### 10th Standard CBSE Maths Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 10 Session 2019 - 2020 CBSE [ Chapter , Marks , Book Back, Creative & Term Based Questions Papers - Syllabus, Study Materials, MCQ's Practice Tests etc..]

#### 10th standard CBSE Mathematics Public Model Question Paper IV 2019-2020 - by Abhimanyu - Bhopal - View & Read

• 1)

If ax2 + bx + c , a≠0 is factorizable into product of two linear factors, then roots of ax2 + bx + c = 0 can be found by equating each factor to

• 2)

If p, q, r, s, t are the terms of an A.P. with common difference -1 the relation between p and t is

• 3)

From a point A, the length of a tangent to a circle is 8cm and distance of A from the circle is 10cm. The length of the diameter of the circle is

• 4)

In which of the following ratios a line segment cannot be divided using ruler and compass?

• 5)

If the height and length of the shadow of a man are the same, then the angle of elevation of the sun is

#### 10th standard CBSE Mathematics Public Model Question Paper III 2019-2020 - by Abhimanyu - Bhopal - View & Read

• 1)

If the length of the rectangle is one more than the twice its width, and the area of the rectangle is 300 square meter. What is the measure of the width of the rectangle?

• 2)

How many terms of AP 54, 51, 48… are required to give a sum of 513

• 3)

The angle between two tangents drawn from an external point to a circle is 110°. The angle subtended at the centre by the segments joining the points of contact to the centre of circle is:

• 4)

In the figure, P divides AB internally in the ratio

• 5)

The ——– is the line drawn from the eye of an observer to the point in the object viewed by the observer

#### 10th standard CBSE Mathematics Public Model Question Paper II 2019-2020 - by Abhimanyu - Bhopal - View & Read

• 1)

The same value of x satisfies the equations 4x + 5 = 0 and 4x2 + (5 + 3p)x + 3p2=0, then p is

• 2)

The nth term of the AP 9, 13, 17, 21, 25, ………….. is:

• 3)

If radii of two concentric circles are 4 cm and 5 cm, then length of each chord of one circle which is tangent to the other circle, is

• 4)

If TP and TQ are two tangents to a circle with centre O so that angle POQ = 110o then angle PTQ is equal to

• 5)

In the following figure α is

#### 10th standard CBSE Mathematics Public Model Question Paper I 2019-2020 - by Abhimanyu - Bhopal - View & Read

• 1)

The solution of x2 + 4x + 4 = 0 is

• 2)

The 8th term of 117, 104, 91, 78, …….is.....

• 3)

In fig., two circles with centres A and B touch each other externally at k. The length of PQ (in cm) is

• 4)

In drawing triangle ABC, it is given that AB = 3 cm, BC = 2 cm and AC = 6 cm. It is not possible to draw the triangle as:

• 5)

The figure shows the observation of point C from point A. The angle of depression from A is:

#### 10th standard CBSE Mathematics Public Model Question Paper V 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

The roots of quadratic equation x2 – 9 = 0 are

• 2)

The first and last terms of an AP are 1 and 11. If the sum of all its terms is 36, then the number of terms will be

• 3)

in figure , if ㄥAOB = 125o, then ㄥCOD is equal to

• 4)

In the given figure, AC: CB is

• 5)

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower is

#### 10th standard CBSE Mathematics Public Model Question Paper IV 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

If  1/2 is a root of the equation x+ kx-5/4 = 0 then the other root of the quadratic equation is

• 2)

A tree in each year grows 4cm less than it grew in previous year. If it grew 1 metre in the first year, in how many years will it have ceased growing and what will be its height then,

• 3)

The angle between two tangents drawn from an external point to a circle is 110°. The angle subtended at the centre by the segments joining the points of contact to the centre of circle is:

• 4)

PT and PS are tangents drawn to a circle, with cantre C, from a point P. If ∠TPS = 50° , then the measure of ΔTCS is

• 5)

If the height and length of the shadow of a man are the same, then the angle of elevation of the sun is

#### 10th standard CBSE Mathematics Public Model Question Paper III 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

The roots of quadratic equation x2 – 9 = 0 are

• 2)

Ramesh’s salary in February 2008 is Rs. 10,000. If he’s promised an increase of Rs. 1000 every year, what would be his salary in Feb 2011

• 3)

In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT is equal to

• 4)

Given a triangle with side AB = 8 cm. To get a line segment AB’ = 3/4 of AB, it is required to divide the line segment AB in the ratio:

• 5)

Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?

#### 10th standard CBSE Mathematics Public Model Question Paper II 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

The roots of quadratic equation x2 – 9 = 0 are

• 2)

Which term of the A.P. 1, 4, 7 … is 88?

• 3)

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=120°, then ∠OPQ is

• 4)

If four sides of a quadrilateral ABCD are tangential to a circle, then

• 5)

Find AB in the given figure

#### 10th standard CBSE Mathematics Public Model Question Paper I 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

The equation 4x2 = 4x has following solution/solutions

• 2)

If p, q, r, s, t are the terms of an A.P. with common difference -1 the relation between p and t is

• 3)

A circle can pass through

• 4)

Which of the following relation would hold true for the sides of the similar triangles in the given diagram?

$\frac { A'B }{ AB } =\frac { A'C }{ AC } =\frac { BC' }{ BC } =\frac { 3 }{ 4 }$
$\frac { A'B }{ AB } =\frac { A'C' }{ AC } =\frac { BC' }{ BC' } =\frac { 3 }{ 4 }$
$\frac { A'B }{ AB } =\frac { A'C' }{ AC } =\frac { BC' }{ BC } =\frac { 4 }{ 3 }$
$\frac { A'B }{ AB } =\frac { A'C' }{ AC } =\frac { BC }{ BC' } =\frac { 4 }{ 2 }$

• 5)

If the angle of elevation of a cloud from a point 100 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is

#### 10th standard CBSE Mathematics Board Exam Model Question Paper IV 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

In the triangles PQR and NLM, angle M will be

• 2)

Consider a constellation of 3 stars A, B and C forming a right triangle with angle ABC = 90° and angle BAC = 30° . If the distance between star A and B is 3√3 x 1013 km, then how much time does light take to travel from star C to B with a speed of 3 x 108 m/s?

• 3)

A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Assuming that the dimples are hemispherical, total surface area which is exposed to the surroundings is

• 4)

A rational number can be expressed as a terminating decimal if its denominator has factors

• 5)

To construct a triangle similar to a given triangle as per given scale factor which may be __________ than or may be __________ than 1.

#### 10th standard CBSE Mathematics Board Exam Model Question Paper II 2019-2020 - by Abhimanyu - Bhopal - View & Read

• 1)

In the triangles PQR and NLM, angle M will be

• 2)

Consider a constellation of 3 stars A, B and C forming a right triangle with angle ABC = 90° and angle BAC = 30° . If the distance between star A and B is 3√3 x 1013 km, then how much time does light take to travel from star C to B with a speed of 3 x 108 m/s?

• 3)

A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Assuming that the dimples are hemispherical, total surface area which is exposed to the surroundings is

• 4)

A rational number can be expressed as a terminating decimal if its denominator has factors

• 5)

To construct a triangle similar to a given triangle as per given scale factor which may be __________ than or may be __________ than 1.

#### 10th standard CBSE Mathematics Board Exam Model Question Paper III 2019-2020 - by Abhimanyu - Bhopal - View & Read

• 1)

In the figure, AE is the bisector of exterior angle CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then CE is equal to

• 2)

In the above fig Q and α respectively are

• 3)

A bucket is in the form of a frustum of a cone ad holds 28.490 liters of water. The radii of the top and bottom are 28cm and 21cm respectively. Find the height of the bucket.

• 4)

Which of the following rational numbers has a denominator that can be expressed as a product of powers of 2 and 5?

• 5)

Find the next term of the series $\sqrt { 2 } ,\sqrt { 8 } ,\sqrt { 18 } ,\sqrt { 32 } ....$

#### 10th standard CBSE Mathematics Board Exam Model Question Paper IV 2019-2020 - by Abhimanyu - Bhopal - View & Read

• 1)

If four sides of a quadrilateral ABCD are tangential to a circle, then

• 2)

Find AB in the given figure

• 3)

In the figure, the shape of a solid copper piece (made of two pieces) with dimensions as shown. The face ABCDEFA has uniform cross section. Assume that the angles at A, B, C, D, E and F are right angles. Calculate the volume of the piece.

• 4)

The prime factorization of 184 is

• 5)

The sum of all the angles of a triangle is________________

#### 10th standard CBSE Mathematics Board Exam Model Question Paper V 2019-2020 - by Abhimanyu - Bhopal - View & Read

• 1)

In the triangles PQR and NLM, angle M will be

• 2)

The angle formed by the line of sight with the horizontal, when the point being viewed is above the horizontal level is called:

• 3)

If the curved surface area of a right circular cylinder is 1760 cm2 and its radius is 10 cm, then what is its height?

