Class 9 Mathematics: CBSE Sample Question Paper With Solutions (2025) | Mathematics (Maths) Class 9 PDF Download

 Page 1


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) (0, -3) b) (0, 3)
c) (3, 0) d) (-3, 0)
1. The point which lies on x-axis at a distance of 3 units in the positive direction of x-axis is [1]
a)
 cm
2 b)
 cm
2
c)
300 cm
2 d)
 cm
2
2. The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is : [1]
1 0 0 3 – v 1 0 3 – v 5 0 3 – v a) b)
c) d)
3. In the figure, O is the centre of the circle. If  , then  is equal to : [1] ? A B C = 2 0 o ? A O C 6 0 o 1 0 o 4 0 o 2 0 o 4. In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? [1]
Page 1 of 17
Page 2


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) (0, -3) b) (0, 3)
c) (3, 0) d) (-3, 0)
1. The point which lies on x-axis at a distance of 3 units in the positive direction of x-axis is [1]
a)
 cm
2 b)
 cm
2
c)
300 cm
2 d)
 cm
2
2. The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is : [1]
1 0 0 3 – v 1 0 3 – v 5 0 3 – v a) b)
c) d)
3. In the figure, O is the centre of the circle. If  , then  is equal to : [1] ? A B C = 2 0 o ? A O C 6 0 o 1 0 o 4 0 o 2 0 o 4. In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? [1]
Page 1 of 17
a) b)
c) d)
A B 1 2 ( A B + C D ) 1 2 ( A B - C D ) 1 2 C D 1 2 a)
x
pqr b) 0
c) x d) 1
5. The value of x
p-q 
x
q-r
 x
r-p
 is equal to
[1]
a) 32 cm b) 8 cm
c) 28 cm d) 4 cm
6. D, E and F are the mid points of sides AB, BC and CA of . If perimetre of  is 16 cm, then
perimetre of . 
[1] ? A B C ? A B C ? D E F a) 2x + y = 0 b) x + 2y = 0
c) x + 2y = 4 d) 2x + y = 5
7. x = 2, y = -1 is a solution of the linear equation [1]
a) 5 b) -2
c) -5 d) 3
8. If x - 3 is a factor of x
2
 - ax -15, then a =
[1]
a) b)
c) 3 d) 5
9. The value of  is [1] 1 5 ÷ 3 1 5 - - v 5 – v 5 3 – v 3 5 – v a) OC = BE b) OE = OC
c) AB = OE d) AB = BE
10. ABCD is a parallelogram. If is produced to E such that ED bisects BC at O. Then which of the following is
correct?
[1]
a) b)
c) d)
11. An irrational number between  is [1]   a n d   1 7 2 7 × 1 7 2 7 - - - - - v ( - ) 1 2 1 7 2 7 ( × ) 1 7 2 7 ( + ) 1 2 1 7 2 7 a) Infinitely many b) Two
12. How many linear equations in ‘x’ and ‘y’ can be satisfied by x = 1, y = 2? [1]
Page 2 of 17
Page 3


