9th Standard CBSE Mathematics Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 9 Session 2019 - 2020 CBSE [ Chapter , Marks , Book Back, Creative & Term Based Questions Papers - Syllabus, Study Materials, MCQ's Practice Tests etc..]

CBSE 9th Mathematics - Probability Model Question Paper - by Harjeet - Indore - View & Read

• 1)

What is the number of outcomes when a coin is tossed?

• 2)

What is the number of outcomes when a cubical dice is thrown?

• 3)

Probability of impossible event is:

• 4)

A coin is tossed 200 times.The head appears 79 times.The probability of a tail is:

• 5)

When a coin is tossed 500 times, the following outcomes were recorded:
Head: 235 times, Tail: 265 times
If now a coin is tossed once again, the probability of getting a Tail is

CBSE 9th Mathematics - Statistics Model Question Paper - by Harjeet - Indore - View & Read

• 1)

Statistics is branch of

• 2)

When the information is gathered from a source which already had the information stored, the data obtained is called

• 3)

Class mark =

• 4)

In the distribution, the frequency of the class 0 - 5 is
0,3,2,5,8,10,13,5,6,6,14,0.

• 5)

The width of the class interval 70.5 - 75.5 is

CBSE 9th Mathematics - Surface Areas and Volumes Model Question Paper - by Harjeet - Indore - View & Read

• 1)

Identify the wrong statement of the following:

• 2)

The number of edges of a cube are

• 3)

If the edges of a cuboid are l, b and h respectively, then the total surface area of the cuboid is

• 4)

The area of the four walls of a room is 300 m2. Its length and height are 15 m and 6 m respectively. Find its breadth.

• 5)

The area of the four walls of a room is 80 cm2 and its height is 4 m. Then, the perimeter of the floor of the room is

CBSE 9th Mathematics - Heron's Formula Model Question Paper - by Harjeet - Indore - View & Read

• 1)

Base of a triangle =

• 2)

The side of an isosceles right triangle of hypotenuse $5\sqrt { 2 }$ cm is

• 3)

The area of an equilateral triangle is $16\sqrt { 3 }$ m2.Its perimeter (in meters) is

• 4)

The diagonals of a rhombus are 10 cm and 8 cm.Its area is

• 5)

Heron's formula is

CBSE 9th Mathematics - Constructions Model Question Paper - by Harjeet - Indore - View & Read

• 1)

Bisector of an angle divides it in to_______equal parts

• 2)

If a 60o angle is bisected twice,what will be measure of each that is constructed?

• 3)

In the figure below,PR is the perpendicular bisectors of a line segment AB=16 cm.Is PA=PB true?

• 4)

Construct ∠POY=30 o. using compass and ruler.

• 5)

Construct an angle of 15o

CBSE 9th Mathematics - Circles Model Question Paper - by Harjeet - Indore - View & Read

• 1)

The centre of a circle lies

• 2)

Equal chords of a circle subtend equal angles at

• 3)

Given a circle with centre O and smallest chord AB is of length 6 cm and the longest chord CD of the circle is of length 10 cm, then the radius of the circle is:

• 4)

In figure, if OA = 5 cm, AB = 8 cm and OD丄AB then CD is equal to:

• 5)

Equal chords of a circle are equidistant from

CBSE 9th Mathematics - Areas of Parallelograms and Triangles Model Question Paper - by Harjeet - Indore - View & Read

• 1)

The areas of a parallelogram and a triangle are equal and they lie on the same base. If the altitude of the parallelogram is 2 cm, then the altitude of triangle is

• 2)

In the figure, the area of parallelogram PQRS is:

• 3)

In the following figure, find the area of quad. ABCD.

• 4)

Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is

• 5)

If a rectangle and a square stand on the same base and between the same parallels, then the ratio of their areas is

9th Standard CBSE Mathematics - Quadrilaterals Model Question Paper - by Harjeet - Indore - View & Read

• 1)

Each angle of a rectangle is

• 2)

If in a quadrilateral, two pairs of adjacent sides are equal, then it is called a

• 3)

In the following figure the measure of $\angle$DAB is

• 4)

The angles of a quadrilateral are in the ratio 2 : 3 : 6 : 7. The largest angle of the quadrilateral is

• 5)

Two consecutive angles of a parallelogram are in the ratio 1 : 3, then what will be the smaller angles?

9th Standard CBSE Mathematics - Triangles Model Question Paper - by Harjeet - Indore - View & Read

• 1)

'Tri' means

• 2)

Two circles are congruent.If the radius of one circle is 3cm, what is the radius of the other circle?

• 3)

Two circles are congruent.If the radius of one circle is 1cm, then the diameter of the other circle is

• 4)

ΔABC≅ΔPQR.If AB=5cm, ㄥB=400and ㄥA=800, then which of the following is true?

• 5)

In two triangles ABC and DEF, ㄥA = ㄥD, ㄥB = ㄥE and AB = EF, then are the two triangles congruent? If yes, by which congruency rule?

CBSE 9th Mathematics - Lines and Angles Model Question Paper - by Harjeet - Indore - View & Read

• 1)

An obtuse angle

• 2)

An right angle

• 3)

The angle of supplementary to $90^{ 0 }$+$9^{ 0 }$ is

• 4)

Which of the following is not a pair of complementary angles?

• 5)

The length of the common perpendiculars at different points on parallel lines is the same and is called

CBSE 9th Mathematics - Introduction to Euclid's Geometry Model Question Paper - by Harjeet - Indore - View & Read

• 1)

The number of line segments determined by three collinear points is:

• 2)

Two planes intersect each other to form a:

• 3)

The thing which coincide with one another are:

• 4)

How many lines can be passed through two distinct points?

• 5)

Write the number of dimension(s) of a surface.

CBSE 9th Mathematics - Linear Equations in Two Variables Model Question Paper - by Harjeet - Indore - View & Read

• 1)

The equation $x+\sqrt{2}=0$ has

• 2)

The condition that the equation ax+by+c=0 represents a linear equation in two variables is:

• 3)

Write a, b, c for the equation 2x=5

• 4)

The equation y=3 in two variables can be written as:

• 5)

The sum of the ages of Apala and Meenu is 48.Write a linear equation in two variables to represent the statement.

CBSE 9th Mathematics - Coordinate Geometry Model Question Paper - by Harjeet - Indore - View & Read

• 1)

The famous mathematician associated with the problem of describing the position of a point in a plane was

• 2)

Which of the following is an example of a geometrical line?

• 3)

If x is negative and y is negative, then the point (x,y) lies in

• 4)

The line of intersection of I and II quadrants is

• 5)

The line of intersection of IV and I quadrants is

CBSE 9th Mathematics - Polynomials Model Question Paper - by Harjeet - Indore - View & Read

• 1)

The expansion for $(x-y)^2$ is

• 2)

The number 0 is called a

• 3)

Which of the following is a polynomial in one variable?

• 4)

Which of the following is a trinomial in x?

• 5)

Degree of the polynomial $4x^4+0x^3+0x^5+5x+7$ is:

9th Standard CBSE Mathematics - Number Systems Model Question Paper - by Harjeet - Indore - View & Read

• 1)

Every rational number is:

• 2)

Two rational numbers between $\frac { 2 }{ 3 }$ and $\frac { 5 }{ 3 }$are:

• 3)

A terminating decimal is:

• 4)

A number is an irrational if and only if its decimal representation is:

• 5)

Which of the following is a rational number?

