a class the teacher asks every student to write an example of A.P. Two friends Geeta and Madhuri writes their progressions as -5, -2, 1,4, ... and 187, 184, 181, .... respectively. Now, the teacher asks various students of the class the following questions on these two progressions. Help students to find the answers of the questions.

(i) Find the 34^th term of the progression written by Madhuri.

(a) 286 (b) 88 (c) -99 (d) 190

(ii) Find the sum of common difference of the two progressions.

(a) 6 (b) -6 (c) 1 (d) 0

(iii) Find the 19^th term of the progression written by Geeta.

(a) 49 (b) 59 (c) 52 (d) 62

(iv) Find the sum of first 10 terms of the progression written by Geeta.

(a) 85 (b) 95 (c) 110 (d) 200

(v) Which term of the two progressions will have the same value?

(a) 31 (b) 33 (c) 32 (d) 30
2)
Anuj gets pocket money from his father everyday. Out of the pocket money, he saves Rs 2.75 on first day, Rs 3 on second day, Rs 3.25 on third day and so on.
On the basis of above information, answer the following questions .

(i) What is the amount saved by Anuj on 14^th day?

(a) Rs 6.25 (b) Rs 6 (c) Rs 6.50 (d) Rs 6.75

(ii) What is the total amount saved by Anuj in 8 days?

(a) Rs 18 (b) Rs 33 (c) Rs 24 (d) Rs 29

(iii) What is the amount saved by Anuj on 30^th day?

(a) Rs 10 (b) Rs 12.75 (c) Rs 10.25 (d) Rs 9.75

(iv) What is the total amount saved by him in the month of June, if he starts savings from 1^st June?

(a) Rs 191 (b) Rs 191.25 (c) Rs 192 (d) Rs 192.5

(v) On which day, he save tens times as much as he saved on day-I?

(a) 9^th (b) 99^th (c) 10^th (d) 100^th
3)
Amit was playing a number card game. In the game, some number cards (having both +ve or -ve numbers) are arranged in a row such that they are following an arithmetic progression. On his first turn, Amit picks up 6^th and 14^thcard and finds their sum to be -76. On the second turn he picks up 8^th and 16^thcard and finds their sum to be -96. Based on the above information, answer the following questions.

(i) What is the difference between the numbers on any two consecutive cards?

(a) 7 (b) -5 (c) 11 (d) -3

(ii) The number on first card is

(a) 12 (b) 3 (c) 5 (d) 7

(iii) What is the number on the 19^th card?

(a) -88 (b) -82 (c) -92 (d) -102

(iv) What is the number on the 23^rdcard?

(a) -103 (b) -122 (c) -108 (d) -117

(v) The sum of numbers on the first 15 cards is

(a) -840 (b) -945 (c) -427 (d) -420

4)

A sequence is an ordered list of numbers. A sequence of numbers such that the difference between the consecutive terms is constant is said to be an arithmetic progression (A.P.).
On the basis of above information, answer the following questions.
(i) Which of the following sequence is an A.P.?

(a) 10,24,39,52,....

(b) 11,24,39,52, ...

(c) 10,24,38,52, ...

(d) 10, 38, 52, 66, ....

(ii) If x, y and z are in A.P., then

(a) x + z = y

(b) x - z = y

(c) x + z = 2y

(d) None of these

(iii) If a₁ a₂, a₃ ..... , a_n are in A.P., then which of the following is true?

(a) a₁ + k, a₂ + k, a₃ + k, , a_n + k are in A.P., where k is a constant.

(b) k - a₁ k - a₂, k - a₃, , k - a_n are in A.P., where k is a constant.

(c) ka₁, ka₂, ka₃ ..... , ka_n are in A.P., where k is a constant.

(d) All of these

(iv) If the n^th term (n > 1) of an A.P. is smaller than the first term, then nature of its common difference (d) is

(a) d > 0	(b) d < 0
(c) d = 0	(d) Can't be determined

(v) Which of the following is incorrect about A.P.?

(a) All the terms of constant A.P. are same.

(b) Some terms of an A.P. can be negative.

(c) All the terms of an A.P. can never be negative.

(d) None of these

5)
Jack is much worried about his upcoming assessment on A.P. He was vigorously practicing for the exam but unable to solve some questions. One of these questions is as shown below. If the 3^rd and the 9^th terms of an A.P. are 4 and - 8 respectively, then help Jack in solving the problem.

(i) What is the common difference?

(a) 2 (b) -1 (c) -2 (d) 4

(ii) What is the first term?

(a) 6 (b) 2 (c) -2 (d) 8

(iii) Which term of the A.P. is -160?

(a) 80^th (b) 85^th (c) 81^th (d) 84^th

(iv) Which of the following is not a term of the given A.P.?

(a) -123 (b) -100 (c) 0 (d) -200

(v) What is the 75^th term of the A.P.?

(a) -140 (b) -102 (c) -150 (d) -158

CBSE 10th Standard Maths Subject Arithmetic Progressions Case Study Questions 2021 - by QB365 - Question Bank Software - May 22, 2021 - View & Read

1)
In a pathology lab, a culture test has been conducted. In the test, the number of bacteria taken into consideration in various samples is all3-digit numbers that are divisible by 7, taken in order.

On the basis of above information, answer the following questions.
(i) How many bacteria are considered in the fifth sample?

(a) 126 (b) 140 (c) 133 (d) 149

(ii) How many samples should be taken into consideration?

(a) 129 (b) 128 (c) 130 (d) 127

(iii) Find the total number of bacteria in the first 10 samples.

(a) 1365 (b) 1335 (c) 1302 (d) 1540

(iv) How many bacteria are there in the 7^th sample from the last?

(a) 952 (b) 945 (c) 959 (d) 966

(v) The number of bacteria in 50^th sample is

(a) 546 (b) 553 (c) 448 (d) 496
2)
In a class the teacher asks every student to write an example of A.P. Two friends Geeta and Madhuri writes their progressions as -5, -2, 1,4, ... and 187, 184, 181, .... respectively. Now, the teacher asks various students of the class the following questions on these two progressions. Help students to find the answers of the questions.

(i) Find the 34^th term of the progression written by Madhuri.

(a) 286 (b) 88 (c) -99 (d) 190

(ii) Find the sum of common difference of the two progressions.

(a) 6 (b) -6 (c) 1 (d) 0

(iii) Find the 19^th term of the progression written by Geeta.

(a) 49 (b) 59 (c) 52 (d) 62

(iv) Find the sum of first 10 terms of the progression written by Geeta.

(a) 85 (b) 95 (c) 110 (d) 200

(v) Which term of the two progressions will have the same value?

(a) 31 (b) 33 (c) 32 (d) 30
3)
Anuj gets pocket money from his father everyday. Out of the pocket money, he saves Rs 2.75 on first day, Rs 3 on second day, Rs 3.25 on third day and so on.
On the basis of above information, answer the following questions .

(i) What is the amount saved by Anuj on 14^th day?

(a) Rs 6.25 (b) Rs 6 (c) Rs 6.50 (d) Rs 6.75

(ii) What is the total amount saved by Anuj in 8 days?

(a) Rs 18 (b) Rs 33 (c) Rs 24 (d) Rs 29

(iii) What is the amount saved by Anuj on 30^th day?

(a) Rs 10 (b) Rs 12.75 (c) Rs 10.25 (d) Rs 9.75

(iv) What is the total amount saved by him in the month of June, if he starts savings from 1^st June?

(a) Rs 191 (b) Rs 191.25 (c) Rs 192 (d) Rs 192.5

(v) On which day, he save tens times as much as he saved on day-I?

(a) 9^th (b) 99^th (c) 10^th (d) 100^th
4)
Amit was playing a number card game. In the game, some number cards (having both +ve or -ve numbers) are arranged in a row such that they are following an arithmetic progression. On his first turn, Amit picks up 6^th and 14^thcard and finds their sum to be -76. On the second turn he picks up 8^th and 16^thcard and finds their sum to be -96. Based on the above information, answer the following questions.

(i) What is the difference between the numbers on any two consecutive cards?

(a) 7 (b) -5 (c) 11 (d) -3

(ii) The number on first card is

(a) 12 (b) 3 (c) 5 (d) 7

(iii) What is the number on the 19^th card?

(a) -88 (b) -82 (c) -92 (d) -102

(iv) What is the number on the 23^rdcard?

(a) -103 (b) -122 (c) -108 (d) -117

(v) The sum of numbers on the first 15 cards is

(a) -840 (b) -945 (c) -427 (d) -420

5)

A sequence is an ordered list of numbers. A sequence of numbers such that the difference between the consecutive terms is constant is said to be an arithmetic progression (A.P.).
On the basis of above information, answer the following questions.
(i) Which of the following sequence is an A.P.?

(a) 10,24,39,52,....

(b) 11,24,39,52, ...

(c) 10,24,38,52, ...

(d) 10, 38, 52, 66, ....

(ii) If x, y and z are in A.P., then

(a) x + z = y

(b) x - z = y

(c) x + z = 2y

(d) None of these

(iii) If a₁ a₂, a₃ ..... , a_n are in A.P., then which of the following is true?

(a) a₁ + k, a₂ + k, a₃ + k, , a_n + k are in A.P., where k is a constant.

(b) k - a₁ k - a₂, k - a₃, , k - a_n are in A.P., where k is a constant.

(c) ka₁, ka₂, ka₃ ..... , ka_n are in A.P., where k is a constant.

(d) All of these

(iv) If the n^th term (n > 1) of an A.P. is smaller than the first term, then nature of its common difference (d) is

(a) d > 0	(b) d < 0
(c) d = 0	(d) Can't be determined

(v) Which of the following is incorrect about A.P.?

(a) All the terms of constant A.P. are same.

(b) Some terms of an A.P. can be negative.

(c) All the terms of an A.P. can never be negative.

(d) None of these

CBSE 10th Standard Maths Subject Quadratic Equations Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
A quadratic equation can be defined as an equation of degree 2. This means that the highest exponent of the polynomial in it is 2. The standard form of a quadratic equation is ax²+ bx + c = 0, where a, b, and c are real numbers and \(a \neq 0\) Every quadratic equation has two roots depending on the nature of its discriminant, D = b2 - 4ac.Based on the above information, answer the following questions.
(i) Which of the following quadratic equation have no real roots?

\((a) -4 x^{2}+7 x-4=0\) \((b) -4 x^{2}+7 x-2=0\)

\((c) -2 x^{2}+5 x-2=0\) \((d) 3 x^{2}+6 x+2=0\)

(ii) Which of the following quadratic equation have rational roots?