• 4)

What is the HCF of 1076 and 584

• 5)

A Segment AB is divided at point P such that $\frac { PB }{ AB } =\frac { 3 }{ 7 }$ then find the radio AP : PB.

#### 10th standard CBSE Mathematics Board Exam Model Question Paper I 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

PT and PS are tangents drawn to a circle, with cantre C, from a point P. If ∠TPS = 50° , then the measure of ΔTCS is

• 2)

The length of shadow of a tower on the plane ground is √3 times the height of the tower. The angle of elevation of sun is :

• 3)

If the radius of the base of a right circular cylinder is halved keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

• 4)

There is a circular path around a sport field. Sonia takes 18min to drive one around of the field, while Ravi takes 12min for the same. Suppose they both start at the same point at the same time, and go in the same direction, after how minutes will they meet again at the starting point?

• 5)

The difference of any two sides of a triangle is always __________ than the third side.

#### 10th standard CBSE Mathematics Board Exam Model Question Paper II 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

Given a triangle with side AB = 8 cm. To get a line segment AB’ = 3/4 of AB, it is required to divide the line segment AB in the ratio:

• 2)

If sun’s elevation is 60° then a pole of height 6 m will cast a shadow of length

• 3)

What is $1-\sqrt { 3 }$?

• 4)

A school has three sections of Class 10. They need to have enough books in the class library so that they can be distributed equally in the three sections . What is the minimum number of books required if the number of students in section A , B and C are 30, 32 and 36 respectively?

• 5)

The sum of any two sides of a triangle is always _____________ than the third side.

#### 10th standard CBSE Mathematics Board Exam Model Question Paper III 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

In the triangles PQR and NLM, angle M will be

• 2)

The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 60 m then, the height of the first tower is

• 3)

A sequence a1, a2, a3,.......... an, an+1,..... is called an A.P. If there exists constant d such that

• 4)

In the figure, if AB, AC and line I are tangents to the circle and semi-perimeter of  $\triangle APQ$= 14 cm, then AC = ___________cm.

• 5)

When are the two triangles said to be similar?

#### 10th standard CBSE Mathematics Board Exam Model Question Paper IV 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that ∠BAX is an acute angle and then points  are located at equal distances on the ray AX and the point B is joined to

• 2)

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower is

• 3)

If H and h be the heights of two cylinders, then the ratio of curved surface areas of two cylinders with equal radii is

• 4)

‘a’ and ‘b’ are two prime numbers . What is their HCF

• 5)

The sum of all the angles of a triangle is________________

#### CBSE 10th Mathematics - Public Model Question Paper 2019 - 2020 - by Abhimanyu - Bhopal - View & Read

• 1)

In the figure, P divides AB internally in the ratio

• 2)

Write the HCF of the smallest composite number and the smallest even number

• 3)

In reduced scale-factor, the geometric figure to be constructed is .______________in size.

• 4)

Three points A, B and C are collinear, if any one of the following takes place:
........... + AB = CB

• 5)

A right circular cylinder of radius r cm and height h cm (h>2r) just enclosed a sphere of diameter

#### CBSE 10th Mathematics - Arithmetic Progressions Model Question Paper - by Abhimanyu - Bhopal - View & Read

• 1)

Amit starts his exercise regime with 25 push ups on Monday. He plans to increase 5 push ups every following Monday. How many push ups will he be doing on the 3rd Monday since he started?

• 2)

Which term of the A.P 10,8,6,… will be the first negative term?

• 3)

An AP has first term -3 and a common difference -1. Find the 3rd term of the A.

• 4)

Find the fifth term of an A.P whose first term is -1 and common difference is -3.

• 5)

If for an A.P sn= + 3n What is the nth term?

#### 10th Standard CBSE Mathematics - Quadratic Equations Model Question Paper - by Abhimanyu - Bhopal - View & Read

• 1)

The roots of quadratic equation x2 – 9 = 0 are

• 2)

If x = -2 is a root of equation x2 – 4x + K = 0 then value of K is

• 3)

Which of the following is not a quadratic equation?

• 4)

The condition for equation ax2 + bx + c = 0 to be quadratic is

• 5)

Solve 9x2= 36

#### CBSE 10th Mathematics - Full Syllabus One Mark Question Paper with Answer Key - by Abhimanyu - Bhopal - View & Read

• 1)

If x = 1 is a root of equation x2 – Kx + 5 = 0 then value of K is

• 2)

Solve 9x2= 36

• 3)

The roots of quadratic equation x2 – 9 = 0 are

• 4)

The roots of quadratic equation ax² + bx + c = 0 is given by

• 5)

If 4 is a root of the equation x2 + 3x + k = 0 , then k is

#### Second quarter exam 2019 - by Ramu tuition centre - View & Read

• 1)

If the perimeter and area of a circle are numerically equal, then the radius of the circle is

• 2)

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is

• 3)

The ratio of radii of two circles is in the ratio of 1:5. Calculate the ratio of their perimeters

• 4)

The area of a sector of a circle of radius 5 cm is 5 cm2. The angle contained by the sector will be

• 5)

The inner circumference of a circular track is 440m, and the track is 14m wide. The cost of levelling the track at 25 paise/m2 will be

#### SECOND QUARTERLY EXAM 2019 - by Ramu tuition centre - View & Read

• 1)

In the given figure, PA and PB are tangents from P to a circle with centre O. If ∠AOB = 130°, then find ∠APB.

• 2)

in figure , if ㄥAOB = 125o, then ㄥCOD is equal to

• 3)

The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm, is :

• 4)

Number of tangents, that can be drawn to a circle, parallel to a given chord is

• 5)

A circle can pass through

#### CBSE 10th Mathematics - Full Portion Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A motor boat whose speed is 24km/h in still water takes 1 hour more to go 32 km upstream than no return downstream to the same spot. Find the speed of the steam.

• 2)

If the pth terms of an AP is $\frac{1}{q}$ and the qth term is $\frac{1}{p}$, show that the sum of pq terms is $\frac{1}{2}$ (pq + 1).

• 3)

Check graphically, whether the following pair of linear equations is consistent. If yes, solve it graphically.
2x-y=0, x+y=0

• 4)

Solve the following pair of linear equations graphically:
2x + 3y = 12 and x - y = 1.
Find the area of the region bounded by the two lines representing the above equations and Y-axis.

#### CBSE 10th Mathematics - Full Portion Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

p2x2+(p2-q2)x-q2=0

• 2)

Find the roots of the following quadratic equation (if they exist) by the method of completing square $5x^{2} - 6x-2 = 0$ .

• 3)

Find the numbers of terms in A.P.: 5, 12, 19, 28, ....., 159.

• 4)

In the given figure, TBP and TCQ are tangents to the circle whose centre isO.Also $\angle PBA=60^0\ and \ \angle ACQ=70^0.$Determine $\angle BAC\ and \ \angle BTC.$

• 5)

In the given figure, if AB = AC, then prove that BC = 2CE.

#### CBSE 10th Mathematics - Full Portion Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Check whether the following are quadratic equations: x2-2x=(-2)(3-x)

• 2)

Check whether the following are quadratic equations: (2x-1)(x-3)=(x+5)(x-1)

• 3)

Find the roots of the following quadratic equation, if they exist, by the method of completing the square: 2x2+x+4=0

• 4)

Out of a group of children, ${7\over 2}$ times the square root of the number are creative, the two remaining ones are visionary. What is the total number of children ? How many persons in the group are creative?
Write one-one characteristics each of creativity and vision.

• 5)

Solve for x : $\sqrt { 6x+7 } -(2x-7)=0$

#### 10th Standard CBSE Mathematics - Triangles Five Marks Model Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

If $\triangle ABC\sim \triangle DFE$$\angle A={ 30 }^{ ° }$$\angle C={ 50 }^{ ° }$ , AB = 5 cm, AC = 8 cm and DF = 75 cm, then find DE and $\angle F$

• 2)

If the areas of two similar triangles are respectively 81 cm2 and 49 cm Find the ratio of their corresponding medians.

• 3)

If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, find the length of the sides of the rhombus.

• 4)

E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF || QR. PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm

• 5)

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

#### 10th CBSE Mathematics - Introduction to Trigonometry Four Marks Model Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

If sinA=$\frac {12}{13}$ , what is the value of cos A?