CBSE 9th Mathematics - Full Syllabus One Mark Question Paper with Answer Key - by Harjeet - Indore - View & Read

• 1)

The rational number between -1/5 and -2/5 is

• 2)

Two rational numbers between $\frac { 2 }{ 3 }$ and $\frac { 5 }{ 3 }$are:

• 3)

The decimal expansion of $\sqrt { 2 }$ is

• 4)

The value of $\sqrt [ 4 ]{ { \left( 64 \right) }^{ -2 } }$ is

• 5)

$\sqrt [ 3 ]{ \frac { 54 }{ 250 } }$ equals:

CBSE 9th Mathematics - Full Portion Five Marks Questions - by Harjeet - Indore - View & Read

• 1)

Prove that: ${ \left( \frac { { x }^{ { a }^{ 2 } } }{ { x }^{ { b }^{ 2 } } } \right) }^{ \frac { 1 }{ a+b } }.{ \left( \frac { { x }^{ { b }^{ 2 } } }{ { x }^{ { c }^{ 2 } } } \right) }^{ \frac { 1 }{ b+c } }.{ \left( \frac { { x }^{ { c }^{ 2 } } }{ { x }^{ { a }^{ 2 } } } \right) }^{ \frac { 1 }{ c+a } }=1$

• 2)

Geetha told her classmate Radha that "$\sqrt { \frac { \left( \sqrt { 2 } -1 \right) }{ \left( \sqrt { 2 } +1 \right) } }$ is an irrational number." Radha replied that "you are wrong" and further claimed that "If there is a number 'x' such that x3 is an irrational number, then x5 is also irrational". Geetha said, "No Radha, you are wrong". Radha took some time and after verification accepted her mistakes and thanked Geetha for pointing out these mistakes.
(i) Justify both the statements.
(ii) What value is depicted from this question?

• 3)

In the figure, AD = AE, BD = EC. Prove that $\triangle$ABC is an isosceles triangle.

• 4)

In $\triangle$ABC, if AB is the greatest side, then prove that LC > 60°.

• 5)

AD and BC are equal perpendiculars to a line segment AB (see figure).

(i) Show that CD bisects AB.
(ii) Which mathematical concept is used in this problem?
(iii) What is its value?

CBSE 9th Mathematics - Full Portion Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Find three rational numbers $\frac { 3 }{ 5 }$ and $\frac { 7 }{ 8 }$

• 2)

Find your rational numbers between $\frac { 1 }{ 5 }$ and $\frac { 1 }{ 6 }$

• 3)

Express $0.15\overline { 9 }$ in $\frac { p }{ q }$ , where p and q are integers and $q\neq 0$

• 4)

(i) express 2.4 $\overline { 248 }$ in the form of $p\over q$ where $p\over q$ is in its lowest form.
(ii) What is the value of p?
(iii) what is the value of q?
(iv) what name can be given to the number p?
(v) what name can be given to the number q?
(vi) Apala declares that p and q are co-prime. IS she correct? If so, which value of Apala is depicted by her declaration?
(vii) Which mathematical concept has been converted in this problem?
(viii) Write the formulae used in the solution.

• 5)

Find the value of 'p' if ${ 5 }^{ p-3 }\times { 3 }^{ 2p-8 }=225$

CBSE 9th Mathematics - Full Portion Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Find six rational numbers between 3 and 4.

• 2)

Write the following in decimal form and say what kind of decimal expansion each has:
$\frac { 3 }{ 13 }$

• 3)

Express $2.\overline { 93 }$ in the form of $\frac { p }{ q }$, where p and q are integers, $q\neq 0$

• 4)

Simplify: $(\sqrt{x})^{-\frac{2}{3}}\sqrt{y^{4}}\div\sqrt{(xy)^{-\frac{1}{2}}}$

• 5)

Simplify: $\left( \sqrt { 3 } +1 \right) \left( 1-\sqrt { 12 } \right) +\frac { 9 }{ \left( \sqrt { 3 } +\sqrt { 12 } \right) }$

CBSE 9th Mathematics - Full Portion Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

Find two rational numbers between 3/4 and 5/9.

• 2)

Write three rational numbers between -2/5 and -1/5.

• 3)

Express $18.\overline { 48 }$ in the form of p/q, where p and q are integers, $q\neq 0$ .

• 4)

Simplify $\sqrt { 2 } (\sqrt { 6 } -\sqrt { 8 } )+\sqrt { 3 } (\sqrt { 27 } -\sqrt { 6 } )$

• 5)

If x=5 and y=2, find the value of $(i)\quad \left( { x }^{ y }+{ y }^{ y } \right) \quad (ii)\quad { \left( { x }^{ y }+{ y }^{ y } \right) }^{ -1 }$

9th Standard CBSE - Probability Five Marks Model Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

A survey of 500 families was conducted to know their opinion about a particular detergent powder. If 375 families liked the detergent powder and the remaining families disliked it, find the probability that a family chosen at random
(i) likes the detergent powder
(ii) does not like it.

• 2)

Out of the past 250 consecutive days, its weather forecasts were correct 175 times.
(i) What is the probability that on a given day it was correct?
(ii) What is the probability that it was not correct on a given day?

• 3)

A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is
(i) black
(ii) not green.

• 4)

Cards marked with 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
(a) a number less than 14
(b) a number which is a perfect square
(e) a prime number less than 20

• 5)

At a hospital, a doctor compiled the following data about 400 patients whom he could cure of hepatitis:

 Time for cure No.of patients <1 month 210 1-2 months 105 2-3 months 60 >3 months 25

Another case of hepatitis is reported. What is the probability that this patient will be cured in
(i) less than 2 months?
(ii) 1 month or more but not more than 3 months?

9th CBSE Mathematics - Statistics Five Marks Model Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

Draw a histogram representing the following frequency distribution:

 Marks No. of students 0-10 3 10-20 5 20-30 8 30-40 10 40-50 7 50-60 2
• 2)

Draw a frequency polygon to represent the following information:

Class Frequency
25-29 5
30-34 15
35-39 23
40-44 20
45-49 10
50-54 7
• 3)

Draw a histogram and frequency polygon of the following data:

Marks No.of students
20-30 5
30-40 12
40-50 6
50-60 20
60-70 18
70-80 10
80-90 16
90-100 3
• 4)

The mean of 10,12,18,13,x and 17 is 15. Find the value of x.

• 5)

Arithmetic mean of terms 21,16,24,x,29,15 is 23. Find this value of x.

9th CBSE Mathematics - Surface Areas and Volumes Five Marks Model Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

Two cubes of side 6 cm each, are joined end to end. Find the surface area of the resulting cuboid.

• 2)

The length of a hall is 20 m and width 16 m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.

• 3)

The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m2 is Rs 1248. Find the dimensions of the box.

• 4)

A cylindrical vessel, without lid, has to be tin-coated including both of its sides. If the radius of its base is $\frac { 1 }{ 2 } m$ and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 50 per 1000 cm.               $\left( Use\pi =3.14 \right)$

• 5)

The radius and vertical height of a cone are 5 cm and 12 cm respectively. Find the curved surface area.

9th CBSE Mathematics - Heron's Formula Four Marks Model Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

Find the area of a right-angled $\Delta$ABC, right angled at B in which AB = 24 metre and BC = 10 metre.

• 2)

lf the area of an equilateral triangle is $81\sqrt { 3 }$cm2, find its perimeter.

• 3)

The base of an isosceles triangle measures 24 cm and its area is 60 cm2, Find its perimeter.

• 4)

An isosceles triangle has perimeter 30 m and each of the equal sides is 12 cm.Find area of the triangle.

• 5)

Sides of a triangle are in the ratio 13:14:15 and its perimeter is 84 cm.Find its area.

9th Standard CBSE Mathematics - Constructions Four Marks Model Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

Construct an equilateral triangle with one side 6 cm.

• 2)

Construct an equilateral triangle LMN, one of whose sides is 5 cm. Bisect $\angle M$ of the triangle.

• 3)

Draw a line segment AB = 5 cm. From the point A draw a line segment AD = 6 cm making an angle of 60°. Draw perpendicular bisector of AD.

• 4)

(i)Construct a ΔABC in which AB=5.8cm, BC+CA=8.4cm and B=600
(ii)Measure AC
(iii)Measure BC
(iv)Is ACV+BC=8.4cm?
(v)Meenu says that ㄥACB=840 .Verify by measurement.Can you say that Meenu is right?Which value is depicted by Meenu's statement?

• 5)

(i) Construct a triangle ABC in which BC = 5 cm, ㄥB = 45°and AB-AC= 2.8cm.
(ii)Measure AB.
(iii)Measure AC
(iv) Verify that AB - AC = 2.8 cm.
(v)Hari comments that ㄥACB = 112°. Is he true? Which value is depicted by comment of Hari?

9th Standard CBSE Mathematics - Probability Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Out of the past 250 consecutive days, its weather forecasts were correct 175 times.
(i) What is the probability that on a given day it was correct?
(ii) What is the probability that it was not correct on a given day?

• 2)

A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is
(i) black
(ii) not green.