\((a) x^{2}+x-1=0\) \((b) x^{2}-5 x+6=0\)

\((c) 4 x^{2}-3 x-2=0\) \((d) 6 x^{2}-x+11=0\)

(iii) Which of the following quadratic equation have irrational roots?

\((a) 3 x^{2}+2 x+2=0\) \((b) 4 x^{2}-7 x+3=0\)

\((c) 6 x^{2}-3 x-5=0\) \((d) 2 x^{2}+3 x-2=0\)

(iv) Which of the following quadratic equations have equal roots?

\((a) x^{2}-3 x+4=0\) \((b) 2 x^{2}-2 x+1=0\)

\((c) 5 x^{2}-10 x+1=0\) \((d) 9 x^{2}+6 x+1=0\)

(v) Which of the following quadratic equations has two distinct real roots?

\((a) x^{2}+3 x+1=0\) \((b) -x^{2}+3 x-3=0\)

\((c) 4 x^{2}+8 x+4=0\) \((d) 3 x^{2}+6 x+4=0\)
2)
In our daily life we use quadratic formula as for calculating areas, determining a product's profit or formulating the speed of an object and many more.
Based on the above information, answer the following questions.
(i) If the roots of the quadratic equation are 2, -3, then its equation is

(a) x² - 2x + 3 = 0 (b) x²+ x - 6 = 0 (c) 2x² - 3x + 1 = 0 (d) x² - 6x - 1= 0

(ii) If one root of the quadratic equation 2x² + kx + 1 = 0 is -1/2, then k =

(a) 3 (b) -5 (c) -3 (d) 5

(iii) Which of the following quadratic equations, has equal and opposite roots?

(a) x²- 4=0 (b) 16x²- 9=0 (c) 3x²+ 5x - 5=0 (d) Both (a) and (b)

(iv) Which of the following quadratic equations can be represented as (x - 2)² + 19 = 0?

(a) x²+ 4x+15=0 (b) x²- 4x+15=0 (c) x² - 4x+23=0 (d) x² + 4x+23=0

(v) If one root of a qua drraattiic equation is \(\frac{1+\sqrt{5}}{7}\),then I.ts other root is

\((a) \frac{1+\sqrt{5}}{7}\) \((b) \frac{1-\sqrt{5}}{7}\) \((c) \frac{-1+\sqrt{5}}{7}\) \((d) \frac{-1-\sqrt{5}}{7}\)
3)
Quadratic equations started around 3000 B.C. with the Babylonians. They were one of the world's first civilisation, and came up with some great ideas like agriculture, irrigation and writing. There were many reasons why Babylonians needed to solve quadratic equations. For example to know what amount of crop you can grow on the square field;
Based on the above information, represent the following questions in the form of quadratic equation.
(i) The sum of squares of two consecutive integers is 650.

(a) x² + 2x - 650=0 (b) 2x² + 2x - 649=0 (c) x² - 2x - 650=0 (d) 2x² + 6x - 550=0

(ii) The sum of two numbers is 15 and the sum of their reciprocals is 3/10.

(a) x²+ 10x-150=0 (b) 15x²-x + 150=0 (c) x²-15x + 50=0 (d) 3x² - 10x + 15 = 0

(iii) Two numbers differ by 3 and their product is 504.

(a) 3x²- 504=0 (b) x²- 504x+3=0 (c) 504x²+3=x (d) x² + 3x - 504 = 0

(iv) A natural number whose square diminished by 84 is thrice of 8 more of given number.

(a) x² + 8x-84=0 (b) 3x² - 84x+3=0 (c) x² -3x-108=0 (d) x² -11x+60=0

(v) A natural number when increased by 12, equals 160 times its reciprocal.

(a) x² - 12x + 160 = 0 (b) x² - 160x + 12 = 0 (c) 12x² - x - 160 = 0 (d) x² + 12x - 160 = 0
4)
Amit is preparing for his upcoming semester exam. For this, he has to practice the chapter of Quadratic Equations. So he started with factorization method. Let two linear factors of \(a x^{2}+b x+c \text { be }(p x+q) \text { and }(r x+s)\)
\(\therefore a x^{2}+b x+c=(p x+q)(r x+s)=p r x^{2}+(p s+q r) x+q s .\)
Now, factorize each of the following quadratic equations and find the roots.
(i) 6x² + x - 2 = 0

\((a) 1,6\) \((b) \frac{1}{2}, \frac{-2}{3}\) \((c) \frac{1}{3}, \frac{-1}{2}\) \((d) \frac{3}{2},-2\)

(ii) 2x²-+ x - 300 = 0

\((a) 30, \frac{2}{15}\) \((b) 60, \frac{-2}{5}\) \((c) 12, \frac{-25}{2}\) (d) None of these

(iii) x²- 8x + 16 = 0

(a) 3,3 (b) 3,-3 (c) 4,-4 (d) 4,4

(iv) 6x²- 13x + 5 = 0

\((a) 2, \frac{3}{5}\) \((b) -2, \frac{-5}{3}\) \((c) \frac{1}{2}, \frac{-3}{5}\) \((d) \frac{1}{2}, \frac{5}{3}\)

(v) 100x²- 20x + 1 = 0

\((a) \frac{1}{10}, \frac{1}{10}\) \((b) -10,-10\) \((c) -10, \frac{1}{10}\) \((d) \frac{-1}{10}, \frac{-1}{10}\)

5)

If p(x) is a quadratic polynomial i.e., p(x) = ax²- + bx + c, \(a \neq 0\), then p(x) = 0 is called a quadratic equation. Now, answer the following questions.
(i) Which of the following is correct about the quadratic equation ax²- + bx + c = 0 ?

(a) a, band c are real numbers, \(c \neq 0\)	(b) a, band c are rational numbers, \(a \neq 0\)
(c) a, band c are integers, a, band \(c \neq 0\)	(d) a, band c are real numbers, \(a \neq 0\)

(ii) The degree of a quadratic equation is

(a) 1

(b) 2

(c) 3

(d) other than 1

(iii) Which of the following is a quadratic equation?

(a) x(x + 3) + 7 = 5x - 11	(b) (x - 1)² - 9 = (x - 4)(x + 3)
(c) x²-(2x + 1) - 4 = 5x²- 10	(d) x(x - 1)(x + 7) = x(6x - 9)

(iv) Which of the following is incorrect about the quadratic equation ax²- + bx + c = 0 ?

(a) If a\(\alpha\)2 + b\(\alpha\). + c = 0, then x = -\(\alpha\) is the solution of the given quadratic equation.

(b)The additive inverse of zeroes of the polynomial ax²- + bx + c is the roots of the given equation.

(c) If a is a root of the given quadratic equation, then its other root is -\(\alpha\).

(d) All of these

(v) Which of the following is not a method of finding solutions of the given quadratic equation?

(a) Factorisation method	(b) Completing the square method
(c) Formula method	(d) None of these

CBSE 10th Standard Maths Subject Quadratic Equations Case Study Questions 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
A quadratic equation can be defined as an equation of degree 2. This means that the highest exponent of the polynomial in it is 2. The standard form of a quadratic equation is ax²+ bx + c = 0, where a, b, and c are real numbers and \(a \neq 0\) Every quadratic equation has two roots depending on the nature of its discriminant, D = b2 - 4ac.Based on the above information, answer the following questions.
(i) Which of the following quadratic equation have no real roots?

\((a) -4 x^{2}+7 x-4=0\) \((b) -4 x^{2}+7 x-2=0\)

\((c) -2 x^{2}+5 x-2=0\) \((d) 3 x^{2}+6 x+2=0\)

(ii) Which of the following quadratic equation have rational roots?

\((a) x^{2}+x-1=0\) \((b) x^{2}-5 x+6=0\)

\((c) 4 x^{2}-3 x-2=0\) \((d) 6 x^{2}-x+11=0\)

(iii) Which of the following quadratic equation have irrational roots?

\((a) 3 x^{2}+2 x+2=0\) \((b) 4 x^{2}-7 x+3=0\)

\((c) 6 x^{2}-3 x-5=0\) \((d) 2 x^{2}+3 x-2=0\)

(iv) Which of the following quadratic equations have equal roots?

\((a) x^{2}-3 x+4=0\) \((b) 2 x^{2}-2 x+1=0\)

\((c) 5 x^{2}-10 x+1=0\) \((d) 9 x^{2}+6 x+1=0\)

(v) Which of the following quadratic equations has two distinct real roots?

\((a) x^{2}+3 x+1=0\) \((b) -x^{2}+3 x-3=0\)

\((c) 4 x^{2}+8 x+4=0\) \((d) 3 x^{2}+6 x+4=0\)
2)
In our daily life we use quadratic formula as for calculating areas, determining a product's profit or formulating the speed of an object and many more.
Based on the above information, answer the following questions.
(i) If the roots of the quadratic equation are 2, -3, then its equation is

(a) x² - 2x + 3 = 0 (b) x²+ x - 6 = 0 (c) 2x² - 3x + 1 = 0 (d) x² - 6x - 1= 0

(ii) If one root of the quadratic equation 2x² + kx + 1 = 0 is -1/2, then k =

(a) 3 (b) -5 (c) -3 (d) 5

(iii) Which of the following quadratic equations, has equal and opposite roots?

(a) x²- 4=0 (b) 16x²- 9=0 (c) 3x²+ 5x - 5=0 (d) Both (a) and (b)

(iv) Which of the following quadratic equations can be represented as (x - 2)² + 19 = 0?

(a) x²+ 4x+15=0 (b) x²- 4x+15=0 (c) x² - 4x+23=0 (d) x² + 4x+23=0

(v) If one root of a qua drraattiic equation is \(\frac{1+\sqrt{5}}{7}\),then I.ts other root is

\((a) \frac{1+\sqrt{5}}{7}\) \((b) \frac{1-\sqrt{5}}{7}\) \((c) \frac{-1+\sqrt{5}}{7}\) \((d) \frac{-1-\sqrt{5}}{7}\)
3)
Quadratic equations started around 3000 B.C. with the Babylonians. They were one of the world's first civilisation, and came up with some great ideas like agriculture, irrigation and writing. There were many reasons why Babylonians needed to solve quadratic equations. For example to know what amount of crop you can grow on the square field;
Based on the above information, represent the following questions in the form of quadratic equation.
(i) The sum of squares of two consecutive integers is 650.