• 2)

If $\sqrt { 3 } \sin { \theta } =\cos { \theta }$, find the value of $\frac { \tan { \theta } (1+\cot { \theta } ) }{ \sin { \theta } +\cos { \theta } } .$

• 3)

Find the value of $(\sin { { 30 }^{ 0 } } +\cos { { 30 }^{ 0 } } )-(\sin { { 60 }^{ 0 } } +\cos { { 60 }^{ 0 } } ).$

• 4)

Evaluate ${ \left( \frac { \sin { { 25 }^{ 0 } } }{ \cos { { 65 }^{ 0 } } } \right) }^{ 2 }+{ \left( \frac { \tan { { 65 }^{ 0 } } }{ \cot { { 25 }^{ 0 } } } \right) }^{ 2 }-2\cos ^{ 2 }{ { 45 }^{ 0 } } .$

• 5)

Prove that $\frac { \sec ^{ 2 }{ \theta } -\sin ^{ 2 }{ \theta } }{ \tan ^{ 2 }{ \theta } } =1+\cot ^{ 2 }{ \theta } -\cos ^{ 2 }{ \theta }$

#### 10th CBSE Mathematics - Statistics Four Marks Model Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

Find the mean of the following distribution by direct method.

 Class interval Number of workers 0-10 10-20 20-30 30-40 40-50 7 10 15 8 10
• 2)

Using assumed mean method find the mean of the following frequency distribution.

 Class Frequency 63-65 66-68 69-71 72-74 75-77 4 3 7 8 3
• 3)

Find the mode of given data.

 Marks Frequency 0-10 10-20 20-30 30-40 40-50 20 24 40 36 20
• 4)

On sports day of a school, agewise participation of students is shown in the following distribution:

 Age in years Number of students 5-7 7-9 9-11 11-13 13-15 15-17 17-19 x 15 18 30 50 48 x

Find the mode of the data. Also, find missing frequencies when sum of frequencies is 181.

• 5)

The following table gives the literacy rate (in %) of 25 cities.

 Literacy rate Number of cities 50-60 60-70 70-80 80-90 9 6 8 2

Find the median class and modal class.

#### 10th Standard CBSE Mathematics - Pair of Linear Equation in Two Variables Four Marks Model Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

Five years ago, Jacob's age was seven times that of his son. After five years, the age of Jacob will be three times that of his son. Represent this situation algebraically and graphically.

• 2)

Solve graphically the following pair of equations.
2x-y+3=0 and 3x-5y+1=0

• 3)

Two straight paths are represented by the lines 7x-5y=3 and 21x-15y=5. Check whether the paths cross each other.

• 4)

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.

• 5)

In $\triangle ABC,\quad \angle C=5\angle B=3(\angle A+\angle B)$ find all angles of $\triangle ABC$ .

#### 10th CBSE Mathematics - Polynomials Four Marks Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

Find the degree of the following polynomial
(i) $7y^{ 5 }+6y^{ 2 }-1$
(ii) $\frac { y^{ 4 }+3y^{ 2 }+y }{ y }$

• 2)

If 2 is a zero of polynomial f(x)=ax2-3(a-1)x-1, then find the value of a.

• 3)

Find the zeroes of quadratic polynomial y2+92y+1920.

• 4)

If α and β are the zeroes of the polynomial 2y2+7y+5, then find the value of α+β+αβ.

• 5)

Find the quadratic polynomial, whose sum of zeroes is 8 and their products is 12. Then, find the zeroes of the polynomial.

#### 10th Standard CBSE Mathematics - Surface Areas and Volumes Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A tent is in the shape of a cylinder surmounted by a conical top.If the height and diameter of the cylindrical part are 2.1m and 4m respectively, and the slant height of the top is 2.8m, find the area of the canvas used for making the tent.Find the cost of the canvas of the tent at the rate of Rs.500 per m2.Also find the volume air enclosed in the tent.

• 2)

A juice seller serves his customers using a glass as shown in figure.The inner diameter of the cylindrical glass is 5cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass.If the height of the glass is 10cm, find the apparent capacity of the glass and its actual capacity.[$\pi$=3.14]

• 3)

A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.

• 4)

Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of 80 cm/second into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour?

• 5)

Metal spheres, each of radius 2 cm are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of the liquid. [Use $\pi$ = 3.14]

#### 10th Standard CBSE Mathematics - Real Number Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Show that the square of an odd positive integer is of the form 8m + 1, where m is some whole number.

• 2)

Use Euclid's division algorithm to the HCF of the following three numbers.
(i) 441, 567 and 693
(ii) 1620, 1725 and 255

• 3)

If the LCM of 26 and 91 is 182. find their HCF.

• 4)

If the HCF of 150 and 100 is 50, find the LCM of 150 and 100.

• 5)

Without actually performing the long division, state whether $\frac{543}{225}$ has a terminating decimal expansion or non-terminating recurring decimal expansion.

#### 10th Standard CBSE Mathematics - Polynomials Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find the zeroes of quadratic polynomial y2+92y+1920.

• 2)

If zeroes α and β of a polynomial x2-7x+k are such that α-β=1, then find the value of k.

• 3)

If α and β are the zeroes of the quadratic polynomial f(x)=3x2-5x-2, then evaluate α33.

• 4)

If α and β are zeroes of the quadratic polynomial p(x)=6x2+x-1, then find the value of $\frac { \alpha }{ \beta } +\frac { \alpha }{ \alpha } +2\left( \frac { 1 }{ \alpha } +\frac { 1 }{ \beta } \right) +3\alpha \beta$

• 5)

On dividing polynomial p(x) by 3x+1, the quotient is 2x-3 and the remainder is -2. Find p(x).

#### CBSE 10th Mathematics - Pair of Linear Equation in Two Variables Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Solve graphically, the pair of linear equations x-y=-1 and 2x+y-10=0. Also, find the vertices of the triangle formed by these lines and X-axis.

• 2)

Solve graphically, the pair of linear equations 3x+y-11=0,x-y-1=0. Also, find the vertices of the triangle formed by these lines and Y-axis.

• 3)

Two straight paths are represented by the lines 7x-5y=3 and 21x-15y=5. Check whether the paths cross each other.

• 4)

The sum of the digits of a two-digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.

• 5)

The area of a rectangle gets reduced by 80 sq units, if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, then the area is increased by 50 q units. Find the length and the breadth of the rectangle.

#### 10th Standard CBSE Mathematics - Triangles Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, find the length of the sides of the rhombus.

• 2)

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?

• 3)

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.

• 4)

Find the value of unknown variables, if $\triangle ABC$ and $\triangle PQR$are similar.

• 5)

In $\triangle PQR$ and $\triangle MST$ , $\angle P={ 55 }^{ ° }$$\angle Q={ 25 }^{ ° }$$\angle M={ 100 }^{ ° }$ and $\angle S={ 25 }^{ ° }$. Is $\triangle QPR\sim \triangle TSM$ ? Why?

#### 10th Standard CBSE Mathematics - Introduction to Trigonometry Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

If sin C=$\frac {15}{17}$ , find the value of sin A.

• 2)

In a $\triangle ABC,\angle B={ 90 }^{ 0 }$ If AB=2 cm and AC=3 cm, find the value of sin A,

• 3)

If 17 cosA = 8, find 15 cosecA - 8 sec B.

• 4)

Find the value of
(i) $\sin { \theta } \cos { \theta }$   for $\theta ={ 30 }^{ 0 }$
(ii) $3\tan ^{ 2 }{ { 45 }^{ 0 } } +2\sin { { 45 }^{ 0 } } \cos { { 45 }^{ 0 } }$

• 5)

If $\sin { \theta } -\cos { \theta } =0,(0\le \theta \le { 90 }^{ 0 })$ find the value of $\theta$ .

#### 10th Standard CBSE Mathematics - Statistics Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

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

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

Find the mode of given data.

 Marks Frequency 0-10 10-20 20-30 30-40 40-50 20 24 40 36 20
• 3)

Compute the median marks for the following data.

Marks Number of students
0 and above 50
10 and above 46
20 and above 40
30and above 20
40 and above 10
50 and above 3
60and above 0
• 4)

If the coordinates of the point of intersection of less than ogive and more than ogive is (12.5,20) then find the value of median.

• 5)

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

 Number of days Number of students 0-6 6-10 10-14 14-20 20-28 28-38 38-40 11 10 7 4 4 3 1

#### 10th Standard CBSE Mathematics - Areas Related to Circles Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. If bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/s, then calculate the number of complete revolutions the wheel makes in raising the bucket.

• 2)

In fig., PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flowers beds (shaped parts).

• 3)

The long and short hands of a clock are 6 cm and 3 cm respectively. Find the sum of distance travelled by their tips in a day.

• 4)

A bus has wheels which are 112 cm in diameter. How many complete revolutions does each wheel make in 20 minutes, when the bus is travelling at a speed of 66 km/h?

• 5)

A road which is 7 m wide surrounds a circular track whose circumference is 352 m. Find the area of the road.