• 3)

A die is rolled 25 times and outcomes are recorded as under:

 Outcomes Frequency 1 9 2 4 3 5 4 6 5 1 6 0

It is thrown one more time. Find the probability of getting
(a) an even number
(b) a multiple of 3
(c) a prime number.

• 4)

The percentages of marks obtained by a student in examination are given below:

 Examination subjects % marks I 58 II 64 III 76 IV 62 V 85

Find the probability that the student gets
(i) a first class i.e. at least 60% marks
(ii) a distinction i.e. 75% or above
(iii) marks between 70% and 80%

• 5)

An insurance company selected 1600 drivers at random in a particular city to find a relationship between age and number of accidents. The data obtained are given in the following table:

 Age of drivers          (in years) No.of accidents(in one year) 0 1 2 3 More than 3 18-25 320 125 75 45 30 25-40 400 45 50 15 10 40-55 150 85 13 8 10 Above 55 150 25 17 20 7

Find the number of drivers
(a) in the age of 25-40 years and has more than 2 accidents in the year.
(b) in the age above 40 years and has accidents more than 1 but less than 3.

CBSE 9th Mathematics - Statistics Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

The class marks of a frequency distribution are 104, 114, 124, 134, 144, 154, 164. Find the class size and class intervals.

• 2)

The following data gives the number (in thousands) of applicants registered with an Employment Exchange during 2005-2010.

 Year No.of applications registered (in thousands) 2005 19 2006 21 2007 23 2008 30 2009 32 2010 36

Construct a bar graph to represent the above data.

• 3)

The marks scored by 750 students in examination are given in the form a frequency distribution table.

 Marks No. of students 600-640 16 640-680 45 680-720 156 720-760 284 760-800 172 800-840 59 840-880 18

Draw a histogram to represent the above data.

• 4)

The following table gives the performance of 90 students in a mathematics test of 100 marks.

Marks Number of students
0-20 07
20-30 10
30-40 10
40-50 20
50-60 20
60-70 15
70-above 08
Total 90

Represent the given information with the help of a histogram.

• 5)

Draw a frequency polygon to represent the following information:

Class Frequency
25-29 5
30-34 15
35-39 23
40-44 20
45-49 10
50-54 7

CBSE 9th Mathematics - Surface Areas and Volumes Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

A cast-iron pipe has an external diameter of 75 mm. If it is 4.2 m long, find the area of the outer surface.   $\left[ Assume\pi =\frac { 22 }{ 7 } \right]$

• 2)

Find the curved surface area of a closed cylindrical petrol storage tank that is 3.8 m in diameter and 4.9 m in height.

• 3)

The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.

• 4)

Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4 : 3.

• 5)

A hemispherical bowl made of steel is of 1 cm thickness. The inner radius of the bowl is 6 cm. Find the total surface area of the bowl, in terms of $\pi .$

CBSE 9th Maths - Heron's Formula Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Find the area of a right-angled $\Delta$ABC, right angled at B in which AB = 24 metre and BC = 10 metre.

• 2)

lf the area of an equilateral triangle is $81\sqrt { 3 }$cm2, find its perimeter.

• 3)

An isosceles triangle has perimeter 30 m and each of the equal sides is 12 cm.Find area of the triangle.

• 4)

Sides of a triangle are in the ratio 13:14:15 and its perimeter is 84 cm.Find its area.

• 5)

The perimeter of a triangle field is 300 cm and its sides are in the ratio 5:12:13.Find the length of the perpendicular from the opposite vertex to the side whose length is 130 cm.

9th Standard CBSE Mathematics - Constructions Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Construct an equilateral triangle with one side 6 cm.

• 2)

Construct an equilateral triangle LMN, one of whose sides is 5 cm. Bisect $\angle M$ of the triangle.

• 3)

Draw a line segment AB = 5 cm. From the point A draw a line segment AD = 6 cm making an angle of 60°. Draw perpendicular bisector of AD.

• 4)

(i)Construct a ΔABC in which AB=5.8cm, BC+CA=8.4cm and B=600
(ii)Measure AC
(iii)Measure BC
(iv)Is ACV+BC=8.4cm?
(v)Meenu says that ㄥACB=840 .Verify by measurement.Can you say that Meenu is right?Which value is depicted by Meenu's statement?

• 5)

(i) Construct a triangle ABC in which BC = 5 cm, ㄥB = 45°and AB-AC= 2.8cm.
(ii)Measure AB.
(iii)Measure AC
(iv) Verify that AB - AC = 2.8 cm.
(v)Hari comments that ㄥACB = 112°. Is he true? Which value is depicted by comment of Hari?

9th Standard CBSE Mathematics - Quadrilaterals Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Prove that each angle of a rectangle is a right angle.

• 2)

"A diagonal of a parallelogram divides it into two congruent triangles:"  Prove it.

• 3)

In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles.

• 4)

In triangle, ABC points M and N  on sides AB and AC respectively are taken so that AM = $1\over2$ AB and AN = $1\over4$ AC Prove that MN= $1\over4$BC

• 5)

ABCD is a square and on the side DC, an equilateral triangle is constructed. Prove that:
(i) AE = BE
(ii) ㄥDAE=15°

CBSE 9th Mathematics - Areas of Parallelograms and Triangles Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

ABCD is a quadrilateral and BD is one of its diagonals as shown in figure. Show that ABCD is a parallelogram and find its area.

• 2)

In the given figure, AB 11DC. Show that ar(BDE) = ar(ACED).

• 3)

Areas of triangles on the same bases and between the same parallels are equal in. Prove it.

• 4)

In the given figure, ABED is a parallelogram in which DE = EC. Show that: area (ABF) = area (BEC).

• 5)

Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals.

9th Standard CBSE Mathematics - Circles Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

In the figure, diameter AB and a chord AC have a 'common end point A. If the length of AB is 20 cm and of AC is 12 cm, how far is AC from the centre of the circle?

• 2)

Prove that the perpendicular from the centre of a circle to a chord, bisects the chord.

• 3)

Prove that the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

• 4)

Bisector AD of  $\angle BAC$ of $\Delta ABC$ passes through the centre O of the circumcircle of
$\Delta ABC$ Prove that AB = AC.

• 5)

Find the angle marked as x in each of following figures where O is the centre of the circle:
(i)

(ii)

(iii)

(iv)

(v)

9th Standard CBSE Mathematics - Triangles Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

In a rectangle ABCD, E is a point which bisects BC Prove that AE = ED

• 2)

In figure OA = OB, OC = OD and $\angle AOB=\angle COD$. Prove that AC = BD

• 3)

In the given figure, if AB = FE, BC=ED, $AB\bot BD$ and $FE\bot EC$, then prove that
(i) $\triangle ABD\cong \triangle FEC$
(ii) $AD\cong FC$

• 4)

In figure, $\angle QPR=\angle PQR$ and M and N are respectively points on sides QR and PR of $\triangle PQR$ , such that QM = PN. Prove that OP = OQ, where O is the point of intersecting of PM and QN.

• 5)

Prove that the angles opposite to equal sides of a triangle are equal. Is the converse true?

9th Standard CBSE Mathematics - Lines and Angles Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Rays OA,OB,OC,OD and OE have the common initial point O Show that
$\angle$AOB+$\angle$BOC+$\angle$COD+$\angle$DOE+$\angle$EOA=$360^{ 0 }$
Draw a ray OP opposite to ray OA
​​​​​​​

• 2)

If two lines are perpendicular to the same line prove that they are parallel to each other.

• 3)

If l,m,n are three lines such that l || m and n $\bot$ l , then prove that n $\bot$m

• 4)

In figure PQ || RS and T is any point as shown in the figure then show that
$\angle PQT+\angle QTS+\angle RST=360^{ 0 }$

• 5)

In figure l || m , show that $\angle 1+\angle 2-\angle 3=180^{ 0 }$

9th Standard CBSE Mathematics - Circles Four Mark Model Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

Prove that the perpendicular from the centre of a circle to a chord, bisects the chord.

• 2)

AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that  EB = ED and AE = CE.

• 3)

In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P. If $\angle DBC=70°$ and $\angle BAC=30°$ , find $\angle BCD$.

• 4)

ABCD is a cyclic quadrilateral with AD || BC Prove that AB = DC.

• 5)

Prove that the opposite angles of an isosceles trapezium are supplementary.