(a) x² + 2x - 650=0 (b) 2x² + 2x - 649=0 (c) x² - 2x - 650=0 (d) 2x² + 6x - 550=0

(ii) The sum of two numbers is 15 and the sum of their reciprocals is 3/10.

(a) x²+ 10x-150=0 (b) 15x²-x + 150=0 (c) x²-15x + 50=0 (d) 3x² - 10x + 15 = 0

(iii) Two numbers differ by 3 and their product is 504.

(a) 3x²- 504=0 (b) x²- 504x+3=0 (c) 504x²+3=x (d) x² + 3x - 504 = 0

(iv) A natural number whose square diminished by 84 is thrice of 8 more of given number.

(a) x² + 8x-84=0 (b) 3x² - 84x+3=0 (c) x² -3x-108=0 (d) x² -11x+60=0

(v) A natural number when increased by 12, equals 160 times its reciprocal.

(a) x² - 12x + 160 = 0 (b) x² - 160x + 12 = 0 (c) 12x² - x - 160 = 0 (d) x² + 12x - 160 = 0
4)
Amit is preparing for his upcoming semester exam. For this, he has to practice the chapter of Quadratic Equations. So he started with factorization method. Let two linear factors of \(a x^{2}+b x+c \text { be }(p x+q) \text { and }(r x+s)\)
\(\therefore a x^{2}+b x+c=(p x+q)(r x+s)=p r x^{2}+(p s+q r) x+q s .\)
Now, factorize each of the following quadratic equations and find the roots.
(i) 6x² + x - 2 = 0

\((a) 1,6\) \((b) \frac{1}{2}, \frac{-2}{3}\) \((c) \frac{1}{3}, \frac{-1}{2}\) \((d) \frac{3}{2},-2\)

(ii) 2x²-+ x - 300 = 0

\((a) 30, \frac{2}{15}\) \((b) 60, \frac{-2}{5}\) \((c) 12, \frac{-25}{2}\) (d) None of these

(iii) x²- 8x + 16 = 0

(a) 3,3 (b) 3,-3 (c) 4,-4 (d) 4,4

(iv) 6x²- 13x + 5 = 0

\((a) 2, \frac{3}{5}\) \((b) -2, \frac{-5}{3}\) \((c) \frac{1}{2}, \frac{-3}{5}\) \((d) \frac{1}{2}, \frac{5}{3}\)

(v) 100x²- 20x + 1 = 0

\((a) \frac{1}{10}, \frac{1}{10}\) \((b) -10,-10\) \((c) -10, \frac{1}{10}\) \((d) \frac{-1}{10}, \frac{-1}{10}\)

5)

If p(x) is a quadratic polynomial i.e., p(x) = ax²- + bx + c, \(a \neq 0\), then p(x) = 0 is called a quadratic equation. Now, answer the following questions.
(i) Which of the following is correct about the quadratic equation ax²- + bx + c = 0 ?

(a) a, band c are real numbers, \(c \neq 0\)	(b) a, band c are rational numbers, \(a \neq 0\)
(c) a, band c are integers, a, band \(c \neq 0\)	(d) a, band c are real numbers, \(a \neq 0\)

(ii) The degree of a quadratic equation is

(a) 1

(b) 2

(c) 3

(d) other than 1

(iii) Which of the following is a quadratic equation?

(a) x(x + 3) + 7 = 5x - 11	(b) (x - 1)² - 9 = (x - 4)(x + 3)
(c) x²-(2x + 1) - 4 = 5x²- 10	(d) x(x - 1)(x + 7) = x(6x - 9)

(iv) Which of the following is incorrect about the quadratic equation ax²- + bx + c = 0 ?

(a) If a\(\alpha\)2 + b\(\alpha\). + c = 0, then x = -\(\alpha\) is the solution of the given quadratic equation.

(b)The additive inverse of zeroes of the polynomial ax²- + bx + c is the roots of the given equation.

(c) If a is a root of the given quadratic equation, then its other root is -\(\alpha\).

(d) All of these

(v) Which of the following is not a method of finding solutions of the given quadratic equation?

(a) Factorisation method	(b) Completing the square method
(c) Formula method	(d) None of these

CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
From Bengaluru bus stand, if Riddhima buys 2 tickets to Malleswaram and 3 tickets to Yeswanthpur, then total cost is Rs 46; but if she buys 3 tickets to Malleswaram and 5 tickets to Yeswanthpur, then total cost is Rs 74.

Consider the fares from Bengaluru to Malleswaram and that to Yeswanthpur as Rs x and Rs y respectively and answer the following questions.
(i) 1^st situation can be represented algebraically as

(a) 3x-5y=74 (b) 2x+5y=74 (c) 2x-3y=46 (d) 2x+3y=46

(ii) 2^nd situation can be represented algebraically as

(a) 5x + 3y = 74 (b) 5x- 3y= 74 (c) 3x + 5y = 74 (d) 3x-5y=74

(iii), Fare from Ben~aluru to Malleswaram is

(a) Rs 6 (b) Rs 8 (c) Rs 10 (d) Rs 2

(iv) Fare from Bengaluru to Yeswanthpur is

(a) Rs 10 (b) Rs 12 (c) Rs 14 (d) Rs 16

(v) The system oflinear equations represented by both situations has

(a) infinitely many solutions (b) no solution

(c) unique solution (d) none of these
2)
Mr Manoj Jindal arranged a lunch party for some of his friends. The expense of the lunch are partly constant and partly proportional to the number of guests. The expenses amount to Rs 650 for 7 guests and Rs 970 for 11 guests .

Denote the constant expense by Rs x and proportional expense per person by Rs y and answer the following questions.
(i) Represent both the situations algebraically.

(a) x + 7y = 650, x + 11y = 970 (b) x - 7y = 650, x - 11y = 970

(c) x+ 11y=650,x+7y=970 (d) 11x + 7y = 650, 11x - 7y = 970

(ii) Proportional expense for each person is

(a) Rs 50 (b) Rs 80 (c) Rs 90 (d) Rs 100

(iii) The fixed (or constant) expense for the party is

(a) Rs 50 (b) Rs 80 (c) Rs 90 (d) Rs 100

(iv) If there would be 15 guests at the lunch party, then what amount Mr Jindal has to pay?

(a) Rs 1500 (b) Rs 1300 (c) Rs 1200 (d) Rs 1290

(v) The system of linear equations representing both the situations will have

(a) unique solution (b) no solution

(c) infinitely many solutions (d) none of these
3)
A boat in the river Ganga near Rishikesh covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in \(6 \frac{1}{2}\) hours. Consider speed of the boat in still water be x km/hr and speed of the stream be y km/hr and answer the following questions.

(i) Represent the 1^st situation algebraically.

\((a) \frac{24}{x-y}+\frac{36}{x+y}=6\) \((b) \frac{24}{x+y}+\frac{36}{x-y}=6\) \((c) 24 x+36 y=6\) \((d) 24 x-36 y=6\)

(ii) Represent the 2^ndsituation algebraically.

\((a) \frac{36}{x+y}+\frac{24}{x-y}=\frac{13}{2}\) \((b) \frac{36}{x-y}+\frac{24}{x+y}=\frac{13}{2}\) \((c) 36 x-24 y=\frac{13}{2}\) \((d) 36 x+24 y=\frac{13}{2}\)

(iii) If u \(=\frac{1}{x-y} \text { and } v=\frac{1}{x+y}, \text { then } u=\)

\((a) \frac{1}{4}\) \((b) \frac{1}{12}\) \((c) \frac{1}{8}\) \((d) \frac{1}{6}\)

(iv) Speed of boat in still water is

(a) 4 km/hr (b) 6 km/hr (c) 8 km/hr (d) 10 krn/hr

(v) Speed of stream is

(a) 3 km/hr (b) 4 km/hr (c) 2 km/hr (d) 5 km/hr
4)
Puneet went for shopping in the evening by metro with his father who is an expert in mathematics. He told Puneet that path of metro A is given by the equation 2x + 4y = 8 and path of metro B is given by the equation 3x + 6y = 18. His father put some questions to Puneet. Help Puneet to solve the questions.

(i) Equation 2x + 4y = 8 intersects the x-axis and y-axis respectively at

(a) (4,0), (0, 2) (b) (0,4), (2,0) (c) (4,0), (2,0) (d) (0,4), (0, 2)

(ii) Equation 3x + 6y = 18 intersects the x-axis and y-axis respectively at

(a) (6,0), (0, 8) (b) (0,6), (0, 8) (c) (6,0), (0, 3) (d) (0,6), (0, 3)

(iii) Coordinates of point of intersection of two given equations are

(a) (1,2) (b) (2,4) (c) (3,7) (d) does not exist

(iv) Represent the equations, 2x + 4y = 8 and 3x + 6y = 18 graphically.

(d) None of these

(v) System oflinear equations represented by two given lines is

(a) inconsistent (b) having infinitely many solutions

(c) consistent (d) overlapping each other
5)
Raman usually go to a dry fruit shop with his mother. He observes the following two situations.
On 1st day: The cost of 2 kg of almonds and 1 kg of cashew was Rs 1600.
On 2nd day: The cost of 4 kg of almonds and 2 kg of cashew was Rs 3000.
Denoting the cost of 1 kg almonds by Rs x and cost of 1 kg cashew by Rs y, answer the following questions.

(i) Represent algebraically the situation of day-I.

(a) x + 2y = 1000 (b) 2x + y = 1600 (c) x - 2y = 1000 (d) 2x - y = 1000

(ii) Represent algebraically the situation of day- II.

(a) 2x + y= 1500 (b) 2x- y= 1500 (c) x + 2y=1500 (d) 2x + y = 750

(iii) The linear equation represented by day-I, intersect the x axis at

(a) (0,800) (b) (0,-800) (c) (800,0) (d) (-800,0)

(iv) The linear equation represented by day-II, intersect the y-axis at

(a) (1500,0) (b) (0, -1500) (c) (-1500,0) (d) (0,1500)

(v) Linear equations represented by day-I and day -II situations, are

(a) non parallel (b) parallel

(c) intersect at one point (d) overlapping each other.

CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Case Study Questions 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
A part of monthly hostel charges in a college is fixed and the remaining depends on the number of days one has taken food in the mess. When a student Anu takes food for 25 days, she has to pay Rs 4500 as hostel charges, whereas another student Bindu who takes food for 30 days, has to pay Rs 5200 as hostel charges.

Considering the fixed charges per month by Rs x and the cost of food per day by Rs y, then answer the following questions.
(i) Represent algebraically the situation faced by both Anu and Bindu.