#### CBSE Mathematics 10th - Coordinate Geometry Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find the points of trisection of the line segment determined by (7,5) and (16,-1).

• 2)

Find the coordinates of the points o trisection of the line segment joining the points A(2,-2) and B(-7,4)

• 3)

Find the coordinates of the points P,Q and R which divide the line segment joining A(5,4) and B(11,6) into four equal parts.

• 4)

In what ratio does the point (-4,6) divide the line segment joining the point A(-6,10) and B(3,-8)?

• 5)

Find the value of p for which the points (3,6), (7,p) and (-5,2) are collinear.

#### 10th Standard CBSE Mathematics - Probability Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A coin is tossed. If it results in a head a coin is tossed, otherwise a die is thrown. Describe the following events:
(i) A = getting atleast one head
(ii) B = getting an even number
(iii) C = getting a tail
(iv) D = getting a tail and an odd number

• 2)

20 cards numbered 1, 2, 3, ...., 20 are put in a box and mixed thoroughly. Shashi draws a cards from the box. Find the probability that the number on the card is

(i) odd    (ii) even  (iii) a prime

(iv) divisible by 3    (v) divisible by 3 and 2 both.

• 3)

At a fete cards bearing numbers 1 to 500, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number the player wins prize.

(i) What is the probability that the first player wins a prize?

(ii) The second player wins prize, if the first has not won.

• 4)

A letter is at drawn at random from the word 'MATHEMATICS'.Find the probability of drawing each of the different letters in the given word.

• 5)

A box of 24 solar cells contain 8 defective cells.One cell is drawn at random.What is the probability that the cell is not defective and it is not replaced and a second cell is selected at random from the rest, what is the probability that second cell is defective?

#### 10th Standard CBSE Mathematics - Some Applications of Trigonometry Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of the bird, from a point on the ground is 45o . The bird flies away from the point of observation horizontally and remains at a constant height. After 2 seconds, the angle of elevation of the bird from the point of observation becomes 30o . Find the speed of flying of the bird.

• 2)

At the foot of a mountain, the elevation of its summit is 45o . After ascending 1000 m towards the mountain up a slope of 30o inclination, the elevation is found to be 60o . Find the height of the mountain.

• 3)

A path separates two walls. A ladder leaning against one wall rests at a point on the path. It reaches a height of 90 m on the wall and makes an angle of 60o with the ground. If while resting at the same point on the path, it were made to lean against the other wall, it would have made an angle of 45o with the ground. Find the height it would have reached on the second wall.

• 4)

Two stations due south of a leaning tower which leans towards north are at distances a and b from its foot. If $\alpha$ and $\beta$ be the elevation  of the top of the tower from these stations, prove that its inclination $\theta$ to the horizontal is given by $cot\theta =\frac { b\quad cot\alpha -a\quad cot\beta }{ b-a }$.

• 5)

From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometre stones on the opposite sided of the aeroplane are found to be $\alpha$ and $\beta$, show that the height of the aeroplane is $\frac { tan\alpha tan\beta }{ tan\alpha +tan\beta }$.

#### 10th Standard CBSE Mathematics - Constructions Fours Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Draw an isosceles triangle ABC in which AB = AC = 6cm and BC = 5cm. Construct a triangle PQR similar to $\triangle ABC$ in which PQ = 8cm.  Also justify the construction.

• 2)

Draw a $\Delta ABC$ with sides BC = 6cm, AB = 5cm and $\angle ABC=60°$, Then, construct a triangle whose sides are 3/4 of the corresponding sides of the $\Delta ABC$

• 3)

Draw two equal circles with centres A and B and distance between A and B is 6 cm. Construct a pair of tangents from centres A and B to each other. Measure the lengths of the tangents. What type of 31. figure is enclosed by these four tangents?

• 4)

Draw a circle of radius 3.5 cm. Take a point T out side the circle at a distance of 7 cm from the centre and construct a pair of tangents from this point T to the circle and justify your construction.

#### 10th Standard CBSE Maths - Real Number Four Mark Model Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

A number when divided by 53 gives 34 as quotient and 21 as remainder. Find the number.

• 2)

The product of two consecutive positive integers is divisible by 2. Is this statement true or false? Give reason.

• 3)

Use the Euclid's division algorithm to find the HCF of
(i) 650 and 1170
(ii) 870 and 225

• 4)

If two positive integers p and q can be expressed as p = ab2 and q = a3b; where a,b being prime numbers, find the LCM (p,q)

• 5)

Find the HCF and LCM of 60, 84 and 108 by using the prime factorisation method.

#### 10th CBSE Mathematics - Surface Areas and Volumes Four Mark Model Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder.If the height of the cylinder is 20cm and radius of the base is 3.5cm, find the total surface area of the article.

• 2)

A juice seller serves his customers using a glass as shown in figure.The inner diameter of the cylindrical glass is 5cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass.If the height of the glass is 10cm, find the apparent capacity of the glass and its actual capacity.[$\pi$=3.14]

• 3)

A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.

• 4)

A tent consists of a frustum of cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum are 14 m and 26 m respectively, the height of the frustum is 8 m and the slant height of the surmounted conical portion is 12 m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal.)

• 5)

A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled into it. The diameter of the pencil is 7 mm; the diameter of the graphite is 1 mm and the length of the pencil is 10 cm. Calculate the weight of the whole pencil if the specific gravity of the wood is 0.7 g/cm3 and that of the graphite is 2.1 g/cm3 .

#### 10th Standard CBSE Mathematics - Circles Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

In figure, the sides AB, BC and CA of triangle ABC touch a circle with centre O and radius r at P, Q and R respectively.Prove that
(i) AB + CQ = AC + BQ
(ii)area ($\Delta$ABC) = $1\over2$ (perimeter of $\Delta$ABC) x r

• 2)

Two circles touch each other externally at C.AB and CD are two common tangents.If D lies on AB such that CD=6cm, then find AB.

• 3)

QR is a tangent Q.PR||AQ, where AQ is a chord through A and P is a centre, the end point of the diameter AB.Prove that BR is tangent at B.

• 4)

In the given figure, the diameters, of two wheels have measures 4cm and 2cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angles.

• 5)

With the vertices of a triangle ABC as centres, three circles are described each touching the other two externally. If the sides of the triangle are 4 cm, 6 cm, and 8 cm, find the radii of the circles.

#### 10th Standard CBSE Mathematics - Arithmetic Progressions Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find the sum of the integers between 100 and 200 that is not divisible by 9.

• 2)

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

• 3)

150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped the second day, four more workers dropped the third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed.

• 4)

Interior angles of a polygon are in AP. If the smallest angle is 120o and common difference is 5o , find the number of sides of the polygon.

• 5)

A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief?

#### 10th Standard CBSE Mathematics - Quadratic Equations Four Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find three consecutive positive integers whose product is equal to sixteen times their sum.

• 2)

Solve for x ${x-2\over x-3}+{x-4\over x-5}={10\over 3}, x\ne3,5$

• 3)

The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

• 4)

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

• 5)

Solve for x : $({{4x-3}\over2x+1})-10({2x+1\over4x-3})=3; x\ne{-1\over2};x\ne{3\over4}$

#### CBSE 10th Standard Mathematics - Areas Related to Circles Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

The diameters of the front and rear wheels of tractor are 80 cm and 2 m respectively.  Find the number of revolutions that rear wheel will make to cover the distance which the front wheel covers in 1400 revolutions. [Use $\pi={22\over 7}$]

• 2)

An elastic belt is placed round the rim of a pulley of radius 5 cm. One point on the belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm away from O. Find the length of the belt that is in contact with the rim of the pulley. Also find the shaded area . ( Use $\pi =3.14,\sqrt { 3 } =1.73)$

• 3)

In fig., PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flowers beds (shaped parts).

• 4)

The long and short hands of a clock are 6 cm and 3 cm respectively. Find the sum of distance travelled by their tips in a day.

• 5)

Find the diameter of the circle, which has circumference equal to the sum of the circumference of two circles with radii 7 cm and 14 cm.

#### 10th CBSE Mathematics - Coordinate Geometry Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

The three vertices of a parallelogram ABCD are A(3,-4), B(-1,-3) and C(-6,2). Find the coordinates of vertex D and find the area of ABCD.

• 2)

In $\Delta PAB,$ PA=PB and area of $\Delta PAB=10$sq.units. Find the coordinates of P if coordinates of A and B are (1,2) and (3,8) respectively.

• 3)

A(0,3), B(-1,-2) and C(4,2) are vertices of a $\Delta ABC$. D is a point on the side BC such that ${BD\over DC}={1\over2}$. P is a point on AD such that $AP={2\sqrt5\over3}$units. Find coordinates of P.