9th CBSE Mathematics - Areas of Parallelograms and Triangles Four Mark Model Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

ABCD is a quadrilateral and BD is one of its diagonals as shown in figure. Show that ABCD is a parallelogram and find its area.

• 2)

In the figure, diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O. Show that ar ($\Delta$ AOD)= ar($\Delta$ BOC).

• 3)

Prove that the area of a trapezium is equal to half of the product of its height and sum of parallel sides.

• 4)

The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

• 5)

$\Delta$ABC and $\Delta$ ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar ($\Delta$ ABC) = ar ($\Delta$ABD)

CBSE 9th Mathematics - Introduction to Euclid's Geometry Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Solve the equation x -15 = 25 and state Euclid's Axiom used here.

• 2)

In the given figure, if AB = CD, then prove that AC = BD. Also, write the Euclid's Axiom used for proving it.

• 3)

In figure, AC = XD, C is the midpoint of AB and D is the midpoint of XY. Using an Euclid's axiom, show that AB = XY.

• 4)

In the given figure, it is given that $\angle$1 = $\angle$4 and $\angle$3 = $\angle$2. By which Euclid's axiom, it can be shown that if $\angle$2 = $\angle$4, then $\angle$1 = $\angle$3.

• 5)

In figure, C is the mid-point of AB and Dis the mid-point of AC. Prove that
AD = $1\over2$  AB.

CBSE 9th Mathematics - Coordinate Geometry Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

From the given figure, write the points whose
(a) ordinate = 0
(b) abscissa = 0
(c) abscissa = -3
(d) ordinate = 4

• 2)

See figure and write the following:
(i) Coordinates of point P
(ii) Abscissa of point Q
(iii) The point identified by the coordinates (-4,4)
(iv) The point identified by the coordinates (-3,-6)

• 3)

In figure, ABCD is a rectangle with length 6 cm and breadth 3 cm.O is the mid point of AB.Find the coordinates of A, B C and D.

• 4)

Plot the following points on a graph sheet and join them in order B(-5,3), E(-3,-2), S(4,-2), T(1,3).Also mention the quadrants in which the points lie.

• 5)

Plot the points A, B, C, D from the table:

 Points x y A B C D 8 -5 13 -4 10 13 -5 -16

(a) Write the coordinates of A, B, C, D.

9th Standard CBSE Mathematics - Polynomials Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Write the various coefficients in the following polynomials:
7

• 2)

How many terms are there in the following polynomials?
3x2 - 5x + 7

• 3)

If $x=-2$ is the root of the equation $\sqrt { 2 } (x+p)=0$ and is also the zero the zero of the polynomial  ${ px }^{ 2 }+kx+2\sqrt { 2 }$ then find the value of k.

• 4)

The polynomial $p(x)=kx^3+9x^2+4x-8$ when divided by (x+3) leaves a remainder 10 (1-k). Find the value of k.

• 5)

The polynomial $p(x)=2{ x }^{ 3 }-3{ x }^{ 2 }+ax-3a+9$when divided by x+1, leaves the remainder 16. Find the value of a. Also, find the remainder when p(x) is divided by x+2.

CBSE 9th Mathematics - Linear Equations in Two Variables Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Draw the graph of linear equation 4x + 3y = 36. From the graph, find the value of y when x = 3 and value of x when y = 6.

• 2)

Draw the graph of the equations x = 3 and 4x = 3y in the same graph.Find the area of the triangle formed by these two lines and the x-axis

• 3)

If x is the number of hours a labourer is on work and y his wages in rupees then y = 4x + 3. Draw the work wages graph of this equation. From the graph, find the wages of a labourer who puts in 4 hours of work

• 4)

A part of family budget on milk is constant and is fixed at Rs.500, while the other is variable and it depends on the need for milk at the rate of Rs.20 per litre.If extra milk taken is x litre and total expenditure on milk is Rs y, then write a linear equation for this problem. Draw its graph.

• 5)

Draw the graph of ${2\over3}x-y=2$ and find the points where it cuts the co-ordinate axes.

9th Standard CBSE Mathematics - Number Systems Four Marks Questions - by Harjeet - Indore - View & Read

• 1)

Simplify: $\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } } -\frac { 2 }{ \sqrt { 5 } -\sqrt { 3 } } -\frac { 3 }{ \sqrt { 2 } +\sqrt { 5 } }$

• 2)

If √2=1.414 and √3=1.732, then calculate $\frac { 4 }{ 3\sqrt { 3 } -2\sqrt { 2 } } +\frac { 3 }{ 3\sqrt { 3 } -2\sqrt { 2 } }$

• 3)

If $x=\frac { 1 }{ 3-2\sqrt { 2 } }$ and $y=\frac { 1 }{ 3+2\sqrt { 2 } }$, then find the value of x+y+xy.

• 4)

If x=2+√3, then find the value of x2+$\frac{1}{x^{2}}$

• 5)

If x=√2-1, then find the value of $(x-\frac{1}{x})^{3}$ .

9th Standard CBSE Mathematics - Quadrilaterals Five Mark Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

ABCD is a parallelogram and line segments AX, CY bisects the angles A and C respectively. Show that AX II CY.

• 2)

Prove that the opposite angles of an isosceles trapezium are supplementary.

• 3)

Show that the bisectors of angles of a parallelogram enclose a rectangle.

• 4)

In the figure, ABCD is a parallelogram. E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

• 5)

In the given figure, D, E and F are the mid-points of the sides AB, BC and CA respectively of ΔABC. Show that ΔABC is divided into four congruent triangles by joining the point D, E and F.

9th Standard CBSE Mathematics - Triangles Five Mark Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

In a rectangle ABCD, E is a point which bisects BC Prove that AE = ED

• 2)

In the given figure, if AB = FE, BC=ED, $AB\bot BD$ and $FE\bot EC$, then prove that
(i) $\triangle ABD\cong \triangle FEC$
(ii) $AD\cong FC$

• 3)

Prove that the medians of an equilateral triangle are equal.

• 4)

In the given figure $BL\bot AC,MC\bot LN$, AL = CN and BL = CM. Prove  that $\triangle ABC\cong \triangle NML$

• 5)

In the figure below, ABC is a triangle in which AB = AC. X and Yare points on AB and AC such that AX = AY. Prove that $\triangle ABY\cong \triangle ACX$ .

9th Standard CBSE Mathematics - Probability Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

1500 families with 2 children were selected randomly, and the following data were recorded:

 Number of girls in a family 2 1 0 Number of families 475 814 211

Compute the probability of a family, chosen at random, having
(i) 2 girls  (ii) 1 girl (iii) No girl
also, check whether the sum of these probabilities is 1.

• 2)

In a particular section of Class IX, 40 students were asked about the months of their birth, the following graph was prepared for the data so obtained. Find the probability that a student of the class was born in August.

• 3)

To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table:

 Opinion Number of students like 135 dislike 65

Find the probability that a student chosen at random
(i) likes statistics,
(ii) does not like it

• 4)

Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):
4.97, 5.05 ,5.08 ,5.03 ,5.00 ,4.86, 5.08, 4.98 ,5.04, 5.07 ,5.00
Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

• 5)

In a cricket match, a batsman hits a boundary 6 times out of 30 balls she plays.Find the probability that she did not hit a boundary.

CBSE 9th Mathematics - Statistics Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Give five examples of data that you can collect from your day-to-day life.

• 2)

Classify the data as primary or secondary data.

• 3)

The blood groups of 30 students of Class VIII are recorded as follows:
A,B,O,O,AB,O,A,O,B,A,O,B, A,O,O,
A,AB,O,A,A,O,O,AB,B,A,O,B,A,B,O.
Represent this data in the form of a frequency distribution table. Which is the most common and which is the rarest, blood group among these students.

• 4)

The length of 40 leaves of a plant are measured a correct one millimeter, and the obtained data is represented in the following table:

 Length (in mm) Number of leaves 118-126 3 127-135 5 136-144 9 145-153 12 154-162 5 163-171 4 172-180 2

(i) Draw a histogram to represent the given data.
(ii) Is there any suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

• 5)

The following table gives the distribution of students of two sections according to the marks obtained by them:

 Section A                                                             Section B Marks Freqeuncy Marks Freqency 0-10 3 0-10 5 20-20 9 10-20 19 20-30 17 20-30 15 30-40 12 30-40 10 40-50 9 40-50 1

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

9th Standard CBSE Mathematics - Surface Areas and Volumes Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

The length, breadth and height of a room are 5 m, 4 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m2.