(a) x + 25y = 4500, x + 30y = 5200 (b) 25x + y = 4500, 30x + Y = 5200

(c) x - 25y = 4500, x - 30y = 5200 (d) 25x - y = 4500, 30x - Y = 5200

(ii) The system of linear equations, represented by above situations has

(a) No solution (b) Unique solution

(c) Infinitely many solutions (d) None of these

(iii) The cost of food per day is

(a) Rs 120 (b) Rs 130 (c) Rs 140 (d) Rs 1300

(iv) The fixed charges per month for the hostel is

(a) Rs 1500 (b) Rs 1200 (c) Rs 1000 (d) Rs 1300

(v) If Bindu takes food for 20 days, then what amount she has to pay?

(a) Rs 4000 (b) Rs 3500 (c) Rs 3600 (d) Rs 3800
2)
Points A and B representing Chandigarh and Kurukshetra respectively are almost 90 km apart from each other on the highway. A car starts from Chandigarh and another from Kurukshetra at the same time. If these cars go in the same direction, they meet in 9 hours and if these cars go in opposite direction they meet in 9/7 hours. Let X and Ybe two cars starting from points A and B respectively and their speed be x km/hr and y km/hr respectively.

Then, answer the following questions.
(i) When both cars move in the same direction, then the situation can be represented algebraically as

(a) x - y = 10 (b) x + y = 10 (c) x + y = 9 (d) x - y = 9

(ii) When both cars move in opposite direction, then the situation can be represented algebraically as

(a) x - y=70 (b) x + y=90 (c) x + y=70 (d) x + y=10

(iii) Speed of car X is

(a) 30 km/hr (b) 40 km/hr (c) 50 km/hr (d) 60 km/hr

(iv) Speed of car Y is

(a) 50km//hr (b) 40 km/hr (c) 30 km/hr (d) 60 km/hr

(v) If speed of car X and car Y, each is increased by 10 km/hr, and cars are moving in opposite direction, then after how much time they will meet?

(a) 5 hrs (b) 4 hrs (c) 2 hrs (d) 1 hr
3)
In a office, 8 men and 12 women together can finish a piece of work in 10 days, while 6 men and 8 women together can finish it in 14 days. Let one day's work of a man be l/x and one day's work of a woman be 1/y.

Based on the above information, answer the following questions.
(i) 1^stsituation can be represented algebraically as

\((a) \frac{80}{x}-\frac{120}{y}=1\) \((b) \frac{120}{x}-\frac{80}{y}=1\) \((c) \frac{120}{x}+\frac{80}{y}=1\) \((d) \frac{80}{x}+\frac{120}{y}=1\)

(ii) 2^nd situation can be represented algebraically as

\((a) \frac{112}{x}-\frac{84}{y}=1\) \((b) \frac{84}{x}-\frac{112}{y}=1\) \((c) \frac{84}{x}+\frac{112}{y}=1\) \((d) \frac{112}{x}+\frac{84}{y}=1\)

(iii) One woman alone can finish the work in

(a) 220 days (b) 140 days (c) 280 days (d) 160 days

(iv) One man alone can finish the work in

(a) 140 days (b) 220 days (c) 160 days (d) 280 days

(v) If 14 men and 28 women work together, then in what time, the work will be completed?

(a) 2 days (b) 3 days (c) 4 days (d) 5 days
4)
A boat in the river Ganga near Rishikesh covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in \(6 \frac{1}{2}\) hours. Consider speed of the boat in still water be x km/hr and speed of the stream be y km/hr and answer the following questions.

(i) Represent the 1^st situation algebraically.

\((a) \frac{24}{x-y}+\frac{36}{x+y}=6\) \((b) \frac{24}{x+y}+\frac{36}{x-y}=6\) \((c) 24 x+36 y=6\) \((d) 24 x-36 y=6\)

(ii) Represent the 2^ndsituation algebraically.

\((a) \frac{36}{x+y}+\frac{24}{x-y}=\frac{13}{2}\) \((b) \frac{36}{x-y}+\frac{24}{x+y}=\frac{13}{2}\) \((c) 36 x-24 y=\frac{13}{2}\) \((d) 36 x+24 y=\frac{13}{2}\)

(iii) If u \(=\frac{1}{x-y} \text { and } v=\frac{1}{x+y}, \text { then } u=\)

\((a) \frac{1}{4}\) \((b) \frac{1}{12}\) \((c) \frac{1}{8}\) \((d) \frac{1}{6}\)

(iv) Speed of boat in still water is

(a) 4 km/hr (b) 6 km/hr (c) 8 km/hr (d) 10 krn/hr

(v) Speed of stream is

(a) 3 km/hr (b) 4 km/hr (c) 2 km/hr (d) 5 km/hr
5)
Puneet went for shopping in the evening by metro with his father who is an expert in mathematics. He told Puneet that path of metro A is given by the equation 2x + 4y = 8 and path of metro B is given by the equation 3x + 6y = 18. His father put some questions to Puneet. Help Puneet to solve the questions.

(i) Equation 2x + 4y = 8 intersects the x-axis and y-axis respectively at

(a) (4,0), (0, 2) (b) (0,4), (2,0) (c) (4,0), (2,0) (d) (0,4), (0, 2)

(ii) Equation 3x + 6y = 18 intersects the x-axis and y-axis respectively at

(a) (6,0), (0, 8) (b) (0,6), (0, 8) (c) (6,0), (0, 3) (d) (0,6), (0, 3)

(iii) Coordinates of point of intersection of two given equations are

(a) (1,2) (b) (2,4) (c) (3,7) (d) does not exist

(iv) Represent the equations, 2x + 4y = 8 and 3x + 6y = 18 graphically.

(d) None of these

(v) System oflinear equations represented by two given lines is

(a) inconsistent (b) having infinitely many solutions

(c) consistent (d) overlapping each other

CBSE 10th Standard Maths Subject Polynomials Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
While playing in garden, Sahiba saw a honeycomb and asked her mother what is that. She replied that it's a honeycomb made by honey bees to store honey. Also, she told her that the shape of the honeycomb formed is parabolic. The mathematical representation of the honeycomb structure is shown in the graph.

Based on the above information, answer the following questions.
(i) Graph of a quadratic polynomial is in___________shape.

(a) straight line (b) parabolic

(c) circular (d) None of these

(ii) The expression of the polynomial represented by the graph is

(a) x²-49 (b) x²-64 (c) x²-36 (d) x²-81

(iii) Find the value of the polynomial represented by the graph when x = 6.

(a) -2 (b) -1 (c) 0 (d) 1

(iv) The sum of zeroes of the polynomial x² + 2x - 3 is

(a) -1 (b) -2 (c) 2 (d) 1

(v) If the sum of zeroes of polynomial at² + 5t + 3a is equal to their product, then find the value of a.

(a) -5 (b) -3 \(\text { (c) } \frac{5}{3}\) \(\text { (d) } \frac{-5}{3}\)
2)
Pankaj's father gave him some money to buy avocado from the market at the rate of p(x) = x²- 24x + 128. Let a , \(\beta\) are the zeroes of p(x).
Based on the above information, answer the following questions.

(i) Find the value of a and \(\beta\), where a < \(\beta\).

(a) -8, -16 (b) 8,16 (c) 8,15 (d) 4,9

(ii) Find the value of \(\alpha\) + \(\beta\) + \(\alpha\)\(\beta\).

(a) 151 (b) 158 (c) 152 (d) 155

(iii) The value of p(2) is

(a) 80 (b) 81 (c) 83 (d) 84

(iv) If \(\alpha\) and \(\beta\) are zeroes of \(x^{2}+x-2, \text { then } \frac{1}{\alpha}+\frac{1}{\beta}=\)

(a) 1/2 (b) 1/3 (c) 1/4 (d) 1/5

(v) If sum of zeroes of \(q(x)=k x^{2}+2 x+3 k\) is equal to their product, then k =

(a) 2/3 (b) 1/3 (c) -2/3 (d) -1/3
3)
In a soccer match, the path of the soccer ball in a kick is recorded as shown in the following graph.

Based on the above i!;formation, answer the following questions.
(i) The shape of path of the soccer ball is a

(a) Circle (b) Parabola (c) Line (d) None of these

(ii) The axis of symmetry of the given parabola is

(a) y-axis (b) x-axis

(c) line parallel to y-axis (d) line parallel to x-axis

(iii) The zeroes of the polynomial, represented in the given graph, are

(a) -1,7 (b) 5,-2 (c) -2,7 (d) -3,8

(iv) Which of the following polynomial has -2 and -3 as its zeroes?

\((a) x^{2}-5 x-5\) \((b) x^{2}+5 x-6\) \((c) x^{2}+6 x-5\) \((d) x^{2}+5 x+6\)

(v) For what value of 'x', the value of the polynomial \(f(x)=(x-3)^{2}+9 \text { is } 9 ?\)

(a) 1 (b) 2 (c) 3 (d) 4
4)
Shweta and her husband Sunil who is an architect by profession, visited France. They went to see Mont Blanc Tunnel which is a highway tunnel between France and Italy, under the Mont Blanc Mountain in the Alps, and has a parabolic cross-section. The mathematical representation of the tunnel is shown in the graph.

Based on the above information, answer the following questions.
(i) The zeroes of the polynomial whose graph is given, are

(a) -2,8 (b) -2, -8 (c) 2,8 (d) -2, 0

(ii) What will be the expression of the polynomial given in diagram?

\((a) x^{2}-6 x+16\) \((b) -x^{2}+6 x+16\) \((c) x^{2}+6 x+16\) \((d) -x^{2}-6 x-16\)

(iii) What is the value of the polynomial, represented by the graph, when x = 4?