• 4)

If A(-3,5), B(-2,-7), C(1,-8) and D(6,3) are the vertices of a quadrilateral ABCD, find its area.

• 5)

Find the values of k so that the area of the triangle with vertices (1,-1), (-4,2k) and (-k,-5) in 24sq.units.

#### 10th Standard CBSE Mathematics - Statistics Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find the mean of the following frequency distribution using assumed mean method.

 Class Frequency 2-8 8-14 14-20 20-26 26-32 6 3 12 11 8
• 2)

Find the mean of the following data, by using step deviation method.

 Class Frequency 10-20 20-30 30-40 40-50 50-60 60-70 4 28 15 20 17 16
• 3)

In a health checkup, the number of heart beats of  women were recorded in the following table

 Number of heart beats/minute Number of women 65-69 70-74 75-79 80-84 2 18 16 4

Find the mean of the data.

• 4)

An NGO working for welfare of cancer patients, maintained its records as follows:

 Age of patients (in years) Number of patients 0-20 20-40 40-60 60-80 35 315 120 50

find mode.

• 5)

If the mode of the following series is 54, then find the value of f.

 Class Frequency 0-15 15-30 30-45 45-60 60-75 75-90 3 5 f 16 12 7

#### 10th Standard CBSE Mathematics - Introduction to Trigonometry Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Evaluate cos230+ sin2450$\frac {1}{3}$ tan600.

• 2)

Find the value of $\frac { \cos { { 60 }^{ 0 } } +\sin { { 45 }^{ 0 } } -\cot { { 30 }^{ 0 } } }{ \tan { { 60 }^{ 0 } } +\sec { { 45 }^{ 0 } } -cosec{ 30 }^{ 0 } } .$

• 3)

If $2\cos { 3\theta } =\sqrt { 3 }$ find the value of $\theta$ .

• 4)

If sin (A – B) = $\frac{1}{2}$ cos (A + B) = $\frac{1}{2}$ 0° < A + B $\leq$ 90°, A > B, find A and B.

• 5)

If tan (3x + 300) = 1, find the value of x.

#### 10th Standard CBSE Mathematics - Triangles Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

If $\triangle ABC\sim \triangle PQR$, AB = 6.5 cm, PQ = 10.4 cm and perimeter of $\triangle ABC$ = 60 cm, find the perimeter of $\triangle PQR$.

• 2)

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.

• 3)

Find the value of the height 'h' in the adjoining figure. at which the tennis ball must be hit, so that it will just pass over the net and land 6 m away from the base of the net.

• 4)

In the given figure of $\triangle ABC$$DE\parallel AC$. If $DC\parallel AP$, where point P lies on BC produced, then prove that $\frac { BE }{ EC } =\frac { BC }{ CP }$.

• 5)

ABCD is a trapezium with $AB\parallel DC$. E and F are two points on non-parallel sides AD and BC respectively, such that EF is parallel to AB. Show that
$\frac { AE }{ ED } =\frac { BF }{ FC }$

#### CBSE 10th Mathematics - Pair of Linear Equation in Two Variables Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Solve the following pair of linear equations.
41x+53y=135 and 53x+41y=147

• 2)

If the lines given by 2x+Ky=1 and 3x-5y=7 has unique solution, then find the value of K.

• 3)

Find the value of 'k' for which the system of equations kx-5y=2; 6x+2y=7 has no solution.

• 4)

For what value of k, will the following pair of linear equations have infinitely many solutions?
2x+3y=4 and (k+2)x+6y=3k+2

• 5)

The sum of a two-digit number and number obtained by reversing the order of digits 99. If the digits of the number differ by 3, then find the numbers.

#### 10th Standard CBSE Mathematics - Polynomials Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find the value of 'a' if X+a is a factor (zero) of the polynomial 2x2+2ax+5x+10.

• 2)

If zeros of the polynomial x2+(a+1)x+b are 2 and -3, then find the value of (a+b).

• 3)

Find the zeros of the quadratic polynomial x2 +7x+10 and verify relationship between the zeros and the coefficients.

• 4)

Find a quadratic polynomial whose one zero is 7 and sum of zeroes is -18.

• 5)

If a and β are the zeroes of the quadratic polynomial p(x)=ax2+bx+c, then evaluate a2β+aβ2 .

#### 10th Standard CBSE Mathematics - Some Applications of Trigonometry Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60o . At a point Y, 40 m vertically above X, the angle of elevation is 45o . Find the height of the PQ and the distance XQ.

• 2)

The angle of elevation of a jet fighter from a point A on the ground is 60o . After a flight of 15 seconds, the angle of elevation changes to 30o. If the jet is flying at a speed of 720 km/hr, find the constant height. $(\sqrt { 3 } =1.732)$ .

• 3)

The angle of elevation of a cloud from a point 60 m above a lake is 30o and the angle of depression of the reflection of the cloud in the lake is 60o . Find the height of the cloud from the surface of the lake.

• 4)

At the foot of a mountain, the elevation of its summit is 45o . After ascending 1000 m towards the mountain up a slope of 30o inclination, the elevation is found to be 60o . Find the height of the mountain.

• 5)

The pilot of an aircraft flying horizontally at a speed of 1200 km/hr. observes that the angle of depression of a point on the ground changes from 30o to 45o in 15 seconds. Find the height at which the aircraft is flying.

#### 10th CBSE Mathematics - Probability Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 2, 2 3, 3, 4 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting (i) sum 7 (ii) sum is a perfect  square.

• 2)

In a game, the entry fee is Rs. 5. The game consists of tossing a coin 3 times. If one or two heads show, Shweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she
(i) loses the entry fee
(ii) gets double entry fee
(iii) just gets her entry fee

• 3)

A coin is tossed. If it results in a head a coin is tossed, otherwise a die is thrown. Describe the following events:
(i) A = getting atleast one head
(ii) B = getting an even number
(iii) C = getting a tail
(iv) D = getting a tail and an odd number

• 4)

At a fete cards bearing numbers 1 to 500, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number the player wins prize.

(i) What is the probability that the first player wins a prize?

(ii) The second player wins prize, if the first has not won.

#### CBSE 10th Mathematics - Real Number Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Write the HCF of the smallest composite number and the smallest prime number.

• 2)

Find the LCM and HCF of 120 and 144 by fundamental theorem of arithmetic.

• 3)

If HCF of two numbers is 2 and their product is 120, find their LCM.

• 4)

If the HCF of 35 and 45 is 5, LCM of 35 and 45 is 63 x a, then find the value of a.

• 5)

Show that $3\sqrt { 2 }$ is an irrational number.

#### 10th CBSE Mathematics - Surface Areas and Volumes Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A teak wood log is cut first in the form of a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is 1.104 m3. How many rectangular planks of size 2.3 m x 0.75 m x 0.04 m can be cut from the cuboid?

• 2)

A rectangular reservoir is 120 m long and 75 m wide. At what speed per hour must water flow into it through a square pipe of 20 cm wide so that the water rises by 2.4 m in 18 hours?

• 3)

The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of bucket is 5390 cm3, then find the value of r Use $\pi=\frac{22}{7}$

• 4)

An open metal bucket is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at Rs.30 per litre. [ $\pi=\frac{22}{7}$]

• 5)

Water flows in a tank 150 m x 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km/h. In what time will the water be 3 m deep?

#### CBSE 10th Mathematics - Areas Related to Circles Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

In fig., ABC is a right-angled triangle, right-angled at A.  Semicircles are drawn on Ab, Ac and BC as diameters.  Find the area of the shaded region.

• 2)

The area of an equilateral triangle in $49\sqrt3\ cm^2$.  Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle.  Find the area of triangle not included in the circles.$[Take\ \sqrt3=1.73]$

• 3)

Find the area of the shared region in figure, where a circular arc of radius 7 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm, as centre.

• 4)

In given figure, an equilateral triangle has been inscribed in a circle of radius 6 cm.  Find the area of the shaded region.  $[Use\ \pi=3.14]$

• 5)

The inner perimeter of a racetrack is 400 m and the outer perimeter is 488 m.  The length of each straight portion is 90 m.  Find the cost of developing the track at the rate of $Rs. \ 12.50/m^2$

#### CBSE 10th Mathematics - Coordinate Geometry Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Show that the points (7,10), (-2,5) and (3,-4) are the vertices of an isosceles right triangle.

• 2)

Show that points A(7,5),B(2,3) and C(6,-7) are the vertices of a right triangle. Also find its area.

• 3)

Point P divides the line segment joining the points A(2,1) and B(5,-8) such that ${AP\over AB}={1\over 3}$. If P lies on the 2x-y+k=0, find the value of k.

• 4)

The line segment AB joining the points A(3,-4) and B(1,2) is trisected at the points P(p,-2) and Q(5/3,q). Find the values of p and q.