• 2)

The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs 10 per m2 is Rs 15000, find the height of the hall.

• 3)

The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm $\times$ 10 cm $\times$ 7.5 cm can be painted out of this container?

• 4)

The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder.

• 5)

It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?

CBSE 9th Mathematics - Heron's Formula Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

There is a slide in a park. One of its side walls has been painted in some colour with a  message' 'KEEP THE PARK GREEN AND CLEAN' '. If the sides of the wall are 15 m, 11 m, and 6 m, find the area painted in colour.

• 2)

Find the area of an equilateral triangle whose perimeter is 60 cm. (Using Heron's formula).

• 3)

(a) Find the area of the triangle.

(b) Find the area of a triangle whose sides are 16 cm, 14 cm, nd 10 cm.
(c) The sides of a triangle are 7 cm, 12 cm, and 13 cm. Find its area.
d) Find the area of a triangle whose sides are 11 m, 60 m and 61 m.

• 4)

The sides of a triangle are in the ratio of 25: 17: 12 and its perimeter is 1080 cm. Find its area.

• 5)

The lengths of the sides of a triangle are in the ratio 3: 4: 5 and its perimeter is 144 cm. Find the area of the triangle.

9th Standard CBSE Mathematics - Constructions Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Construct an equilateral triangle, given its side and justify the construction.

• 2)

Draw lines PQ and RS intersecting at point K.Measure a pair of vertically opposite angles. Bisect them. Arc the bisecting rays forming a straight line?

• 3)

Draw a line segment SR of length 10 cm. Divide it into 4 equal parts using compass

• 4)

Construct angle of  $52\frac { { 1 }^{ o } }{ 2 }$ ,using compass and ruler

• 5)

Construct a triangle ABC such that BC= 6 em, AB=3 cm and median AD = 4.5 em, Write steps of construction.

9th CBSE Mathematics - Lines and Angles Four Mark Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

In the given figure PO $\bot$ AB If x:y:z=1:3:5 then find the degree measure of x,y and z

• 2)

Prove "if two lines  intersect each other then the vertically opposite angles are equal"

• 3)

In the given figure , two straight lines PQ and RS intersect each other at O
If $\angle$POT =$75^{ 0 }$ Find the values of a,b,c

• 4)

If two lines are perpendicular to the same line prove that they are parallel to each other.

• 5)

If l,m,n are three lines such that l || m and n $\bot$ l , then prove that n $\bot$m

9th Standard CBSE Mathematics - Introduction to Euclid's Geometry Five Mark Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

In the given figure, if AB = CD, then prove that AC = BD. Also, write the Euclid's Axiom used for proving it.

• 2)

In the given figure AB = BC and BX = BY. Show that AX = CY. State Euclid's Axiom used.

• 3)

In figure, C is the mid-point of AB and Dis the mid-point of AC. Prove that
AD = $1\over2$  AB.

• 4)

In the fig, we have $\angle1=\angle3 \ and\ \angle2=\angle4.$ Show that $\angle A= \angle C.$ State which axiom you use here. Also give two more axioms other than the axioms used in the above situation.

• 5)

In the fig., if $OX=\frac{1}{2}XY,\ PX=\frac{1}{2}XZ$ and OX=PX, Show that XY=XZ. State which axiom you use here. Also give two more axioms other than the oxiom used in the above situation.

9th Standard CBSE Mathematics - Circles Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

• 2)

Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

• 3)

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

• 4)

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

• 5)

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

9th Standard CBSE Mathematics - Areas of Parallelograms and Triangles Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?

• 2)

In figure, ABCD is a parallelogram, $AE\bot DC$and $CF\bot AD$. If AB = 16cm, AE = 8 cm and CF = 10 cm, find AD.

• 3)

In figure, E is any point on median AD of a, $\Delta$ ABC. Show that ar($\Delta$ABE) = ar($\Delta$ACE).

• 4)

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

• 5)

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar($\Delta$AOD) = ar($\Delta$ BOC).

CBSE 9th Mathematics - Quadrilaterals Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

if the diagonals of a parallelogram are equal, then show that it is a rectangle.

• 2)

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

• 3)

Show that the diagonals of a square are equal and bisect each other at right angles

• 4)

Diagonal AC of a parallelogram ABCD bisects $\angle A$ (see figure). Show that:
(i) it bisects $\angle C$ also
(ii) ABCD is a rhombus.

• 5)

ABCD is a parallelogram and APand CQ are perpendiculars from vertices A and C on diagonal BD respectively. Show that:$(i)\Delta APB\cong \Delta CQD\\ (ii)AP=CQ$

CBSE 9th Mathematics - Triangles Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

In quadrilateral ACBD, AC=AD and AB bisects $\angle A$ (see figure).
Show that $\triangle ABC\cong \triangle ABD$. What can you say about BC and BD?

• 2)

l and m are two parallel lines intersected by another pair of parallel lines p and q (see figure). Show that $\triangle ABC\cong \triangle CDA$

• 3)

ABC is a right angled triangle in which $\angle A={ 90 }^{ 0 }$ and AB = AC.Find $\angle B$ and $\angle C$

• 4)

Show that the angles of an equilateral triangle are 60° each.

• 5)

ABC is an isosceles triangle with AB = AC.draw $AP\bot BC$ to show that $\angle B=\angle C$

9th Standard CBSE Mathematics - Lines and Angles Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

In Figure POQ is a line Ray OR is perpendicular to line PQ OS is another ray lying between rays OP and OR Prove that.
$\angle$ROS =$\frac { 1 }{ 2 } (\angle QOS-\angle POS)$

• 2)

It is given that $\angle$ XYZ=$64^{ 0 }$ and XY produced to point P. Draw a figure from the given information If ray YQ bisects $\angle$ ZYP , Find $\angle$ ZYP find $\angle$XYQ and reflex $\angle$ QYP.

• 3)

In figure if AB $\parallel$ CD .EF $\bot$ CD and $\angle$ AGE,$\angle$ GEF and $\angle$ FGE

• 4)

In figure, POQ is a line. Ray $OR\bot PQ.$ OS is another ray lying between OP and OR.
Prove that : $\angle ROS=\frac{1}{2}[\angle QOS-\angle POS]$

• 5)

Prove that bisectors of pair of vertically opposite angles are in the same straight line.

9th Standard CBSE Mathematics - Linear Equations in Two Variables Four Mark Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

Express the linear equation 7=2x in the form ax+by+c=0 and also write the values of a, b and c.

• 2)

Find the value of 'm' if (-m, 3) is a solution of equation 4x+9y-3=0

• 3)

Determine the point on the graph of the equation 2x+5y=20 where x-coordinate is${5\over2}$ times its ordinate.

• 4)

Draw the graph of the linear equation $y={2\over3}x+{1\over3}$.Check from the graph that (7, 5) is a solution of the linear equation

• 5)

Solve for x:
$3x-12+{3\over7}x=2(x-1)$
What type of graph is it in two dimensions?

9th CBSE Mathematics - Coordinate Geometry Four Mark Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

In which quadrant, can a point have:
(i) abscissa equal to its ordinate
(ii) ordinate equal in magnitude to abscissa
(iii) ordinate equal and opposite of abscissa
(iv) abscissa twice that of the ordinate.

• 2)

From the given figure, write the points whose
(a) ordinate = 0
(b) abscissa = 0
(c) abscissa = -3
(d) ordinate = 4

• 3)

From the given figure, write
(i) The coordinates of the points B and F
(ii) The abscissae of points A and C
(iii) The ordinates of the points A and C.
(iv) The perpendicular distance of the point G from the x-axis.

• 4)

See figure and write the following:
(i) Coordinates of point P
(ii) Abscissa of point Q
(iii) The point identified by the coordinates (-4,4)
(iv) The point identified by the coordinates (-3,-6)

• 5)

In figure, $\triangle ABC$ and $\triangle ABD$ are equilateral triangles.Find the coordinates of points C and D.