(a) 22 (b) 23 (c) 24 (d) 25

(iv) If the tunnel is represented by x² + 3x - 2, then its zeroes are

(a) -1, -2 (b) 1, -2 (c) -1,2 (d) 1,2

(v) If one zero is 4 and sum of zeroes is -3, then representation of tunnel as a polynomial is

\((a) x^{2}-x+24\) \((b) -x^{2}-3 x+28\) \((c) x^{2}+x+28\) \((d) x^{2}-x+28\)
5)
Shray, who is a social worker, wants to distribute masks, gloves, and hand sanitizer bottles in his block. Number of masks, gloves and sanitizer bottles distributed in 1 day can be represented by the zeroes \(\alpha, \beta, \gamma,(\alpha>\beta>\gamma)\) of the polynomial \(p(x)=x^{3}-18 x^{2}+95 x-150 .\)

Based on the above information, answer the following questions.
(i) Find the value of \(\alpha,\beta,\gamma.\)

(a) -10, -5,-3 (b) 3,6,5

(c) 10,5,3 (d) 4,8,9

(ii) The sum of product of zeroes taken two at a time is

(a) 91 (b) 92 (c) 94 (d) 95

(iii) Product of zeroes of polynomial p(x) is

(a) 150 (b) 160 (c) 170 (d) 180

(iv) The value of the polynomial p(x), when x = 4 is

(a) 5 (b) 6 (c) 7 (d) 8

(v) If \(\alpha,\beta,\gamma\) are the zeroes of a polynomial g(x) such that \(\alpha+\beta+\gamma=3, \alpha \beta+\beta \gamma+\gamma \alpha=-16\) and \(\alpha \beta \gamma=-48\) then, g(x) =

\((a) x^{3}-2 x^{2}-48 x+6\) \((b) x^{3}+3 x^{2}++16 x-48\)

\((c) x^{3}-48 x^{2}-16 x+3\) \((d) x^{3}-3 x^{2}-16 x+48\)

CBSE 10th Standard Maths Subject Polynomials Case Study Questions 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
While playing in garden, Sahiba saw a honeycomb and asked her mother what is that. She replied that it's a honeycomb made by honey bees to store honey. Also, she told her that the shape of the honeycomb formed is parabolic. The mathematical representation of the honeycomb structure is shown in the graph.

Based on the above information, answer the following questions.
(i) Graph of a quadratic polynomial is in___________shape.

(a) straight line (b) parabolic

(c) circular (d) None of these

(ii) The expression of the polynomial represented by the graph is

(a) x²-49 (b) x²-64 (c) x²-36 (d) x²-81

(iii) Find the value of the polynomial represented by the graph when x = 6.

(a) -2 (b) -1 (c) 0 (d) 1

(iv) The sum of zeroes of the polynomial x² + 2x - 3 is

(a) -1 (b) -2 (c) 2 (d) 1

(v) If the sum of zeroes of polynomial at² + 5t + 3a is equal to their product, then find the value of a.

(a) -5 (b) -3 \(\text { (c) } \frac{5}{3}\) \(\text { (d) } \frac{-5}{3}\)
2)
Just before the morning assembly a teacher of kindergarten school observes some clouds in the sky and so she cancels the assembly. She also observes that the clouds has a shape of the polynomial. The mathematical representation of a cloud is shown in the figure.

(i) Find the zeroes of the polynomial represented by the graph.

(a) -1/2,7/2 (b) 1/2, -7/2 (c) -1/2, -7/2 (d) 1/2,7/2

(ii) What will be the expression for the polynomial represented by the graph?

\((a) p(x)=12 x^{2}-4 x-7\) \((b) p(x)=-x^{2}-12 x+3\) \((c) p(x)=4 x^{2}+12 x+7\) \((d) p(x)=-4 x^{2}-12 x+7\)

(iii) What will be the value of polynomial represented by the graph, when x = 3?

(a) 65 (b) -65 (c) 68 (d) -68

(iv) If a and \(\beta\) are the zeroes of the polynomial \(f(x)=x^{2}+2 x-8 \text { , then } \alpha^{4}+\beta^{4}=\)

(a) 262 (b) 252 (c) 272 (d) 282

(v) Find a quadratic polynomial where sum and product of its zeroes are 0,\(\sqrt (7)\) respectively.

\((a) k\left(x^{2}+\sqrt{7}\right)\) \((b) k\left(x^{2}-\sqrt{7}\right)\) \((c) k\left(x^{2}+\sqrt{5}\right)\) (d) none of these
3)
Pankaj's father gave him some money to buy avocado from the market at the rate of p(x) = x²- 24x + 128. Let a , \(\beta\) are the zeroes of p(x).
Based on the above information, answer the following questions.

(i) Find the value of a and \(\beta\), where a < \(\beta\).

(a) -8, -16 (b) 8,16 (c) 8,15 (d) 4,9

(ii) Find the value of \(\alpha\) + \(\beta\) + \(\alpha\)\(\beta\).

(a) 151 (b) 158 (c) 152 (d) 155

(iii) The value of p(2) is

(a) 80 (b) 81 (c) 83 (d) 84

(iv) If \(\alpha\) and \(\beta\) are zeroes of \(x^{2}+x-2, \text { then } \frac{1}{\alpha}+\frac{1}{\beta}=\)

(a) 1/2 (b) 1/3 (c) 1/4 (d) 1/5

(v) If sum of zeroes of \(q(x)=k x^{2}+2 x+3 k\) is equal to their product, then k =

(a) 2/3 (b) 1/3 (c) -2/3 (d) -1/3

4)

Two friends Trisha and Rohan during their summer vacations went to Manali. They decided to go for trekking. While trekking they observes that the trekking path is in the shape of a parabola. The mathematical representation of the track is shown in the graph.

Based on the above information, answer the following questions.
(i) The zeroes of the polynomial whose graph is given, are

(a) 4,7

(b) -4,7

(c) 4,3

(d) 7,10

(ii) What will be the expression of the given polynomial p(x)?

\((a) x^{2}-3 x+\mathbf{3} 8\)

\((b) -x^{2}+4 x+28\)

\((c) x^{2}-4 x+28\)

\((d) -x^{2}+3 x+28\)

(iii) Product of zeroes of the given polynomial is

(a) -28

(b) 28

(c) -30

(d) 30

(iv) The zeroes of the polynomial 9x² - 5 are

\((a) \frac{3}{\sqrt{5}}, \frac{-3}{\sqrt{5}}\)

\((b) \frac{2}{\sqrt{5}}, \frac{-2}{\sqrt{5}}\)

\((c) \frac{\sqrt{5}}{3}, \frac{-\sqrt{5}}{3}\)

\((d) \frac{\sqrt{5}}{2}, \frac{-\sqrt{5}}{2}\)

(v) If f(x) = x² - 13x + 1, then f(4) =

(a) 35

(b) -35

(c) 36

(d) -36

5)
Neeru saw a creeper on the boundary of her aunt's house which was in the shape as shown in the figure. Answer the following questions by considering that creeper has same mathematical shape as shown in the figure. Based on the above information, answer the following questions.

(i) The shape represents a _______ polynomial.

(a) Linear (b) Cubic

(c) Quadratic (d) None of these

(ii) How many zeroes does the polynomial (shape of the creeper) have?

(a) 0 (b) 1 (c) 2 (d) 3

(iii) The zeroes of the polynomial, represented by the graph, are

(a) 4, -2 (b) -4,2 (c) 4,2 (d) -5,6

(iv) The expression of the polynomial, represented by the graph, is

\((a) x^{2}+2 x-8\) \((b) x^{2}-2 x-8\) \((c) x^{3}-x+8\) \((d) x^{3}-x^{2}+2 x+8\)

(v) For what value of x, the value of the polynomial, represented by the graph, is -5?

(a) x=3 (b) x=-1 (c) Both (a) and (b) (d) Can't be determined

CBSE 10th Standard Maths Subject Real Number Case Study Questions With Solution 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.
(i) For what value of n, 4ⁿends in 0?

(a) 10 (b) when n is even

(c) when n is odd (d) no value of n

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, aⁿ is a rational number?

(a) when n is any even integer (b) when n is any odd integer

(c) for all n > 1 (d) only when n = 0

(iii) If x and yare two odd positive integers, then which of the following is true?

(a) x² + y² is even (b) x² + y² is not divisible by 4

(c) x² + y² is odd (d) both (a) and (b)

(iv) The statement 'One of every three consecutive positive integers is divisible by 3' is

(a) always true (b) always false

(c) sometimes true (d) None of these

(v) If n is any odd integer, then n2 - 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8
2)
Real numbers are extremely useful in everyday life. That is probably one of the main reasons we all learn how to count and add and subtract from a very young age. Real numbers help us to count and to measure out quantities of different items in various fields like retail, buying, catering, publishing etc. Every normal person uses real numbers in his daily life. After knowing the importance of real numbers, try and improve your knowledge about them by answering the following questions on real life based situations.
(i) Three people go for a morning walk together from the same place. Their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance travelled when they meet at first time after starting the walk assuming that their walking speed is same?

(a) 6120 cm (b) 12240 cm (c) 4080 cm (d) None of these

(ii) In a school Independence Day parade, a group of 594 students need to march behind a band of 189 members. The two groups have to march in the same number of columns. What is the maximum number of columns in which they can march?

(a) 9 (b) 6 (c) 27 (d) 29

(iii) Two tankers contain 768litres and 420 litres of fuel respectively. Find the maximum capacity of the container which can measure the fuel of either tanker exactly.

(a) 4litres (b) 7litres (c) 12litres (d) 18litres

(iv) The dimensions of a room are 8 m 25 cm, 6 m 75 crn and 4 m 50 cm. Find the length of the largest measuring rod which can measure the dimensions of room exactly.

(a) 1 m 25cm (b) 75cm (c) 90cm (d) 1 m 35cm

(v) Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack of each type that one should buy so that there are equal number of pens and notepads

(a) 3 and 2 (b) 2 and 5 (c) 3 and 4 (d) 4 and 5
3)
In a classroom activity on real numbers, the students have to pick a number card from a pile and frame question on it if it is not a rational number for the rest of the class. The number cards picked up by first 5 students and their questions on the numbers for the rest of the class are as shown below. Answer them.
(i) Suraj picked up \(\sqrt{8}\) and his question was - Which of the following is true about \(\sqrt{8}\)?

(a) It is a natural number (b) It is an irrational number

(c) It is a rational number (d) None of these

(ii) Shreya picked up 'BONUS' and her question was - Which of the following is not irrational?

(a) 3-4\(\sqrt{5}\) (b) \(\sqrt{7}\) -6 (c) 2+2\(\sqrt{9}\) (d) 4\(\sqrt{11}\)-6

(iii) Ananya picked up \(\sqrt{5}\) -.\(\sqrt{10}\) and her question was - \(\sqrt{5}\) -.\(\sqrt{10}\) _________is number.

(a) a natural (b) an irrational (c) a whole (d) a rational

(iv) Suman picked up \(\frac{1}{\sqrt{5}}\) and her question was - \(\frac{1}{\sqrt{5}}\) is __________ number.

(a) a whole (b) a rational (c) an irrational (d) anatural

(v) Preethi picked up \(\sqrt{6}\) and her question was - Which of the following is not irrational?