• 5)

If R(x,y) is a point on the line segment joining the points P(a,b) and Q(b,a) then prove that x+y=a+b

#### 10th Standard CBSE Mathematics - Probability Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square.

• 2)

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing : (i) an ace (ii) '2' spades  (iii) '10' of a black suit

• 3)

Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is
(i) an even number    (ii) a number less than 14
(iii) a number which is a perfect square  (iv) a prime number less than 20.

• 4)

A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9. Find the probability that the selected number is their average.

• 5)

If a number x is chosen from the number 1, 2, 3 and a number y is selected from the numbers 1, 4, 9. Find the probability that xy = 10.

#### CBSE 10th Standard Mathematics - Constructions Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

Two line segments AB and AC include an angle of $60^o$ where AB = 5 cm and AC = 7 cm.  Locate points P and Q on AB and AC, respectively such that $AP={3\over 4}$ AB and $AQ={1\over 4}AC.$ Join P and Q and measure the length PQ.

• 2)

Draw an isosceles triangle ABC in which AB = AC = 6cm and BC = 5cm. Construct a triangle PQR similar to $\triangle ABC$ in which PQ = 8cm.  Also justify the construction.

• 3)

Draw two tangents from the end points of the diameter of a circle of radius 4.0 cm. Are these tangents parallel?

• 4)

Draw a $\triangle$ABC with BC = 7 cm, $\angle B=45°$  and $\angle C=60°$. Then, construct another triangle, whose sides are $\frac { 3 }{ 5 }$  times of the corresponding sides of $\Delta ABC$ and justify your construction.

• 5)

Draw a right-angled triangle, in which the sides (other than the hypotenuse) are lengths 8 cm and 6 cm. Then, construct another triangle, whose sides are $\frac { 3 }{ 4 }$  times of the corresponding sides of  given triangle. Justify your construction.

#### 10th Standard CBSE Mathematics - Circles Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

In the figure, AB is diameter of a circle with centre O and QC is a tangent to the circle at C.If $\angle CAB=30^0,\ find \ \angle CQA\ and \angle CBA.$

• 2)

In figure, PA are two tangents drawn from an external point P to a circle with centre O.Prove that OP is the right bisector of line segment AB.

• 3)

AB is a chord of length 24cm of a circle of radius 13cm.The tangents at A and B intersect at a point C.Find the length AC.

• 4)

Two circles with centres O and O' of radii 3cm and 4cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles.Find the length of the common chord PQ.

• 5)

In figure, the common tangent, AB and CD are tangents to two circles with centres O and O' intersect at E. Prove that the points O, E, O' are collinear.

#### 10th Standard CBSE Mathematics - Arithmetic Progressions Five Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

• 2)

Find the sum: $\frac{a - b}{a + b}+\frac{3a - 2b}{a + b}+\frac{5a - 3b}{a + b}+...$ to 11 terms.

• 3)

In the following A.P., find the missing term: 9, ...., ...., ....., 25

• 4)

Find the sum of the first 50 odd natural numbers.

• 5)

If the sum of first p terms of an AP is q and the sum of first q terms is p, then find the sum of first (p + q) terms.

#### 10th Standard CBSE Mathematics - Quadratic Equations Five Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

• 1)

If $\alpha, \beta$ are roots of the equation 2x2-6x+a=0 and $2\alpha+5\beta=12$ find the value of a.

• 2)

Solve for x: $x^2+5x-(a^2+a-6)=0$

• 3)

If twice the area of a smaller square is subtracted from the area of the larger square.the result is $14cm^{ 2 }$ However, if twice the area of the larger square is added to three times the area of the smaller square. the result is $203cm^{ 2 }$ .Find the sides of the two square.

• 4)

In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in maths and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.

• 5)

In a flight of 2800km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100km/h and time increased by 30 minutes. Find the original duration of the flight.

#### 10th Standard CBSE Mathematics - Some Applications of Trigonometry Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A statue 1.46 m tall stand on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60o and from the same point, the angle of elevation of the top of the pedestal is 45o . Find the height of the pedestal. $(\sqrt { 3 } =1.73)$ .

• 2)

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angles of elevation of the top and bottom of the flag pole are 60o and 30o respectively. Find the heights of the tower and flag pole mounted on it.

• 3)

A ladder of length 6 m makes an angle of 45o with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60o with the floor. Find the distance between these two walls of the room.

• 4)

The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30o . If the height of the second pole is 24 m, find the height of the first pole. $(Use\sqrt { 3 } =1.732)$

• 5)

The length of the shadow of a tower standing on level ground is found to 2 x metre longer when the sun's altitude is 30o than when it was 45o. Prove that the height of tower is $x(\sqrt { 3 } +1)$ metres.

#### 10th Standard CBSE Mathematics - Constructions Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Draw an isosceles $\triangle ABC$ in which $BC=5.5cm$ and altitude AL = 3cm.  Then construct another triangle whose sides are $3\over 4$ of the corresponding sides of $\triangle ABC$.

• 2)

Draw a line segment AB of length 7 cm.  Taking A as centre, draw a circle of radius 3 cm and taking B as Centre, draw another circle of radius 2 cm.  Construct tangents to each circle from the centre of the other circle.

• 3)

Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its centre.

• 4)

Draw an equilateral $\Delta ABC$ of each side 4 cm.Construct a triangle similar to it and of scale factor $\frac{3}{5}$.Is the new triangle also an equilateral?

#### CBSE 10th Mathematics - Circles Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

• 2)

In the given figure, ABC is a right-angled triangle, right angled at A, with AB =6cm and AC=8cm.A circle with centre O has been inscribed inside the triangle Calculate the value of r, the radius of the inscribed circle.

• 3)

ABC is a right-angled triangle, right angled at A.A circle is inscribed in it.The lengths of two sides containing the angle are 24cm and 10cm.Find the radius of the incircle.

• 4)

In two concentric circles, a chord of length 24 cm of larger circle becomes a tangent to the smaller circle whose radius is 5 cm. Find the radius of the larger circle.

• 5)

AB is a diameter of a circle. AH and BK are perpendicular from A and B respectively to the tangent at P.Prove that AH + BK = AB.

#### CBSE 10th Mathematics - Arithmetic Progressions Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

If 9th term of an AP is zero, prove that its 29th term is double of its 19th term.

• 2)

Find the value of the middle term of the following AP: -6, -2, 2, ....., 58

• 3)

Determine the AP whose fourth term is 18 and the difference of the ninth term from the fifteenth term is 30.

• 4)

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

• 5)

The 2nd, 31st and the last term of an AP are 7$\frac{3}{4}$$\frac{1}{2}$ and -6$\frac{1}{2}$, respectively. Find the first term and number of terms.

#### CBSE 10th Mathematics - Quadratic Equations Three Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A 2-digit number is such that product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

• 2)

If the price of a book is reduced by Rs.5, a person can buy 5 more books for Rs.300. Find the original list price of a book.

• 3)

If a and b are roots o the equation 2x2+7x+5=0 then write a quadratic equation whose roots are 2a+3 and 2b+3

• 4)

Find the positive value of k, for which the equations x2+kx+64=0 and x2-8x+k=0 will both have real roots.

• 5)

In the following equations determine the set of values of p for which the given equation has real roots: px2+4x+1=0

#### 10th Standard CBSE Mathematics - Polynomials Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

If the product of the zeroes of the polynomial (ax2-6x-6) is 4, then find the value of a.

• 2)

If one zero of the polynomial (a2+9)x2+13x+6a is a reciprocal of the other, then find the value of a.

• 3)

Find the zeroes of the quadratic polynomial 3x2+11x-4, then find the value of  $\frac { m }{ n } +\frac { n }{ m }$ .

• 4)

If m and n are the zeroes of the polynomial 3x2+11x-4, then find the value of $\frac { m }{ n } +\frac { n }{ m }$ .

• 5)

The sum and the product of a zeroes of the polynomial f(x)=4x2-27x+3k2 are equal. Find the value of k.

#### 10th CBSE Mathematics - Pair of Linear Equation in Two Variables Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find a, if the line 3x+ay=8 passes through the intersection of lines represented by equations 3x-2y=10 and 5x+y=8.

• 2)

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.

• 3)

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.

• 4)

Solve the following pair of equations by elimination method.
2x+3y-5=0; 3x-2y-14=0

• 5)

Solve the following pair of equations by elimination method.
3x+2y=7; 2x-5y+8=0

#### 10th CBSE Mathematics - Triangles Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

In the given figure, $\triangle ACB={ 90 }^{ ° }$ and $CD\bot AB$ . Prove that $\frac { { BC }^{ 2 } }{ { AC }^{ 2 } } =\frac { BD }{ AD }$

• 2)

A girl of height 100 cm is walking away from the base of a lamppost at a speed of 1.9 m/s. If the lamp is 5 m above the ground, find the length of her shadow after 4s.