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) (0, -3) b) (0, 3)
c) (3, 0) d) (-3, 0)
1. The point which lies on x-axis at a distance of 3 units in the positive direction of x-axis is [1]
a)
 cm
2 b)
 cm
2
c)
300 cm
2 d)
 cm
2
2. The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is : [1]
1 0 0 3 – v 1 0 3 – v 5 0 3 – v a) b)
c) d)
3. In the figure, O is the centre of the circle. If  , then  is equal to : [1] ? A B C = 2 0 o ? A O C 6 0 o 1 0 o 4 0 o 2 0 o 4. In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? [1]
Page 1 of 17
a) b)
c) d)
A B 1 2 ( A B + C D ) 1 2 ( A B - C D ) 1 2 C D 1 2 a)
x
pqr b) 0
c) x d) 1
5. The value of x
p-q 
x
q-r
 x
r-p
 is equal to
[1]
a) 32 cm b) 8 cm
c) 28 cm d) 4 cm
6. D, E and F are the mid points of sides AB, BC and CA of . If perimetre of  is 16 cm, then
perimetre of . 
[1] ? A B C ? A B C ? D E F a) 2x + y = 0 b) x + 2y = 0
c) x + 2y = 4 d) 2x + y = 5
7. x = 2, y = -1 is a solution of the linear equation [1]
a) 5 b) -2
c) -5 d) 3
8. If x - 3 is a factor of x
2
 - ax -15, then a =
[1]
a) b)
c) 3 d) 5
9. The value of  is [1] 1 5 ÷ 3 1 5 - - v 5 – v 5 3 – v 3 5 – v a) OC = BE b) OE = OC
c) AB = OE d) AB = BE
10. ABCD is a parallelogram. If is produced to E such that ED bisects BC at O. Then which of the following is
correct?
[1]
a) b)
c) d)
11. An irrational number between  is [1]   a n d   1 7 2 7 × 1 7 2 7 - - - - - v ( - ) 1 2 1 7 2 7 ( × ) 1 7 2 7 ( + ) 1 2 1 7 2 7 a) Infinitely many b) Two
12. How many linear equations in ‘x’ and ‘y’ can be satisfied by x = 1, y = 2? [1]
Page 2 of 17
c) Only one d) Three
a) 40° b) 50°
c) 70° d) 60°
13. In a figure, if OP||RS, OPQ = 110° and QRS = 130°, then PQR is equal to [1] ? ? ? a) 5 b) 35
c) 19 d) 13
14. After rationalising the denominator of , we get the denominator as [1]
7 3 - 2 3 v 2 v a) 80° b) 60°
c) 90° d) 70°
15. In the given figure, O is the centre of a circle and chords AC and BD intersect at E. If AEB = 110° and CBE
= 30°, then ADB = ? 
[1] ? ? ? a) Origin b) Points
c) Abscissa d) Ordinate
16. x co-ordinate is known as [1]
a) -2 b) 2
c) 3 d) -3
17. If (-2, 5) is a solution of 2x + my = 11, then the value of ‘m’ is [1]
a) 3(a - b)(b - c)(c - a) b) (a + b)(b + c)(c + a)
c) 3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a) d) 2(a - b)(b - c)(c - a)
18. The value of  is
[1]
+ + ( - ) a 2 b 2 3 ( - ) b 2 c 2 3 ( - ) c 2 a 2 3 ( a - b + ( b - c + ( c - a ) 3 ) 3 ) 3 a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): If the diagonals of a parallelogram ABCD are equal, then ABC = 90
o
 
Reason (R): If the diagonals of a parallelogram are equal, it becomes a rectangle.
[1]
? a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
20. Assertion (A):  is an irrational number. 
Reason (R): Sum of a rational number and an irrational number is always an irrational number.
[1] 2 + 6 – v Page 3 of 17
Page 4


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) (0, -3) b) (0, 3)
c) (3, 0) d) (-3, 0)
1. The point which lies on x-axis at a distance of 3 units in the positive direction of x-axis is [1]
a)
 cm
2 b)
 cm
2
c)
300 cm
2 d)
 cm
2
2. The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is : [1]
1 0 0 3 – v 1 0 3 – v 5 0 3 – v a) b)
c) d)
3. In the figure, O is the centre of the circle. If  , then  is equal to : [1] ? A B C = 2 0 o ? A O C 6 0 o 1 0 o 4 0 o 2 0 o 4. In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? [1]
Page 1 of 17
a) b)
c) d)
A B 1 2 ( A B + C D ) 1 2 ( A B - C D ) 1 2 C D 1 2 a)
x
pqr b) 0
c) x d) 1
5. The value of x
p-q 
x
q-r
 x
r-p
 is equal to
[1]
a) 32 cm b) 8 cm
c) 28 cm d) 4 cm
6. D, E and F are the mid points of sides AB, BC and CA of . If perimetre of  is 16 cm, then
perimetre of . 
[1] ? A B C ? A B C ? D E F a) 2x + y = 0 b) x + 2y = 0
c) x + 2y = 4 d) 2x + y = 5
7. x = 2, y = -1 is a solution of the linear equation [1]
a) 5 b) -2
c) -5 d) 3
8. If x - 3 is a factor of x
2
 - ax -15, then a =
[1]
a) b)
c) 3 d) 5
9. The value of  is [1] 1 5 ÷ 3 1 5 - - v 5 – v 5 3 – v 3 5 – v a) OC = BE b) OE = OC
c) AB = OE d) AB = BE
10. ABCD is a parallelogram. If is produced to E such that ED bisects BC at O. Then which of the following is
correct?
[1]
a) b)
c) d)
11. An irrational number between  is [1]   a n d   1 7 2 7 × 1 7 2 7 - - - - - v ( - ) 1 2 1 7 2 7 ( × ) 1 7 2 7 ( + ) 1 2 1 7 2 7 a) Infinitely many b) Two
12. How many linear equations in ‘x’ and ‘y’ can be satisfied by x = 1, y = 2? [1]
Page 2 of 17
c) Only one d) Three
a) 40° b) 50°
c) 70° d) 60°
13. In a figure, if OP||RS, OPQ = 110° and QRS = 130°, then PQR is equal to [1] ? ? ? a) 5 b) 35
c) 19 d) 13
14. After rationalising the denominator of , we get the denominator as [1]
7 3 - 2 3 v 2 v a) 80° b) 60°
c) 90° d) 70°
15. In the given figure, O is the centre of a circle and chords AC and BD intersect at E. If AEB = 110° and CBE
= 30°, then ADB = ? 
[1] ? ? ? a) Origin b) Points
c) Abscissa d) Ordinate
16. x co-ordinate is known as [1]
a) -2 b) 2
c) 3 d) -3
17. If (-2, 5) is a solution of 2x + my = 11, then the value of ‘m’ is [1]
a) 3(a - b)(b - c)(c - a) b) (a + b)(b + c)(c + a)
c) 3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a) d) 2(a - b)(b - c)(c - a)
18. The value of  is
[1]
+ + ( - ) a 2 b 2 3 ( - ) b 2 c 2 3 ( - ) c 2 a 2 3 ( a - b + ( b - c + ( c - a ) 3 ) 3 ) 3 a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): If the diagonals of a parallelogram ABCD are equal, then ABC = 90
o
 