(a) 15 + 3\(\sqrt{6}\) (b) \(\sqrt{24}\)- 9 (c) 5.\(\sqrt{150}\) (d) None of these
4)
Decimal form of rational numbers can be classified into two types.
(i) Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form \(\frac{p}{\sqrt{q}}\) where p and q are co-prime and the prime faetorisation of q is of the form 2ⁿ·5^m, where n, mare non-negative integers and vice-versa.
(ii) Let x = \(\frac{p}{\sqrt{q}}\) be a rational number, such that the prime faetorisation of q is not of the form 2ⁿ 5^m, where n and m are non-negative integers. Then x has a non-terminating repeating decimal expansion.
(i) Which of the following rational numbers have a terminating decimal expansion?

(a) 125/441 (b) 77/210 (c) 15/1600 (d) 129/(2² x 5² x 7²)

(ii) 23/(2³ x 5²) =

(a) 0.575 (b) 0.115 (c) 0.92 (d) 1.15

(iii) 441/(2² x 5⁷ x 7²) is a_________decimal.

(a) terminating (b) recurring

(c) non-terminating and non-recurring (d) None of these

(iv) For which of the following value(s) of p, 251/(2³ x p²) is a non-terminating recurring decimal?

(a) 3 (b) 7 (c) 15 (d) All of these

(v) 241/(2⁵ x 5³) is a _________decimal.

(a) terminating (b) recurring

(c) non-terminating and non-recurring (d) None of these
5)
HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM. Based on the above information answer the following questions.
(i) If two positive integers x and yare expressible in terms of primes as x = p2q3 and y = p3 q, then which of the following is true?

(a) HCF = pq2 x LCM (b) LCM = pq2 x HCF

(c) LCM = p2q x HCF (d) HCF = p2q x LCM

(ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p?

(a) p is odd (b) p is even (c) p is not prime (d) both (b) and (c)

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively.

(a) 3 (b) 1 (c) 34 (d) 17

(iv) Find the least positive integer which on adding 1 is exactly divisible by 126 and 600.

(a) 12600 (b) 12599 (c) 12601 (d) 12500

(v) If A, Band C are three rational numbers such that 85C - 340A :::109, 425A + 85B = 146, then the sum of A, B and C is divisible by

(a) 3 (b) 6 (c) 7 (d) 9

CBSE 10th Standard Maths Subject Real Number Case Study Questions 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.
(i) For what value of n, 4ⁿends in 0?

(a) 10 (b) when n is even

(c) when n is odd (d) no value of n

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, aⁿ is a rational number?

(a) when n is any even integer (b) when n is any odd integer

(c) for all n > 1 (d) only when n = 0

(iii) If x and yare two odd positive integers, then which of the following is true?

(a) x² + y² is even (b) x² + y² is not divisible by 4

(c) x² + y² is odd (d) both (a) and (b)

(iv) The statement 'One of every three consecutive positive integers is divisible by 3' is

(a) always true (b) always false

(c) sometimes true (d) None of these

(v) If n is any odd integer, then n2 - 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8
2)
Real numbers are extremely useful in everyday life. That is probably one of the main reasons we all learn how to count and add and subtract from a very young age. Real numbers help us to count and to measure out quantities of different items in various fields like retail, buying, catering, publishing etc. Every normal person uses real numbers in his daily life. After knowing the importance of real numbers, try and improve your knowledge about them by answering the following questions on real life based situations.
(i) Three people go for a morning walk together from the same place. Their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance travelled when they meet at first time after starting the walk assuming that their walking speed is same?

(a) 6120 cm (b) 12240 cm (c) 4080 cm (d) None of these

(ii) In a school Independence Day parade, a group of 594 students need to march behind a band of 189 members. The two groups have to march in the same number of columns. What is the maximum number of columns in which they can march?

(a) 9 (b) 6 (c) 27 (d) 29

(iii) Two tankers contain 768litres and 420 litres of fuel respectively. Find the maximum capacity of the container which can measure the fuel of either tanker exactly.

(a) 4litres (b) 7litres (c) 12litres (d) 18litres

(iv) The dimensions of a room are 8 m 25 cm, 6 m 75 crn and 4 m 50 cm. Find the length of the largest measuring rod which can measure the dimensions of room exactly.

(a) 1 m 25cm (b) 75cm (c) 90cm (d) 1 m 35cm

(v) Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack of each type that one should buy so that there are equal number of pens and notepads

(a) 3 and 2 (b) 2 and 5 (c) 3 and 4 (d) 4 and 5
3)
In a classroom activity on real numbers, the students have to pick a number card from a pile and frame question on it if it is not a rational number for the rest of the class. The number cards picked up by first 5 students and their questions on the numbers for the rest of the class are as shown below. Answer them.
(i) Suraj picked up \(\sqrt{8}\) and his question was - Which of the following is true about \(\sqrt{8}\)?

(a) It is a natural number (b) It is an irrational number

(c) It is a rational number (d) None of these

(ii) Shreya picked up 'BONUS' and her question was - Which of the following is not irrational?

(a) 3-4\(\sqrt{5}\) (b) \(\sqrt{7}\) -6 (c) 2+2\(\sqrt{9}\) (d) 4\(\sqrt{11}\)-6

(iii) Ananya picked up \(\sqrt{5}\) -.\(\sqrt{10}\) and her question was - \(\sqrt{5}\) -.\(\sqrt{10}\) _________is number.

(a) a natural (b) an irrational (c) a whole (d) a rational

(iv) Suman picked up \(\frac{1}{\sqrt{5}}\) and her question was - \(\frac{1}{\sqrt{5}}\) is __________ number.

(a) a whole (b) a rational (c) an irrational (d) anatural

(v) Preethi picked up \(\sqrt{6}\) and her question was - Which of the following is not irrational?

(a) 15 + 3\(\sqrt{6}\) (b) \(\sqrt{24}\)- 9 (c) 5.\(\sqrt{150}\) (d) None of these
4)
Decimal form of rational numbers can be classified into two types.
(i) Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form \(\frac{p}{\sqrt{q}}\) where p and q are co-prime and the prime faetorisation of q is of the form 2ⁿ·5^m, where n, mare non-negative integers and vice-versa.
(ii) Let x = \(\frac{p}{\sqrt{q}}\) be a rational number, such that the prime faetorisation of q is not of the form 2ⁿ 5^m, where n and m are non-negative integers. Then x has a non-terminating repeating decimal expansion.
(i) Which of the following rational numbers have a terminating decimal expansion?

(a) 125/441 (b) 77/210 (c) 15/1600 (d) 129/(2² x 5² x 7²)

(ii) 23/(2³ x 5²) =

(a) 0.575 (b) 0.115 (c) 0.92 (d) 1.15

(iii) 441/(2² x 5⁷ x 7²) is a_________decimal.

(a) terminating (b) recurring

(c) non-terminating and non-recurring (d) None of these

(iv) For which of the following value(s) of p, 251/(2³ x p²) is a non-terminating recurring decimal?

(a) 3 (b) 7 (c) 15 (d) All of these

(v) 241/(2⁵ x 5³) is a _________decimal.

(a) terminating (b) recurring

(c) non-terminating and non-recurring (d) None of these
5)
HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM. Based on the above information answer the following questions.
(i) If two positive integers x and yare expressible in terms of primes as x = p2q3 and y = p3 q, then which of the following is true?

(a) HCF = pq2 x LCM (b) LCM = pq2 x HCF

(c) LCM = p2q x HCF (d) HCF = p2q x LCM

(ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p?

(a) p is odd (b) p is even (c) p is not prime (d) both (b) and (c)

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively.

(a) 3 (b) 1 (c) 34 (d) 17

(iv) Find the least positive integer which on adding 1 is exactly divisible by 126 and 600.

(a) 12600 (b) 12599 (c) 12601 (d) 12500

(v) If A, Band C are three rational numbers such that 85C - 340A :::109, 425A + 85B = 146, then the sum of A, B and C is divisible by

(a) 3 (b) 6 (c) 7 (d) 9

CBSE 10th Standard Maths Subject Case Study Questions 2021 - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
Transport department of a city wants to buy some Electric buses for the city. For which they wants to analyse the distance travelled by existing public transport buses in a day.

The following data shows the distance travelled by 60 existing public transport buses in a day.

Daily distance travelled (in km) 200-209 210-219 220-229 230-239 240-249

Number of buses 4 14 26 10 6

Based on the above information, answer the following questions.
(i) The upper limit of a class and lower limit of its succeeding class is differ by

(a) 9 (b) 1 (c) 10 (d) none of these

(ii) The median class is

(a) 229.5-239.5 (b) 230-239 (c) 220-229 (d) 219.5-229.5

(iii) The cumulative frequency of the class preceding the median class is

(a) 14 (b) 18 (c) 26 (d) 10

(iv) The median of the distance travelled is

(a) 222 km (b) 225 km (c) 223 km (d) none of these

(v) If the mode of the distance travelled is 223.78 km, then mean of the distance travelled by the bus is

(a) 225 km (b) 220 km (c) 230.29 km (d) 224.29 km
2)
An electric scooter manufacturing company wants to declare the mileage of their electric scooters. For this, they recorded the mileage (km/ charge) of 50 scooters of the same model. Details of which are given in the following table.

Mileage (km/charge) 100-120 120-140 140-160 160-180

Number of scooters 7 12 18 13

Based on the above information, answer the following questions.
(i) The average mileage is

(a) 140 krn/charge (b) 150 krn/ charge (c) 130 krn/charge (d) 144.8 krn/charge

(ii) The modal value of the given data is

(a) 150 (b) 150.91 (c) 145.6 (d) 140.9

(ill) The median value of the given data is

(a) 140 (b) 146.67 (c) 130 (d) 136.6

(iv) Assumed mean method is useful in determining the

(a) Mean (b) Median (c) Mode (d) All of these

(v) The manufacturer can claim that the mileage for his scooter is

(a) 144 krn/charge (b) 155 krn/charge (c) 165 krn/charge (d) 175krn/charge
3)
Household income in India was drastically impacted due to the COVID-19 loekdown. Most of the companies decided to bring down the salaries of the employees by 50%.
The following table shows the salaries (in percent) received by 25 employees during loekdown.