• 3)

In an equilateral triangle of side$3\sqrt { 3 } cm,$ find the length of the altitude.

• 4)

In the given figure, OA = 3 cm, OB = 4 cm, $\angle$AOB = 90$\unicode{xb0}$, AC = 12 cm and BC = 13 cm, prove that $\angle$CAB = 90$\unicode{xb0}$.

• 5)

In an equilateral triangle of side 24 cm, find the length of the altitude.

#### CBSE 10th Mathematics - Introduction to Trigonometry Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

If $\sec ^{ 2 }{ \theta } =x+\frac { 1 }{ 4x } ,$ find the value of $\sec { \theta } +\tan { \theta } .$

• 2)

Prove that $\sqrt { \sec ^{ 2 }{ \theta } +{ cosec }^{ 2 }\theta } =\tan { \theta } +\cot { \theta } .$

• 3)

Eliminate  $\theta$ from the following equation. $x=a\sec { \theta } ,y=b\tan { \theta }$

• 4)

Using the formula, $\cos { A } =\sqrt { \frac { 1+\cos { 2A } }{ 2 } } ,$ find the value of $\cos { { 15 }^{ 0 } }$

• 5)

If $\sqrt { 3 } \cot ^{ 2 }{ \theta } -4\cot { \theta } +\sqrt { 3 } =0,$ find the value of the $\tan ^{ 2 }{ \theta } +\cot ^{ 2 }{ \theta } .$

#### 10th Standard CBSE Mathematics - Statistics Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Construct the frequency distribution table for the given data.

Marks Number of students
Less than 10 14
Less than 20 22
Less than 30 37
Less than 40 58
Less than 50 67
Less than 60 75
• 2)

Find the mean of the data using an empirical formula when it is given that mode is 50.5 and median in 45.5

• 3)

The regarding marks obtained by 48 students of a class in a class test is given below. Calculate the modal marks of students.

 Marks Obtained Number of students 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 1 0 2 0 0 10 25 7 2 1
• 4)

Given below is the distribution of weekly pocket money received by students of a class. Calculate the pocket money that is received by most of the students.

 Pocket Money (in Rs) Number of students 0-20 20-40 40-60 60-80 80-100 100-120 120-140 2 2 3 12 18 5 2
• 5)

Find the mean of the following distribution

 Class Interval Frequency 0-6 6-12 12-18 18-24 24-30 5 4 1 6 4

#### 10th Standard CBSE Mathematics - Real Number Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Write the HCF and LCM of the smallest odd composite number and the smallest odd prime number. If an odd number p divides q2, then will it divide q3 also? Explain.

• 2)

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.

• 3)

If n is an odd integer, then show that n2 - 1 is divisible by 8.

• 4)

Find the LCM of x and y, if xy = 180 and HCF of (x, y) = 5

• 5)

Find (HCF x LCM) for the numbers 100 and 190.

#### 10th Standard CBSE Mathematics - Surface Areas and Volumes Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

A cubical block of side 7cm is surmounted by a hemisphere.What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

• 2)

A tent is in the shape of a cylinder surmounted by a conical top.If the height and diameter of the cylindrical part are 2.1m and 4m respectively, and the slant height of the top is 2.8m, find the area of the canvas used for making the tent.Also, find the cost of the canvas of the tent at the rate of Rs.500 per m2.(Note that the base of the tent will not be covered with canvas.)

• 3)

From a solid cylindrical whose height is 2.4cm and diameter 1.4cm, a conical cavity of the same height and same diameter is hollowed out.Find the total surface area of the remaining solid to the nearest cm2 .

• 4)

Rachel, an engineering student, was asked make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet.The diameter of the model is 3cm and its length is 12cm.If each cone has a height of 2cm, find the volume of air contained in the model that Rachel made.(Assume the outer and inner dimensions of the model to be nearly the same.)

• 5)

The sum of the radius of the base and the height of a solid cylinder is 37cm.If the total surface area of the of the solid cylinder is 1628cm2, find the volume of the cylinder.$[\pi=22/7]$

#### 10th Standard CBSE Mathematics Unit 8 Areas Related to Circles Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find the area of  a quadrant of a circle whose circumference is 22cm.

• 2)

The length of the minute hand of a clock is 14 cm.  Find the area swept by the minute hand in 5 minutes.

• 3)

Find the area of $\Delta$PQR such that $\angle$=900, PR=10cm and $\angle$ PRQ=300.[Take $\sqrt{3}=1.73$]

• 4)

• 5)

A circular is of diameter 1.5m.It is surrounded by a 2m wide path.Find the cost of constructing the path at the rate of Rs.25 per m2 .

#### CBSE 10th Mathematics Coordinate Geometry Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer. (4,5), (7,6), (4,3), (1,2)

• 2)

What point on the x-axis is equidistant from (7,6) and (-3,4)?

• 3)

Show that the following points are collinear: (2,-2),(-3,8) and (-1,4).

• 4)

An equilateral triangle has two vertices at the points (3,4) and (-2,3). Find the coordinates of the third vertex.

• 5)

Find the centre of a circle passing through (5,-8), (2,-9) and (2,1).

#### CBSE 10th Mathematics - Probability Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

• 2)

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

• 3)

A die is thrown once. Find the probability of getting
(i) a prime number.
(ii) a number lying between 2 and 6.
(iii) an odd number

• 4)

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that is bears
(i) a two digit number
(ii) a perfect square number
(iii) a number divisible by 5

• 5)

A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
(ii) 5 will come up at least once?
[Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment.]

#### 10th Standard CBSE Mathematics - Some Applications of Trigonometry Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30o . Find the height of the tower.

• 2)

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45o and 60o respectively. Find the height of the tower.

• 3)

The angle of elevation of the top of a building from the foot of a tower is 30o and the angle of elevation of the top of the tower from the foot of the building is 60o. If the tower is 50 m high, find the height of the building.

• 4)

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60o and the angle of depression of its foot is 45o. Determine the height of the tower.

• 5)

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30o , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60o . Find the time taken by the car to reach the foot of the tower from this point.

#### CBSE 10th Mathematics - Constructions Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Draw a triangle ABC with side BC = 7 cm,  Then, construct a triangle whose sides are ${4\over 3}$ times the corresponding sides of $\triangle ABC$

• 2)

Construct a triangle ABC in which  $AB=5\ cm, BC=6\ cm$ and $AC=7cm.$ Construct another triangle similar to $\triangle ABC$ such that its sides are $3\over 5$ of the corresponding sides of $\triangle ABC$.

• 3)

Draw line segment AB of length 8 cm.  Taking A as centre, draw a circle of radius 4cm and taking B as centre, draw another circle of radius 3cm.  Construct tangents to each circle from the centre of the other circle.

• 4)

Construct tangents to a circle of radius 3 cm from a point on concentric circle of radius 5 cm and measure its length.

• 5)

Draw two tangents from the end points of the diameter of a circle of radius 3.5 cm. After these tangents parallel?

#### 10th Standard CBSE Mathematics - Circles Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

• 2)

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

• 3)

In figure, $\Delta ABC$ is circumscribing a circle.Find the length of BC.

• 4)

In the given figure, RS is the tangent to the circle at L and MN is a diameter. If, determine $\angle RLM.$

#### CBSE 10th Mathematics Arithmetic Progressions Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Write first four terms of the AP, when the first term a and the common difference d are given as follows: a = -1, d = $\frac{1}{2}$

• 2)

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.. 2, $\frac{5}{2}$ , 3, $\frac{7}{2}$.......

• 3)

Which of the following are APs? If they form an AP, find the common difference d and write three more terms.
a, a2, a3, a4.......

• 4)

In the following APs, find the missing terms in the blanks:
........., 13, ..........., 3

• 5)

For what value of n, are the nth terms of two APs: 63, 65, 67,....... and 3, 10, 17,............ equal?

#### CBSE 10th Mathematics Unit 1 Quadratic Equations Two Marks Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Is x=-2 a solution of the equation x2-2x+8=0?

• 2)

Check whether the following equation is quadratic or not: : (x-1)(x=2)=x+3

• 3)

Is x=-4 a solution of the equation 2x2+5x-12=0

• 4)

Find the roots of the following quadratic equations by fractorisation: $2x^2-x+{1\over 8}=0$

• 5)

Find the roots of the following quadratic equations by applying the quadratic formula: 2x2+x-4=0

#### CBSE 10th Mathematics Unit 15 Statistics Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

If the median of a series exceeds the mean by 3, find by what number the mode exceeds its mean?

• 2)

In the following frequency distribution, find the median class.