Reason (R): If the diagonals of a parallelogram are equal, it becomes a rectangle.
[1]
? a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
20. Assertion (A):  is an irrational number. 
Reason (R): Sum of a rational number and an irrational number is always an irrational number.
[1] 2 + 6 – v Page 3 of 17
Section B
Section C
c) A is true but R is false. d) A is false but R is true.
21. In fig. AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using a Euclid's axiom, show that AB
= XY . 
[2]
22. In fig., if AC = BD, then prove that AB = CD [2]
23. Name the quadrants in which the following points lie : 
(i) p(4, 4) 
(ii) Q(–4, 4) 
(iii) R(–4, –4) 
(iv) S(4, –4)
[2]
24. If x = 3 + 2 , find the value of .
[2]
OR
Prove that: .
2 – v ( + ) x 2 1 x 2 + + + = 1 1 3 + 7 v 1 + 7 v 5 v 1 + 5 v 3 v 1 + 1 3 v 25. The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights? [2]
OR
A hollow spherical shell is made of a metal of density 4.5 g per cm
3
. If its internal and external radii are 8 cm and 9
cm respectively, find the weight of the shell.
26. Locate  on the number line. [3] 1 0 - - v 27. A random survey of the number of children of various age groups playing in a park was found as follows :
Age (in years) Number of children
1-2 5
2-3 3
3-5 6
5-7 12
7-10 9
10-15 10
15-17 4
Draw a histogram to represent the data above.
[3]
28. In Fig. X and Y are respectively the mid-points of the opposite sides AD and BC of a parallelogram ABCD.
Also, BX and DY intersect AC at P and Q, respectively. Show that AP = PQ = QC.
[3]
Page 4 of 17
Page 5


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) (0, -3) b) (0, 3)
c) (3, 0) d) (-3, 0)
1. The point which lies on x-axis at a distance of 3 units in the positive direction of x-axis is [1]
a)
 cm
2 b)
 cm
2
c)
300 cm
2 d)
 cm
2
2. The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is : [1]
1 0 0 3 – v 1 0 3 – v 5 0 3 – v a) b)
c) d)
3. In the figure, O is the centre of the circle. If  , then  is equal to : [1] ? A B C = 2 0 o ? A O C 6 0 o 1 0 o 4 0 o 2 0 o 4. In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? [1]
Page 1 of 17
a) b)
c) d)
A B 1 2 ( A B + C D ) 1 2 ( A B - C D ) 1 2 C D 1 2 a)
x
pqr b) 0
c) x d) 1
5. The value of x
p-q 
x
q-r
 x
r-p
 is equal to
[1]
a) 32 cm b) 8 cm
c) 28 cm d) 4 cm
6. D, E and F are the mid points of sides AB, BC and CA of . If perimetre of  is 16 cm, then
perimetre of . 
[1] ? A B C ? A B C ? D E F a) 2x + y = 0 b) x + 2y = 0
c) x + 2y = 4 d) 2x + y = 5
7. x = 2, y = -1 is a solution of the linear equation [1]
a) 5 b) -2
c) -5 d) 3
8. If x - 3 is a factor of x
2
 - ax -15, then a =
[1]
a) b)
c) 3 d) 5
9. The value of  is [1] 1 5 ÷ 3 1 5 - - v 5 – v 5 3 – v 3 5 – v a) OC = BE b) OE = OC
c) AB = OE d) AB = BE
10. ABCD is a parallelogram. If is produced to E such that ED bisects BC at O. Then which of the following is
correct?
[1]
a) b)
c) d)
11. An irrational number between  is [1]   a n d   1 7 2 7 × 1 7 2 7 - - - - - v ( - ) 1 2 1 7 2 7 ( × ) 1 7 2 7 ( + ) 1 2 1 7 2 7 a) Infinitely many b) Two
12. How many linear equations in ‘x’ and ‘y’ can be satisfied by x = 1, y = 2? [1]
Page 2 of 17
c) Only one d) Three
a) 40° b) 50°
c) 70° d) 60°
13. In a figure, if OP||RS, OPQ = 110° and QRS = 130°, then PQR is equal to [1] ? ? ? a) 5 b) 35
c) 19 d) 13
14. After rationalising the denominator of , we get the denominator as [1]
7 3 - 2 3 v 2 v a) 80° b) 60°
c) 90° d) 70°
15. In the given figure, O is the centre of a circle and chords AC and BD intersect at E. If AEB = 110° and CBE
= 30°, then ADB = ? 
[1] ? ? ? a) Origin b) Points
c) Abscissa d) Ordinate
16. x co-ordinate is known as [1]
a) -2 b) 2
c) 3 d) -3
17. If (-2, 5) is a solution of 2x + my = 11, then the value of ‘m’ is [1]
a) 3(a - b)(b - c)(c - a) b) (a + b)(b + c)(c + a)
c) 3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a) d) 2(a - b)(b - c)(c - a)
18. The value of  is
[1]
+ + ( - ) a 2 b 2 3 ( - ) b 2 c 2 3 ( - ) c 2 a 2 3 ( a - b + ( b - c + ( c - a ) 3 ) 3 ) 3 a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): If the diagonals of a parallelogram ABCD are equal, then ABC = 90
o
 