Salaries received (in percent) 50-60 60-70 70-80 80-90

Number of employees 9 6 8 2

Based on the above information, answer the following questions.
(i) Total number of persons whose salary is reduced by more than 30%, is

(a) 10 (b) 20 (c) 25 (d) 15

(ii) Total number of persons whose salary is reduced by atmost 40%, is

(a) 15 (b) 10 (c) 16 (d) 8

(iii) The modal class is

(a) 50-60 (b) 60-70 (c) 70-80 (d) 80-90

(iv) The median class of the given data is

(a) 50-60 (b) 60-70 (c) 70-80 (d) 80-90

(v) The empirical relationship between mean, median and mode is

(a) 3 Median = Mode + 2 Mean (b) 3 Median = Mode - 2 Mean

(c) Median = 3 Mode - 2 Mean (d) Median = 3 Mode + 2 Mean

4)

A petrol pump owner wants to analyse the daily need of diesel at the pump. For this he collected the data of vehicles visited in 1 hr. The following frequency distribution table shows the classification of the number of vehicles and quantity of diesel filled in them.

Diesel Filled (in Litres)	3-5	5-7	7-9	9-11	11-13
Number of vehicles	5	10	10	7	8

Based on the above data, answer the following questions.
(i) Which of the following is correct?

(a) If x_i and f_i are sufficiently small, then direct method is appropriate choice for calculating mean.

(b) If x_i and f_i are sufficiently large, then direct method is appropriate choice for calculating mean.

(c) If x_i and f_i are sufficiently small, then assumed mean method is appropriate choice for calculating mean.

(d) None of the above.

(ii) Average diesel required for a vehicle is

(a) 8.15 litres

(b) 6 litres

(c) 7 litres

(d) 5.5 litres

(iii) If approximately 2000 vehicles comes daily at the petrol pump, then how much litres of diesel the pump should have?

(a) 16200 litres

(b) 16300 litres

(c) 10600 litres

(d) 15000 litres

(iv) The sum of upper and lower limit of median class is

(a) 22

(b) 10

(c) 16

(d) none of these

(v) If the median of given data is 8litres, then mode will be equal to

(a) 7.5 litres

(b) 7.7 litres

(c) 5.7 litres

(d) 8 litres

5)

Two friends Richa and Sohan have some savings in their piggy bank. They decided to count the total coins they both had. After counting they find that they have fifty \(\begin{equation} ₹ \end{equation} \) 1 coins, forty eight \(\begin{equation} ₹ \end{equation} \) 2 coins, thirty six \(\begin{equation} ₹ \end{equation} \) 5 coins, twenty eight \(\begin{equation} ₹ \end{equation} \)10 coins and eight \(\begin{equation} ₹ \end{equation} \) 20 coins. Now, they said to Nisha, their another friends, to choose a coin randomly.
Find the probability that the coin chosen is

(i) \(\begin{equation} ₹ \end{equation} \)5 coin

(a) \(\begin{equation} \frac{17}{55} \end{equation}\)	(b) \(\begin{equation} \frac{36}{85} \end{equation}\)
(c) \(\begin{equation} \frac{18}{85} \end{equation}\)	(d) \(\begin{equation} \frac{1}{15} \end{equation}\)

(ii) \(\begin{equation} ₹ \end{equation} \) 20 coin

(a) \(\begin{equation} \frac{13}{85} \end{equation}\)	(b) \(\begin{equation} \frac{4}{85} \end{equation}\)
(c) \(\begin{equation} \frac{3}{85} \end{equation}\)	(d) \(\begin{equation} \frac{4}{15} \end{equation}\)

(iii) not a \(\begin{equation} ₹ \end{equation} \) 10 coin

(a) \(\begin{equation} \frac{15}{31} \end{equation}\)	(b) \(\begin{equation} \frac{36}{85} \end{equation}\)
(c) \(\begin{equation} \frac{1}{5} \end{equation}\)	(d) \(\begin{equation} \frac{71}{85} \end{equation}\)

(iv) of denomination of atleast \(\begin{equation} ₹ \end{equation} \)10.

(a) \(\begin{equation} \frac{18}{85} \end{equation}\)	(b) \(\begin{equation} \frac{36}{85} \end{equation}\)
(c) \(\begin{equation} \frac{1}{17} \end{equation}\)	(d) \(\begin{equation} \frac{16}{85} \end{equation}\)

(v) of denomination of atmost \(\begin{equation} ₹ \end{equation} \) 5.

(a) \(\begin{equation} \frac{67}{85} \end{equation}\)	(b) \(\begin{equation} \frac{36}{85} \end{equation}\)
(c) \(\begin{equation} \frac{4}{85} \end{equation}\)	(d) \(\begin{equation} \frac{18}{85} \end{equation}\)

CBSE 10th Standard Maths Subject Case Study Questions With Solution 2021 Part - II - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
Mr Manoj Jindal arranged a lunch party for some of his friends. The expense of the lunch are partly constant and partly proportional to the number of guests. The expenses amount to Rs 650 for 7 guests and Rs 970 for 11 guests .

Denote the constant expense by Rs x and proportional expense per person by Rs y and answer the following questions.
(i) Represent both the situations algebraically.

(a) x + 7y = 650, x + 11y = 970 (b) x - 7y = 650, x - 11y = 970

(c) x+ 11y=650,x+7y=970 (d) 11x + 7y = 650, 11x - 7y = 970

(ii) Proportional expense for each person is

(a) Rs 50 (b) Rs 80 (c) Rs 90 (d) Rs 100

(iii) The fixed (or constant) expense for the party is

(a) Rs 50 (b) Rs 80 (c) Rs 90 (d) Rs 100

(iv) If there would be 15 guests at the lunch party, then what amount Mr Jindal has to pay?

(a) Rs 1500 (b) Rs 1300 (c) Rs 1200 (d) Rs 1290

(v) The system of linear equations representing both the situations will have

(a) unique solution (b) no solution

(c) infinitely many solutions (d) none of these
2)
From a shop, Sudhir bought 2 books of Mathematics and 3 books of Physics of class X for Rs 850 and Suman bought 3 books of Mathematics and 2 books of Physics of class X for Rs 900. Consider the price of one Mathematics book and that of one Physics book be Rs x and Rs y respectively.

Based on the above information, answer the following questions.
(i) Represent the situation faced by Sudhir, algebraically,

(a) 2x + 3y = 850 (b) 3x+2y=850 (c) 2x - 3y = 850 (d) 3x - 2y = 850

(ii) Represent the situation faced by Suman, algebraically

(a) 2x + 3y = 90 (b) 3x + 2y = 900 (c) 2x - 3y = 900 (d) 3x - 2y = 900

(iii) The price of one Physics book is

(a) Rs 80 (b) Rs 100 (c) Rs 150 (d) Rs 200

(iv) The price of one Mathematics book is

(a) Rs 80 (b) Rs 100 (c) Rs 150 (d) Rs 200

(v) The system of linear equations represented by above situation, has

(a) unique solution (b) no solution

(c) infinitely many solutions (d) none of these
3)
Raman usually go to a dry fruit shop with his mother. He observes the following two situations.
On 1st day: The cost of 2 kg of almonds and 1 kg of cashew was Rs 1600.
On 2nd day: The cost of 4 kg of almonds and 2 kg of cashew was Rs 3000.
Denoting the cost of 1 kg almonds by Rs x and cost of 1 kg cashew by Rs y, answer the following questions.

(i) Represent algebraically the situation of day-I.

(a) x + 2y = 1000 (b) 2x + y = 1600 (c) x - 2y = 1000 (d) 2x - y = 1000

(ii) Represent algebraically the situation of day- II.

(a) 2x + y= 1500 (b) 2x- y= 1500 (c) x + 2y=1500 (d) 2x + y = 750

(iii) The linear equation represented by day-I, intersect the x axis at

(a) (0,800) (b) (0,-800) (c) (800,0) (d) (-800,0)

(iv) The linear equation represented by day-II, intersect the y-axis at

(a) (1500,0) (b) (0, -1500) (c) (-1500,0) (d) (0,1500)

(v) Linear equations represented by day-I and day -II situations, are

(a) non parallel (b) parallel

(c) intersect at one point (d) overlapping each other.
4)
Amit is preparing for his upcoming semester exam. For this, he has to practice the chapter of Quadratic Equations. So he started with factorization method. Let two linear factors of \(a x^{2}+b x+c \text { be }(p x+q) \text { and }(r x+s)\)
\(\therefore a x^{2}+b x+c=(p x+q)(r x+s)=p r x^{2}+(p s+q r) x+q s .\)
Now, factorize each of the following quadratic equations and find the roots.
(i) 6x² + x - 2 = 0

\((a) 1,6\) \((b) \frac{1}{2}, \frac{-2}{3}\) \((c) \frac{1}{3}, \frac{-1}{2}\) \((d) \frac{3}{2},-2\)

(ii) 2x²-+ x - 300 = 0

\((a) 30, \frac{2}{15}\) \((b) 60, \frac{-2}{5}\) \((c) 12, \frac{-25}{2}\) (d) None of these

(iii) x²- 8x + 16 = 0

(a) 3,3 (b) 3,-3 (c) 4,-4 (d) 4,4

(iv) 6x²- 13x + 5 = 0

\((a) 2, \frac{3}{5}\) \((b) -2, \frac{-5}{3}\) \((c) \frac{1}{2}, \frac{-3}{5}\) \((d) \frac{1}{2}, \frac{5}{3}\)

(v) 100x²- 20x + 1 = 0

\((a) \frac{1}{10}, \frac{1}{10}\) \((b) -10,-10\) \((c) -10, \frac{1}{10}\) \((d) \frac{-1}{10}, \frac{-1}{10}\)
5)
Meenas mother start a new shoe shop. To display the shoes, she put 3 pairs of shoes in 1^st row,S pairs in 2^nd row, 7 pairs in 3^rd row and so on.

On the basis of above information, answer the following questions.
(i) If she puts a total of 120 pairs of shoes, then the number of rows required are

(a) 5 (b) 6 (c) 7 (d) 10

(ii) Difference of pairs of shoes in 17^throw and 10^th row is

(a) 7 (b) 14 (c) 21 (d) 28

(iii) On next day, she arranges x pairs of shoes in 15 rows, then x =

(a) 21 (b) 26 (c) 31 (d) 42

(iv) Find the pairs of shoes in 30^th row.