 Height (in cm) 140-145 145-150 150-155 155-160 160-165 165-170 Frequency 5 15 25 30 15 10
• 3)

Find median of the data, using an empirical relation when it is given that Mode = 12.4 and Mean = 10.5.

• 4)

Consider the following distribution:

 Marks Obtained 0 or More 10 or More 20 Or More 30 Or More 40 Or More 50 Or More Number of students 63 58 55 51 48 42

(i) Calculate the frequency of the class 30 - 40.
(ii) Calculate the class mark of the class 10 - 25

• 5)

Which central tendency is obtained by the abscissa of point of intersection of less type and more than type ogives ?

#### CBSE 10th Mathematics Unit 14 Introduction to Trigonometry Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find the value of tan2 10° - cot2 80°.

• 2)

Find the value of sin2 41° + sin2 49°.

• 3)

An observer 1.2 metere tall is 28.2 m away from the tower.The angle of elevation of the top of the tower from his eye is 60°.What is the height of the tower?

• 4)

In given figure, if AB = 4 m and AC = 8 rn, then find the angle of elevation of A as observed from C.

• 5)

If the altitude of the Sun is 60°, what is the height of a tower which casts a shadow of length 30m?

#### CBSE 10th Mathematics Unit 13 Triangles Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

In the given figure, if $\angle$A=900$\angle$B=900, OB=4.5 cm, OA=6 cm and AP=4 cm, then find the QB.

• 2)

If ratio of corresponding sides of two similar triangles is 5 : 6, then find ratio of their areas.

• 3)

In given figure DE || BC. If AD=3 cm, DB=4 cm and AD=6 cm, then find EC.

• 4)

In the figure, PQ is parallel to MN. If $\frac { K }{ PM } =\frac { 4 }{ 13 }$ and KN=20.4 cm, then find KQ.

• 5)

If triangle ABC is similar to triangle DEF such that 2AB = DE and BC = 8 cm, then find EF.

#### CBSE 10th Mathematics Unit 12 Pair of Linear Equation in Two Variables Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Find whether the pair of linear equations y = 0 and y = -5 has no solution, unique solution or infinitely many solutions.

• 2)

If am=bl, then find whether the pair of linear equations ax + by = c and lx + my = n has no solutions, unique solution or infinitely many solutions.

• 3)

If ad $\neq$ bc, then find whether the pairs of linear equations ax + by = p and cx + dy = q has no solution, unique solution or infinitely many solutions.

• 4)

Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, then find the equation of the second line.

• 5)

Father's age is 3 times the sum of ages of his two children. After 5 yr, his age will be twice the sum of ages of the two children. Find the age of father.

#### CBSE 10th Mathematics - Polynomials Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Which of the following is not the graph of a quadratic polynomial?

• 2)

If $\alpha$ and $\beta$ are the roots of ax2 - bx + c = 0 $\left( a\neq 0 \right)$, then calculate $\alpha+\beta$.

• 3)

If sum of the zeroes of the quadatic polynomial 3x2 - kx + 6 is 3, then find the value of k.

• 4)

If - 1 is a zero of the polynomial f(x) = x2 - 7x - 8, then calculate the other zero.

• 5)

For a quadratic polynomial, whose one zero is 8 and the product of zeroes is -56.

#### CBSE 10th Mathematics - Real Number Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Explain why 13233343563715 is a composite number?

• 2)

a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Then calculate the least prime factor of (a + b).

• 3)

What is the HCF of the smallest composite number and the smallest prime number?

• 4)

Calculate the HCF of 33 x 5 and 32 x 52.

• 5)

If HCF (a, b) = 12 and a x b = 1,800, then find LCM (a, b).

#### CBSE 10th Mathematics - Surface Areas and Volumes Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Volume of a spherical shell = ...........

• 2)

If the surface area of a sphere is 6161 cm2, then its radius is equal to ...............

• 3)

If the ratio between the volume of two spheres is 27 : 8, then ratio between their surface areas is ..............

• 4)

All faces of a cuboid must be rectangular.

• 5)

Two cubes each of edge 10 cm, are joined end to end. The surface area of the resulting cuboid is 900 cm2.

#### 10th Standard CBSE Mathematics Unit 8 Areas Related to Circles Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

The perimeter of a sector of angle 90° of a circle with radius 14 cm is ...............

• 2)

A wheel has 42 cm diameter, the number of complete revolutions made to cover 792 m is .................

• 3)

The length of the minute hand of a clock is 14 cm. Find the area swept out by the minute hand in 1h.

• 4)

The sum of circumference and the radius of a circle is 51 cm. Find the radius of circle.

• 5)

Find the area of a quadrant of a circle, whose circumference is 22 cm.

#### 10th Standard CBSE Mathematics Unit 7 Coordinate Geometry Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Coordinate geometry is ........ tool for studying geometry.

• 2)

In the fourth quadrant for a point, the abscissa is ....... and the ordinate is ........

• 3)

If the point (0, 0), (1, 2) and (x, y) are collinear, then find x.

• 4)

A circle has its centre at the origin and a point P(5,0) lies on it. The point Q(6,8) lies outside the circle. State whether true or false. Justify your answer.

• 5)

Find the coordinates of the point which divides the line segment joining the points (4,-3) and (8,5) in the ratio 3:1 internally.

#### 10th Standard CBSE Mathematics Unit 6 Probability Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

Sum of the probabilities of each outcome in an experiment is...........

• 2)

Probability of getting 6 with single die is.........

• 3)

Probability of getting a prime number in single throw of a die is.....

• 4)

The sum of probabilities of all the outcomes of an experiment is greater than one.

• 5)

For an event $E,\ P(\overset { - }{ E } )=1-P(E)$ .

#### 10th Standard CBSE Mathematics Unit 5 Some Applications of Trigonometry Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

The length of the shadow of a tree 8m high, when the sun's elevation is 450 , is .......

• 2)

A 6m tall tree casts a shadow of length 4m.If at the same time  a flagpole casts a shadow 50m in length, then the length of the flagpole is...........

• 3)

The length of the shadow of a tree 10 high, when the sun's elevation is 300 , is ..........

• 4)

A 6m long pole casts a shadow of 4m long.At the same time a tree casts a shadow of 28m long, then length of tree is.......

• 5)

If the horizontal distance between the two trees 20m and 28m high is 15m, then distance between their tops is........

#### 10th Standard CBSE Mathematics Unit 3 Circles Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

The common point of the tangent and the circle is called

• 2)

A line segment drawn through the end of a radius and perpendicular to it, is a ___________to the circle.

• 3)

In the given figure, AOB is a diameter of the circle with centre O and AC is a tangent to the circle at A. If $\angle BOC$ = 130°, then find $\angle ACO$

• 4)

In the given figure, PQ and PR are tangents to the circle with centre O such that $\angle QPR={ 50 }^{ ° }$then find $\angle OQR$

• 5)

A circle can have maximum two tangents.

#### 10th Standard CBSE Mathematics Unit 4 Constructions Book Back Questions - by Abhimanyu - Bhopal - View & Read

• 1)

The ratio of the sides of the triangle to be constructed with the corresponding sides of the given triangle is known as their ____________

• 2)

The difference of any two sides of a triangle is always __________ than the third side.

• 3)

The sum of any two sides of a triangle is always _____________ than the third side.

• 4)

A Segment AB is divided at point P such that $\frac { PB }{ AB } =\frac { 3 }{ 7 }$ then find the radio AP : PB.

• 5)

At least three parts are sufficient for construction of a triangle.

### CBSE Education Study Materials

#### 10th CBSE Mathematics 2019 - 2020 Academic Syllabus - by Abhimanyu - Bhopal Aug 21, 2019 Aug 21, 2019

Mathematics 2019 - 2020 Academic Syllabus

#### Top Tips to score 100/100 in CBSE 10th Mathematics - by ADMIN-ENGLISH Jan 23, 2019 Jan 23, 2019

Scoring a perfect 100 might not be that easy, but it is not impossible. Mathematics is a subject ...

#### Best exam strategy to get full marks in 10th Mathematics - by ADMIN-ENGLISH Jan 23, 2019 Jan 23, 2019

Maths is a subject that demands patience, persistence and practice. Aim to solve at least 10-20 q...

#### Most Useful tips to secure 10 CGPA in 10th Mathematics - by ADMIN-ENGLISH Jan 23, 2019 Jan 23, 2019

Mathematics is the easiest and high-scoring subject if you are clear with the concepts. Start pra...

#### CBSEStudy Material - Sample Question Papers with Solutions for Class 10 Session 2019 - 2020

Latest Sample Question Papers & Study Material for class 10 session 2019 - 2020 for Subjects Science, Social Science, English , Hindi in PDF form to free download [ available question papers ] for practice. Download QB365 Free Mobile app & get practice question papers.

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