9th Standard CBSE Mathematics - Polynomials Five Mark Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

Find the remainder when $x^3+3x^2+3x+1$ is divided by $x$

• 2)

Factorise $12x^2-7x+1$

• 3)

Use suitable identities to find the following products: $\left( { y }^{ 2 }+\frac { 3 }{ 2 } \right) \left( { y }^{ 2 }-\frac { 3 }{ 2 } \right) ​​$

• 4)

Write the various coefficients in the following polynomials:
x7 - 3x5 + 4

• 5)

How many terms are there in the following polynomials?
t - 7t2 + 5 - t3

9th CBSE Mathematics - Number Systems Five Mark Question Paper - by Kuldeep Singh - Ahmedabad - View & Read

• 1)

Find three rational numbers $\frac { 3 }{ 5 }$ and $\frac { 7 }{ 8 }$

• 2)

Find two irrational numbers between 2 and 2.5.

• 3)

Evaluate:$\frac { 40 }{ 2\sqrt { 10 } +\sqrt { 20 } +\sqrt { 40 } -2\sqrt { 5 } }$ when it is given that $\sqrt { 10 } =3.162$

• 4)

Simplify: $\frac { 7+3\sqrt { 5 } }{ 3+\sqrt { 5 } } -\frac { 7-3\sqrt { 5 } }{ 3-\sqrt { 5 } }$

• 5)

Prove that $\frac { 1 }{ 3+\sqrt { 7 } } +\frac { 1 }{ \sqrt { 7 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 3 } +1 } =1$

9th Standard CBSE Mathematics - Introduction to Euclid's Geometry Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Which of the following statements are true and which are false? Give reasons for your answers:
(i) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A terminated line can be produced indefinitely on both the sides.
(iv) If two circles are equal, then their radii are Equal.

• 2)

Consider two 'postulates' given below:
(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.
(ii) There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid's postulates? Explain.

• 3)

In Question 4, point C is called a mid-point of line segment AB. Prove that every line
segment has one and only one mid-point.

• 4)

In figure, if AC = BD, then prove that AB = CD.

• 5)

(i) Why is Axiom 5, in the list of Euclid's axioms, considered a 'universal truth'?  (Note that the question is not about the fifth postulate).
(ii) How would you rewrite Eulid's fifth postulate so that it would be easier to understand?

9th Standard CBSE Mathematics - Linear Equations in Two Variables Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Express the following linear equation in the form ax+by+c=0 and indicate the values of a, b and c in each case:
$x-{y\over 5}-10=0$

• 2)

Express the following linear equation in the form ax+by+c=0 and indicate the values of a, b and c in each case:
-2x+3y=6

• 3)

Which one of the following options is true and why?
y=3x+5 hs
(i)a unique solution
(ii)only two solutions
(iii)infinitely many solutions

• 4)

Check which of the following are solutions of equation x-2y=4 and which are not:
(0,2)

• 5)

Check which of the following are solutions of equation x-2y=4 and which are not:
(2,0)

CBSE 9th Mathematics - Coordinate Geometry Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Write the answer of each of the following questions:
(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines interesect

• 2)

How will you describe the position of a table lamp on your study table another person?

• 3)

(Street Plan):A city has two main roads cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.All the other streets of the city run parallel to these roads and are 200 m apart.There are 5 streets in each direction.Using 1 cm = 200 m, draw a model of the city on your notebook.Represent the roads/streets by single line.

There are many cross-streets in your model.A particular cross-street is made by two streets, one running in the North-South direction and another in the East- West direction.Each cross-street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5).Using this convention, find:
(i) how many cross-streets can be referred to as (4,3)?
(ii) how many cross-streets can be referred to as (3,4)?

• 4)

In which quadrant do the given points lie?(-6,2)

• 5)

In which quadrant do the given points lie?(-5,-4)

9th Standard CBSE Mathematics Unit 1 Polynomials Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
${ 4x }^{ 2 }-3x+7$

• 2)

Write the coefficients of x2 in the following:
2 + x2 + x

• 3)

Give one example each of a binomial of degree 35, and of a monomial of degree 100.

• 4)

Write the degree of the following polynomials:
5x3 + 4x2 + 7x

• 5)

Classify the following as linear, quadratic and cubic polynomials:
r2

9th Standard CBSE Mathematics - Number Systems Three Marks Questions - by Harjeet - Indore - View & Read

• 1)

Is zero a rational number?can you write it in the form $\frac { p }{ q }$,where p and q are integers and $q\neq 0$?

• 2)

Find six rational numbers between 3 and 4.

• 3)

Write the following in decimal form and say what kind of decimal expansion each has:
$\frac { 3 }{ 13 }$

• 4)

Write the following in decimal form and say what kind of decimal expansion each has:
$\frac { 2 }{ 11 }$

• 5)

Express the following in the form p/q, where p and q are integers and $q\neq 0$
$0.\overline { 001 }$

9th CBSE Mathematics - Probability Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

In a cricket match, a batsman hits boundary in 20% of the balls he played. Find the probability that he did not hit a boundary.

• 2)

On one page of a telephone directory, there were 200 telephone numbers. The frequency distribution of their unit place digit (for example, in the number 25828573, the unit place digit is 3) is given in the table below:

 Digit 0 1 2 3 4 5 6 7 8 9 Frequency 22 26 22 22 20 10 14 28 16 20

Without looking at the page, the pencil is placed on one of these numbers, i.e., the number is chosen at random. What is the probability that the digit in its unit place is 6?

• 3)

The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times:
(i) What is the probability that on a given day it was correct?
(ii) What is the probability that it was not correct on a given day?

• 4)

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes

Compute the probability of getting

• 5)

A bag has 3 red and 7 black balls. One ball is taken out of the bag. Find the probability that it is a
(i) red ball
(ii) blackball.

CBSE 9th Mathematics - Statistics Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

The marks obtained out of 75 by 30 students of a class in an examination are given below:
42,21,50,37,42,37,38,42,49,52,38,53,57,47,29,59,61,33,17,17,39,44,42,39,14,7,27,19,54,51
Prepare a frequency distribution table in which the size of class intervals is the same and one class intervalis 0-10.

• 2)

The marks obtained by 40 students of class IX in an examination are given below:
12,8,18,8,6,16,12,5,
23,2,10,20,12,9,7,6,
5,3,5,13,21,13,15,20,
24,1,7,16,21,13,23,18,
7,3,18,17,16,16,23,12
Represent the data in the form of a freqency distribyuting using 15-20 (20 not included) as one of the class intervals.

• 3)

Prepare a frequency table from the data follows:

 Marks obtained No. of students More than or equal to 0 50 More than or equal to 20 48 More than or equal to 40 41 More than or equal to 60 30 More than or equal to 80 12
• 4)

Consider the marks, out of 100, obtained by 51 students of a class in a test:

Marks Number of students
0-10 5
10-20 10
20-30 4
30-40 6
40-50 7
50-60 3
60-70 2
70-80 2
80-90 3
90-100 9
Total 51

Draw a frequency polygon corresponding to this frequency distribution table.

• 5)

Find the median of the following data 15,28,72,56,44,32,31,43 and 51. If 32 is replaced by 23, find the new median.

9th Standard CBSE Mathematics - Surface Areas and Volumes Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

The edge of a cube is 10.5 mm. Find its total surface area in cm2

• 2)

If the length of the diagonal of a cube is $6\sqrt { 3 }$ cm, find the edge of the cube.

• 3)

The length, breadth, and height of a cuboid are 15 cm, 10 cm, and 20 cm. Find the surface area of the cuboid.

• 4)

The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm $\times$ 10 cm $\times$7.5 cm can be painted out of this container?

• 5)

The floor of a rectangular hall has a perimeter of 250 m and its length and breadth are in the ratio of 13: 12. If the cost of painting the four walls and ceiling at the rate of Rs. 5 per m2 is Rs.27000, find the height of the hall.

CBSE 9th Mathematics - Heron's Formula Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

Find the area of an equilateral triangle of side 10 cm.

• 2)

Find the area of an isosceles triangle, whose equal sides are of length 15 cm each and third side is 12 cm.

• 3)

The unequal side of an isosceles triangle is 6 cm and its perimeter is 24 cm. Find its area.

• 4)

Find the area of a triangle whose sides are 6.5 cm. 7 cm and 7.5 cm.

• 5)

Find the area of a triangle two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.