(a) 61 (b) 67 (c) 56 (d) 59

(v) The total number of pairs of shoes in 5^th and 8^th row is

(a) 7 (b) 14 (c) 28 (d) 56

CBSE 10th Standard Maths Subject Case Study Questions With Solution 2021 Part - I - by QB365 - Question Bank Software - May 21, 2021 - View & Read

1)
Real numbers are extremely useful in everyday life. That is probably one of the main reasons we all learn how to count and add and subtract from a very young age. Real numbers help us to count and to measure out quantities of different items in various fields like retail, buying, catering, publishing etc. Every normal person uses real numbers in his daily life. After knowing the importance of real numbers, try and improve your knowledge about them by answering the following questions on real life based situations.
(i) Three people go for a morning walk together from the same place. Their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance travelled when they meet at first time after starting the walk assuming that their walking speed is same?

(a) 6120 cm (b) 12240 cm (c) 4080 cm (d) None of these

(ii) In a school Independence Day parade, a group of 594 students need to march behind a band of 189 members. The two groups have to march in the same number of columns. What is the maximum number of columns in which they can march?

(a) 9 (b) 6 (c) 27 (d) 29

(iii) Two tankers contain 768litres and 420 litres of fuel respectively. Find the maximum capacity of the container which can measure the fuel of either tanker exactly.

(a) 4litres (b) 7litres (c) 12litres (d) 18litres

(iv) The dimensions of a room are 8 m 25 cm, 6 m 75 crn and 4 m 50 cm. Find the length of the largest measuring rod which can measure the dimensions of room exactly.

(a) 1 m 25cm (b) 75cm (c) 90cm (d) 1 m 35cm

(v) Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack of each type that one should buy so that there are equal number of pens and notepads

(a) 3 and 2 (b) 2 and 5 (c) 3 and 4 (d) 4 and 5
2)
Decimal form of rational numbers can be classified into two types.
(i) Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form \(\frac{p}{\sqrt{q}}\) where p and q are co-prime and the prime faetorisation of q is of the form 2ⁿ·5^m, where n, mare non-negative integers and vice-versa.
(ii) Let x = \(\frac{p}{\sqrt{q}}\) be a rational number, such that the prime faetorisation of q is not of the form 2ⁿ 5^m, where n and m are non-negative integers. Then x has a non-terminating repeating decimal expansion.
(i) Which of the following rational numbers have a terminating decimal expansion?

(a) 125/441 (b) 77/210 (c) 15/1600 (d) 129/(2² x 5² x 7²)

(ii) 23/(2³ x 5²) =

(a) 0.575 (b) 0.115 (c) 0.92 (d) 1.15

(iii) 441/(2² x 5⁷ x 7²) is a_________decimal.

(a) terminating (b) recurring

(c) non-terminating and non-recurring (d) None of these

(iv) For which of the following value(s) of p, 251/(2³ x p²) is a non-terminating recurring decimal?

(a) 3 (b) 7 (c) 15 (d) All of these

(v) 241/(2⁵ x 5³) is a _________decimal.

(a) terminating (b) recurring

(c) non-terminating and non-recurring (d) None of these
3)
ABC construction company got the contract of making speed humps on roads. Speed humps are parabolic in shape and prevents overspeeding, mini mise accidents and gives a chance for pedestrians to cross the road. The mathematical representation of a speed hump is shown in the given graph.

Based on the above information, answer the following questions.
(i) The polynomial represented by the graph can be _______polynomial.

(a) Linear (b) Quadratic

(c) Cubic (d) Zero

(ii) The zeroes of the polynomial represented by the graph are

(a) 1,5 (b) 1,-5

(c) -1,5 (d) -1,-5

(iii) The sum of zeroes of the polynomial represented by the graph are

(a) 4 (b) 5 (c) 6 (d) 7

(iv) If a and β are the zeroes of the polynomial represented by the graph such that \(\beta>\alpha, \text { then }|8 \alpha+\beta|=\)

(a) 1 (b) 2 (c) 3 (d) 4

(v) The expression of the polynomial represented by the graph is

\(\text { (a) }-x^{2}-4 x-5\) \((b) x^{2}+4 x+5\) \((c) x^{2}+4 x-5\) \((d) -x^{2}+4 x+5\)
4)
Just before the morning assembly a teacher of kindergarten school observes some clouds in the sky and so she cancels the assembly. She also observes that the clouds has a shape of the polynomial. The mathematical representation of a cloud is shown in the figure.

(i) Find the zeroes of the polynomial represented by the graph.

(a) -1/2,7/2 (b) 1/2, -7/2 (c) -1/2, -7/2 (d) 1/2,7/2

(ii) What will be the expression for the polynomial represented by the graph?

\((a) p(x)=12 x^{2}-4 x-7\) \((b) p(x)=-x^{2}-12 x+3\) \((c) p(x)=4 x^{2}+12 x+7\) \((d) p(x)=-4 x^{2}-12 x+7\)

(iii) What will be the value of polynomial represented by the graph, when x = 3?

(a) 65 (b) -65 (c) 68 (d) -68

(iv) If a and \(\beta\) are the zeroes of the polynomial \(f(x)=x^{2}+2 x-8 \text { , then } \alpha^{4}+\beta^{4}=\)

(a) 262 (b) 252 (c) 272 (d) 282

(v) Find a quadratic polynomial where sum and product of its zeroes are 0,\(\sqrt (7)\) respectively.

\((a) k\left(x^{2}+\sqrt{7}\right)\) \((b) k\left(x^{2}-\sqrt{7}\right)\) \((c) k\left(x^{2}+\sqrt{5}\right)\) (d) none of these
5)
In a soccer match, the path of the soccer ball in a kick is recorded as shown in the following graph.

Based on the above i!;formation, answer the following questions.
(i) The shape of path of the soccer ball is a

(a) Circle (b) Parabola (c) Line (d) None of these

(ii) The axis of symmetry of the given parabola is

(a) y-axis (b) x-axis

(c) line parallel to y-axis (d) line parallel to x-axis

(iii) The zeroes of the polynomial, represented in the given graph, are

(a) -1,7 (b) 5,-2 (c) -2,7 (d) -3,8

(iv) Which of the following polynomial has -2 and -3 as its zeroes?

\((a) x^{2}-5 x-5\) \((b) x^{2}+5 x-6\) \((c) x^{2}+6 x-5\) \((d) x^{2}+5 x+6\)

(v) For what value of 'x', the value of the polynomial \(f(x)=(x-3)^{2}+9 \text { is } 9 ?\)

(a) 1 (b) 2 (c) 3 (d) 4

Age group of children (in years)	6-8	8-10	10-12	12-14	14-16
Number of children	43	58	70	42	27

(a) Mean	(b) Mode
(c) Both (a) and (b)	(d) Neither (a) nor (b)

Daily distance travelled (in km)	200-209	210-219	220-229	230-239	240-249
Number of buses	4	14	26	10	6

Mileage (km/charge)	100-120	120-140	140-160	160-180
Number of scooters	7	12	18	13

Salaries received (in percent)	50-60	60-70	70-80	80-90
Number of employees	9	6	8	2

(a) 3 Median = Mode + 2 Mean	(b) 3 Median = Mode - 2 Mean
(c) Median = 3 Mode - 2 Mean	(d) Median = 3 Mode + 2 Mean

Time (in hours)	15-19	20-24	25-29	30-34	35-39
Number of workers	10	15	12	8	5

(a) reflex angle	(b) straight
(c) an obtuse angle	(d) an acute angle

\((a) 15 \mathrm{~m}\)	\((b) 15 \sqrt{2} \mathrm{~m}\)
\((c) \frac{15}{\sqrt{3}} \mathrm{~m}\)	\((d) \frac{15}{\sqrt{2}} \mathrm{~m}\)

(a) Similar Triangles	(b) Pythagoras Theorem
(c) Application of Trigonometry	(d) None of these

(a) vertically opposite angles	(b) alternate interior angles
(c) alternate exterior angles	(d) corresponding angles

(a) Ankit	(b) Radha
(c) Both are at equal distance	(d) Can't be determined

(a) AB + BC = CD + DA	(b) AB + AD = BC + CD
(c) AB + CD = AD + BC	(d) All of these

(a) \(\angle\)POQ = 180°	(b) PQ is a diameter
(c) \(\angle\)APQ = \(\angle\)PQD = 90°	(d) All of these

(a) I \|\| m	(b) l \(\perp\)m
(c) line I and line m intersects and makes an angle of 60°	(d) can't be determined

(a) PQ is a tangent to both the circles	(b) Two circles are concentric
(c) PQ is a tangent to bigger circle only	(d) PQ is a tangent to smaller circle only

(a) rhombus	(b) rectangle
(c) square	(d) none of these

(a) Quadrilateral AROP is a square.	(b) Quadrilateral BROQ is a square.
(c) Quadrilateral CQOP is a square.	(d) None of these

(a) ABC forms a scalene triangle	(b) ABC forms an isosceles triangle
(c) ABC forms an equilateral triangle	(d) None of these

(a) a straight line	(b) an equilateral triangle
(c) a scalene triangle	(d) an isosceles triangle

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(a) Should he travel back to college	(b) Should try his luck to move towards city B
(c) Should be travel back to city A	(d) None of these

(a) mid-point of points of intersection with x-axis	(b) mid-point of points of intersection with y-axis
(c) both (a) and (b)	(d) none of these

(a) 185000km²	(b) 179000km²
(c) 186000km²	(d) 2025000 km²

(a) Thales theorem	(b) Pythagoras theorem
(c) Converse ofthales theorem	(d) Converse of Pythagoras theorem

(a) m²+n²= r²	(b) m²+n²+r²-=0
(c) m² + n² = 2r²	(d) none of these

\((a) -4 x^{2}+7 x-4=0\)	\((b) -4 x^{2}+7 x-2=0\)
\((c) -2 x^{2}+5 x-2=0\)	\((d) 3 x^{2}+6 x+2=0\)

\((a) x^{2}+x-1=0\)	\((b) x^{2}-5 x+6=0\)
\((c) 4 x^{2}-3 x-2=0\)	\((d) 6 x^{2}-x+11=0\)

\((a) 3 x^{2}+2 x+2=0\)	\((b) 4 x^{2}-7 x+3=0\)
\((c) 6 x^{2}-3 x-5=0\)	\((d) 2 x^{2}+3 x-2=0\)

\((a) x^{2}-3 x+4=0\)	\((b) 2 x^{2}-2 x+1=0\)
\((c) 5 x^{2}-10 x+1=0\)	\((d) 9 x^{2}+6 x+1=0\)

\((a) x^{2}+3 x+1=0\)	\((b) -x^{2}+3 x-3=0\)
\((c) 4 x^{2}+8 x+4=0\)	\((d) 3 x^{2}+6 x+4=0\)