Reason (R): If the diagonals of a parallelogram are equal, it becomes a rectangle.
[1]
? a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
20. Assertion (A):  is an irrational number. 
Reason (R): Sum of a rational number and an irrational number is always an irrational number.
[1] 2 + 6 – v Page 3 of 17
Section B
Section C
c) A is true but R is false. d) A is false but R is true.
21. In fig. AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using a Euclid's axiom, show that AB
= XY . 
[2]
22. In fig., if AC = BD, then prove that AB = CD [2]
23. Name the quadrants in which the following points lie : 
(i) p(4, 4) 
(ii) Q(–4, 4) 
(iii) R(–4, –4) 
(iv) S(4, –4)
[2]
24. If x = 3 + 2 , find the value of .
[2]
OR
Prove that: .
2 – v ( + ) x 2 1 x 2 + + + = 1 1 3 + 7 v 1 + 7 v 5 v 1 + 5 v 3 v 1 + 1 3 v 25. The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights? [2]
OR
A hollow spherical shell is made of a metal of density 4.5 g per cm
3
. If its internal and external radii are 8 cm and 9
cm respectively, find the weight of the shell.
26. Locate  on the number line. [3] 1 0 - - v 27. A random survey of the number of children of various age groups playing in a park was found as follows :
Age (in years) Number of children
1-2 5
2-3 3
3-5 6
5-7 12
7-10 9
10-15 10
15-17 4
Draw a histogram to represent the data above.
[3]
28. In Fig. X and Y are respectively the mid-points of the opposite sides AD and BC of a parallelogram ABCD.
Also, BX and DY intersect AC at P and Q, respectively. Show that AP = PQ = QC.
[3]
Page 4 of 17
Section D
29. Find the solution of the linear equation x + 2y = 8 which represents a point on
i. The x-axis
ii. The y-axis
[3]
30. The marks scored by 750 students in an examination are given in the form of a frequency distribution table.
Marks: 600-640 640-680 680-720 720-760 760-800 800-840 840-880
No. of 
Students:
16 45 156 284 172 59 18
Represent this data in the form of a histogram and construct a frequency polygon.
[3]
OR
Read the bar graph given in Figure and answer the following questions: 
i. What information is given by the bar graph?
ii. In which years the areas under the sugarcane crop were the maximum and the minimum?
iii. State whether true or false: 
The area under the sugarcane crop in the year 1982-83 is three times that of the year 1950-51.
31. If both ( x- 2) and  are factors of  , Show that p = r. [3] ( x - ) 1 2 p + 5 x + r x 2 32. In the given figure, AB  CD, , . Find the value of the reflex BOD and hence
the value of x. 
[5]
OR
In the given figure, AB || CD. Prove that p + q - r = 180. 
? ? A B O = 4 0 ° ? C D O = 3 5 ° ? 33. What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? [5]
Page 5 of 17