CBSE 9th Mathematics - Circles Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

Find the length of a chord of a circle which is at a distance of 4 cm from the centre of the circle with radius 5 cm.

• 2)

Two concentric circles are with centre O. A, B, C, D are the points of intersection with a line. If AD = 12 cm and BC = 8 cm, find the length of AB, CD, AC and BD.

• 3)

Two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. Find the distance between their centres.

• 4)

In the figure, O is the centre of the circle. Arc BCD subtends an angle of 140° at the centre. BC is produced to P and CD is joined. Find measure of $\angle DCP$.

• 5)

In the figure, $\angle AOB= 90°$  and, $\angle ABC= 30°$ then find the measure of  $\angle CAO$.

CBSE 9th Mathematics Areas of Parallelograms and Triangles Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

In the figure, PQRS is a parallelogram with PQ = 12 cm, altitudes corresponding to PQ and SP are respectively 8 cm and 10 cm. Find SP.

• 2)

In a parallelogram ABCD, AB = 8 cm. The altitudes corresponding to sides AB and AD are respectively 4 cm and 5 cm. Find measure of AD.

• 3)

In the given figure, ABC and DBC are triangles on the same base and between parallel lines I and m. If AB = 3 cm, BC = 5 cm, $\angle A=90°$, find area of $\Delta$ DBC.

• 4)

In the figure, ar( $\Delta$ABE) = 50 cm2. Find the area of the parallelogram ABCD. Give reasons.

• 5)

In the figure, ABCD is a parallelogram. AB = 12 cm, DM = 6 cm and BN = 9 cm. Find the length of AD.

CBSE 9th Mathematics Quadrilaterals Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

The angles A, B, C and D of a quadrilateral have measures in the ratio 2 : 4 : 5 : 7. Find the measures of these angles. What type of quadrilateral is it? Give reasons.

• 2)

In a parallelogram PQRS, if $\angle$QRS=2x, $\angle$PQS=4x, and $\angle$PSQ=4x, find the angles of the parallelogram.

• 3)

If an angle of a parallelogram in two-third of its adjacent angle then find the measure of all the angles,

• 4)

In the figure, ABCD is a parallelogram in which AB is produced to E so that AB = BE
(a) Prove that ED bisects BC
(b) If AD = 10 cm, find OB.

• 5)

In $\Delta$ ABC, D, E and F are midpoints of sides AB, BC and CA. If AB = 6 cm,BC = 7.2 cm and AC = 7.8 crn find the perimeter of  $\Delta$DEF.

CBSE 9th Mathematics - Triangles Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see figure). Show that these altitudes are equal.

• 2)

In ΔABC, if ㄥA = 50° and ㄥB = 60°, determine the shortest and the longest side of the triangle.

• 3)

In a ΔDEF, if ㄥD = 30°, ㄥE = 60° then which side of the triangle is longest and which side is shortest?

• 4)

In ΔABC, ㄥA = 60°, ㄥB = 40°, which side of this triangle is the smallest? Give reasons for your answer.

• 5)

In ΔPQR, ㄥP = 100° and ㄥR = 60°, which side of the triangle is the longest. Give reasons for your answer.

CBSE 9th Mathematics Lines and Angles Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

Find the supplement of $\frac { 4 }{ 3 }$ of right angle

• 2)

If (3x-$58^{ 0 }$) and (x+$38^{ 0 }$) are supplementary angles,find x and the angles.

• 3)

In figure $\angle$ DOB =$87^{ 0 }$ and $\angle$ COA =$82^{ 0 }$ If $\angle$BOA $35^{ 0 }$ and Find $\angle$ COB and $\angle$COD

• 4)

An exterior angle of a triangle is $115^{ 0 }$ and one of the interior opposite angles is $35^{ 0 }$
Find the other two angles of the triangle

• 5)

find the angles of a traingle PQR if $\angle p-\angle q=45^{ 0 }$ and $\angle Q-\angle R=30^{ 0 }$

9th Standard CBSE Mathematics - Introduction to Euclid's Geometry Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

Consider the following statement: There exists a pair of straight lines that are everywhere equidistant from one another. Is this statement a

• 2)

State any two Eulis's axioms.

• 3)

State any two Euclid's axioms.

• 4)

In the given figure AC= DC, CB=CE, Show that AB=DE.

Write Euclid's axiom to support this.

• 5)

In the given figure, we have AB=AD and AC=AD. Prove that AB=AC. State the Euclid's axiom to support this.

9th Standard CBSE Mathematics - Linear Equations in Two Variables Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

Write  the following as an equation in two variables:
5y=2

• 2)

Express y in terms of x, it being given that 3x+y-9=0.Check whether the points (3,0) and (2, 2) lie on the equation

• 3)

Find three different solutions for the equation 6x-8y+32=0

• 4)

Given the point (1, 2), can you give the equation of a line on which it lies? How many such equations are there?

• 5)

Draw the graph of the linear equation y = m.x + c for m = 2 and c = 1. Read from the graph the value of y when x = $3\over 2$

CBSE 9th Mathematics - Coordinate Geometry Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

In which quadrant do the given point lie? (2,-1)

• 2)

In which quadrant do the given point lie?(-1,7)

• 3)

In which quadrant do the given point lie? (-4,-5)

• 4)

In which quadrant do the given point lie? (-3,5)

• 5)

In which quadrant do the given point lie? (4,-1)

CBSE 9th Mathematics - Polynomials Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

Write the coefficient of x3 of the following polynomials:
$1+{ x }^{ 2 }+{ x }^{ 4 }-x-{ x }^{ 3 }$

• 2)

Write the coefficient of x3 of the following polynomials:
$4x+{ x }^{ 3 }+{ x }^{ 6 }-{ 7x }^{ 2 }$

• 3)

Find the degree of the polynomials given below:
​​​​​​​$2-{ y }^{ 2 }-{ y }^{ 3 }+{ 2y }^{ 8 }$

• 4)

Point out which of the following polynomials are monomials, binomials or trinomials?
${ x }^{ 3 }+2x-3$

• 5)

Find a zero of the polynomial p(x)=2x+1

CBSE 9th Mathematics - Number Systems Two Marks Questions - by Harjeet - Indore - View & Read

• 1)

Find two rational numbers between 0.1 and 0.2.

• 2)

Express $0.\overline { 001 }$ as a rational number in the form p/q, where p and q are integers and $q\neq 0$

• 3)

Represent $0.\overline { 237 }$ in the form p/q, where p and q are integers and $q\neq 0$

• 4)

Simplify: 172.175

• 5)

Simplify: (52)-7

CBSE 9th Mathematics Unit 15 Probability Book Back Questions - by Harjeet - Indore - View & Read

• 1)

The minimum probability of an event is

• 2)

What is the number of outcomes when a coin is tossed?

• 3)

What is the number of outcomes when a cubical dice is thrown?

• 4)

An experiment has two outcomes E and F P(E)+P(F) is equal to:

• 5)

Which of the following cannot be the experiment probability of an event?

CBSE 9th Mathematics Unit 14 Statistics Book Back Questions - by Harjeet - Indore - View & Read

• 1)

The word 'Latum' is a

• 2)

Statistics is branch of

• 3)

'Number of absentees in each day in your class for a month' form

• 4)

When the information is gathered from a source which already had the information stored, the data obtained is called

• 5)

The upper limit of the class 36 - 40 is

CBSE 9th Mathematics Unit 12 Surface Areas and Volumes Book Back Questions - by Harjeet - Indore - View & Read

• 1)

Which of the following is a plane figure?

• 2)

The total surface area of a cube of side a is

• 3)

The lateral surface area of a cuboid of length l, breadth b and height h is

• 4)

The dimensions of a box are 1 m, 80 cm and 50 cm. The area of its four walls is

• 5)

The area of the four walls of a room is 300 m2. Its length and height are 15 m and 6 m respectively. Find its breadth.

CBSE 9th Mathematics Unit 11 Heron's Formula Book Back Questions - by Harjeet - Indore - View & Read

• 1)

Area of a triangle =

• 2)

Area of a triangle having base 6 cm and altitude 8 cm is

• 3)

Area of a triangle is 60 cm2.Its base is 15 cm.Its altitude is

• 4)

The side of an isosceles right triangle of hypotenuse $5\sqrt { 2 }$ cm is

• 5)

Side of an equilateral triangle is 4 cm. Its area is

CBSE 9th Mathematics - Constructions Book Back Questions - by Harjeet - Indore - View & Read

• 1)

Bisector of an angle divides it in to_______equal parts

• 2)

If a 60o angle is bisected twice,what will be measure of each that is constructed?

• 3)

In the figure below,PR is the perpendicular bisectors of a line segment AB=16 cm.Is PA=PB true?

• 4)

Construct ∠POY=30 o. using compass and ruler.

• 5)

Construct an angle of 15o

CBSE 9th Standard Mathematics Unit 10 Circles Book Back Questions - by Harjeet - Indore - View & Read

• 1)

The path traced by the tip of the second's hand is a

• 2)

The shape of the coin of RS 1 is

• 3)

The wheels of a vehicle are in

• 4)

The longest chord of a circle is called

• 5)

The centre of a circle lies

CBSE 9th Standard Mathematics Unit 9 Areas of Parallelograms and Triangles Book Back Questions - by Harjeet - Indore - View & Read

• 1)

Area of a triangle is equal to

• 2)

In the following figure, find the area of quad. ABCD.

• 3)

If length of the diagonal of a square is 8 cm, then its area will be

• 4)

If P, Q, Rand S are the midpoints of a rectangle of area 36 sq. cm, then PQRS is a parallelogram of area

• 5)

Which of the following figures lie on the same base and between the same parallels?

9th Standard CBSE Mathematics - Quadrilaterals Book Back Questions - by Harjeet - Indore - View & Read

• 1)

How many sides does a quadrilateral have?

• 2)

If only one pair of opposite sides of a quadrilateral are parallel, then the quadrilateral is a

• 3)

Which of the following is false?

• 4)

Which of the following is not true?

• 5)

A blackboard is

9th Standard CBSE Mathematics - Triangles Book Back Questions - by Harjeet - Indore - View & Read

• 1)

A closed figure formed by three intersecting lines is called

• 2)

A triangle has

• 3)

The symbol for congruence is

• 4)

The symbol for correspondence is

• 5)

Two circles are congruent.If the radius of one circle is 3cm, what is the radius of the other circle?

9th Standard CBSE Mathematics Unit 6 Lines and Angles Book Back Questions - by Harjeet - Indore - View & Read

• 1)

The minimum number of points required to draw a line is

• 2)

How many types of angles are formed between the edges of plane surfaces?

• 3)

Two angles whose sum is $90^{ 0 }$ are called

• 4)

The sum of two complimentary angles is

• 5)

An angle which is greater than $90^{ 0 }$ and less than $180^{ 0 }$ is called

9th Standard CBSE Mathematics Unit 5 Introduction to Euclid's Geometry Book Back Questions - by Harjeet - Indore - View & Read

• 1)

In Indus Valley Civilisation (about 300 b.C), The brick used for construction work were having dimension in the ration

• 2)

Pythagoras was a student of

• 3)

Number of dimension(s) a surface:

• 4)

How many numbers of lines do pass through two distinct points?

• 5)

The number of lines that can pass through a given point is:

9th Standard CBSE Mathematics Unit 3 Coordinate Geometry Book Back Questions - by Harjeet - Indore - View & Read

• 1)

The famous mathematician associated with the problem of describing the position of a point in a plane was

• 2)

North-South direction and East-West direction

• 3)

If x is positive and y is negative, then the point (x,y) lies in

• 4)

If x is negative and y is negative, then the point (x,y) lies in

• 5)

The line of intersection of I and II quadrants is

9th Standard CBSE Mathematics Unit 4 Linear Equations in Two Variables Book Back Questions - by Harjeet - Indore - View & Read

• 1)

Write a, b, c for the equation 2y-x=7

• 2)

A linear equation in two variables has

• 3)

Total number of legs in a herd of goats and hens is 40. Represent this in the form of linear equation of two variable.

• 4)

If the point (2,3) lies on the 4y=ax+5, then a=______

• 5)

If (0,2) is a solution of the linear equation 2x+3y=k, then find the value of k.

9th Standard CBSE Mathematics Chapter 2 Polynomials Book Back Questions - by Harjeet - Indore - View & Read

• 1)

Which of the following is a polynomial in one variable?

• 2)

The degree of the polynomial $(x^3+5)(4-x^5)$ is:

• 3)

The coefficient of x2 in the polynomial $7+4x-x^2+x^3$ is:

• 4)

What is x+$\frac { 1 }{ x }$?

• 5)

What is the zero of the zero polynomial?

9th Standard CBSE Mathematics Unit 1 Number Systems Book Back Questions - by Harjeet - Indore - View & Read

• 1)

If $\sqrt { x }$ is an irrational number, then x is:

• 2)

The simplified form of $\frac { { 13 }^{ \frac { 1 }{ 5 } } }{ { 13 }^{ \frac { 1 }{ 3 } } }$ is

• 3)

If ${ 8 }^{ x }=\frac { 64 }{ { 2 }^{ x } }$ , then the value of x is

• 4)

Calculate the decimal which represents the fraction $\frac{7}{8}$

• 5)

Is the product of two irrational numbers always an irrational number?

9th Standard CBSE Mathematics Unit 10 Circles One Mark Question and Answer - by Harjeet - Indore - View & Read

• 1)

The path traced by the tip of the second's hand is a

• 2)

The shape of the coin of RS 1 is

• 3)

The wheels of a vehicle are in

• 4)

The longest chord of a circle is called

• 5)

The minute hand of a clock is at 12 and the smaller hour's hand is at 2. The angle between the hands of the clock is

9th Standard CBSE Mathematics Unit 9 Areas of Parallelograms and Triangles One Mark Question with Answer Key - by Harjeet - Indore - View & Read

• 1)

Area of a parallelogram is equal to

• 2)

Area of a triangle is equal to

• 3)

The areas of a parallelogram and a triangle are equal and they lie on the same base. If the altitude of the parallelogram is 2 cm, then the altitude of triangle is

• 4)

In the figure, the area of parallelogram PQRS is:

• 5)

In the figure, ABCD is a parallelogram of area 128 cm2 . If CF = 16 cm, the length of AD is

9th Standard CBSE Mathematics Unit 9 Quadrilaterals One Mark Question and Answer - by Harjeet - Indore - View & Read

• 1)

How many sides does a quadrilateral have?

• 2)

What is the number of vertices of a quadrilateral?

• 3)

How many angles are three in a quadrilateral have?

• 4)

How many diagonals does a quadrilateral have?

• 5)

How many pairs of opposite sides a quadrilateral have?

9th Standard CBSE Mathematics Unit 7 Triangles One Mark Question and Answer - by Harjeet - Indore - View & Read

• 1)

A closed figure formed by three intersecting lines is called

• 2)

'Tri' means

• 3)

Two circles are congruent.If the radius of one circle is 3cm, what is the radius of the other circle?

• 4)

Two circles are congruent.If the radius of one circle is 1cm, then the diameter of the other circle is

• 5)

Two circles are congruent.If the diameter of one circle is 2cm, then the radius of the other circle is

9th Standard CBSE Mathematics Unit 6 Lines and Angles One Mark Question with Answer - by Harjeet - Indore - View & Read

• 1)

The minimum number of points required to draw a line is

• 2)

In how many points two intersecting lines intersect?

• 3)

The sum of two complimentary angles is

• 4)

The angles whose sum is $180^{ 0 }$ are called

• 5)

The sum of two supplementary angles  is

9th CBSE Mathematics Unit 5 Introduction to Euclid's Geometry One Mark Question Paper with Answer Key - by Harjeet - Indore - View & Read

• 1)

In Indus Valley Civilisation (about 300 b.C), The brick used for construction work were having dimension in the ration

• 2)

In ancient India, the shapes of altars used for household rituals were

• 3)

In ancient India, alters with combination of shapes like rectangles, triangles and trapeziums were used for

• 4)

Pythagoras was a student of

• 5)

Number of dimension(s) a surface:

CBSE Education Study Materials

9th CBSE Mathematics 2019 - 2020 Academic Syllabus - by Harjeet - Indore Aug 21, 2019 Aug 21, 2019

Mathematics 2019 - 2020 Academic Syllabus

CBSEStudy Material - Sample Question Papers with Solutions for Class 9 Session 2019 - 2020

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