Final Exam Class 9 Mathematics Set 2

 Page 1


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-
Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with sub-parts of the
values of 1,1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2 Questions of Section
C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks
questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take  wherever required if not stated.
11. Use of calculators is not allowed.
Section A
p = 2 2 / 7 a) b)
c) d)
1. An irrational number between 2 and 2.5 is [1]
2 2 . 5 - - - - v 1 2 . 5 - - - - v 5 – v 1 1 - - v a) y = 5x – 3 b) x = 5y – 3
c) y = 5x + 3 d) x = 5y + 3
2. The taxi fare in a city is as follows: For the first kilometer, the fare is ?8 and for the subsequent distance it is ?5
per kilometer. Taking the distance covered as x km and total fare as ?y, write a linear equation for this
information.
[1]
a) (4, 0) b) (1, 4)
3. The point whose ordinate is 4 and which lies on y-axis is [1]
Page 2


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-
Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with sub-parts of the
values of 1,1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2 Questions of Section
C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks
questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take  wherever required if not stated.
11. Use of calculators is not allowed.
Section A
p = 2 2 / 7 a) b)
c) d)
1. An irrational number between 2 and 2.5 is [1]
2 2 . 5 - - - - v 1 2 . 5 - - - - v 5 – v 1 1 - - v a) y = 5x – 3 b) x = 5y – 3
c) y = 5x + 3 d) x = 5y + 3
2. The taxi fare in a city is as follows: For the first kilometer, the fare is ?8 and for the subsequent distance it is ?5
per kilometer. Taking the distance covered as x km and total fare as ?y, write a linear equation for this
information.
[1]
a) (4, 0) b) (1, 4)
3. The point whose ordinate is 4 and which lies on y-axis is [1]
c) (4, 2) d) (0, 4)
a) vertical axis only b) horizontal axis only
c) vertical axis and horizontal axis d) horizontal axis and vertical axis
4. A histogram is a pictorial representation of the grouped data in which class intervals and frequency are
respectively taken along
[1]
a) three b) many
c) only one d) two
5. How many linear equations can be satisfied by x = 2 and y = 3? [1]
a) lines and curves b) points
c) surfaces d) curves
6. The boundaries of surfaces are [1]
a) 12° b) 8°
c) 15° d) 18°
7. In Fig. if  and , then the value of x is [1] = 5 y x = 4 z x a) trapezium b) Parallelogram
c) rectangle d) square
8. The figure formed by joining the mid-points of the adjacent sides of a rhombus is a [1]
a) 2 b) 3
c) 1 d) 0
9. The value of x
3
 + y
3
 + 15xy - 125 when x + y = 5 is
[1]
a) (0, 3) b) (3, 2)
c) (3, 0) d) (2, 3)
10. The graph of the line x = 3 passes through the point. [1]
a) 35° b) 110°
c) 70° d) 55°
11. ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, BAD = 
[1]
? 12. The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD = 50
o
, then DPC =
[1]
? ?
Page 3


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-
Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with sub-parts of the
values of 1,1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2 Questions of Section
C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks
questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take  wherever required if not stated.
11. Use of calculators is not allowed.
Section A
p = 2 2 / 7 a) b)
c) d)
1. An irrational number between 2 and 2.5 is [1]
2 2 . 5 - - - - v 1 2 . 5 - - - - v 5 – v 1 1 - - v a) y = 5x – 3 b) x = 5y – 3
c) y = 5x + 3 d) x = 5y + 3
2. The taxi fare in a city is as follows: For the first kilometer, the fare is ?8 and for the subsequent distance it is ?5
per kilometer. Taking the distance covered as x km and total fare as ?y, write a linear equation for this
information.
[1]
a) (4, 0) b) (1, 4)
3. The point whose ordinate is 4 and which lies on y-axis is [1]
c) (4, 2) d) (0, 4)
a) vertical axis only b) horizontal axis only
c) vertical axis and horizontal axis d) horizontal axis and vertical axis
4. A histogram is a pictorial representation of the grouped data in which class intervals and frequency are
respectively taken along
[1]
a) three b) many
c) only one d) two
5. How many linear equations can be satisfied by x = 2 and y = 3? [1]
a) lines and curves b) points
c) surfaces d) curves
6. The boundaries of surfaces are [1]
a) 12° b) 8°
c) 15° d) 18°
7. In Fig. if  and , then the value of x is [1] = 5 y x = 4 z x a) trapezium b) Parallelogram
c) rectangle d) square
8. The figure formed by joining the mid-points of the adjacent sides of a rhombus is a [1]
a) 2 b) 3
c) 1 d) 0
9. The value of x
3
 + y
3
 + 15xy - 125 when x + y = 5 is
[1]
a) (0, 3) b) (3, 2)
c) (3, 0) d) (2, 3)
10. The graph of the line x = 3 passes through the point. [1]
a) 35° b) 110°
c) 70° d) 55°
11. ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, BAD = 
[1]
? 12. The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD = 50
o
, then DPC =
[1]
? ? a)
70
o b)
100
o
c)
80
o d)
90
o
a) b)
c) d)
13. In the given figure, ABCD is a cyclic quadrilateral in which   and 
, AC and BD intersect at P. the measure of  is 
[1]
? B A D = , 7 5 o ? A B D = 5 8 o ? A D C = 7 7 o ? D P C 1 0 5 o 9 4 o 9 2 o 9 0 o a) non-terminating non-recurring b) non-terminating recurring
c) a finite decimal d) 1.41421
14. The decimal expansion of the number  is [1] 2 – v a) (x, y) b) (x, 0)
c) (0, y) d) (x, x)
15. Any point on the x-axis is of the form [1]
a) 55° b) 40°
c) 85° d) 90°
16. In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure
of the other interior angle is
[1]
a) 0 b) 2
c) 3 d) 1
17. If p(x) = x
3
 - x
2
 + x + 1, then the value of  is
[1]
p ( - 1 ) + p ( 1 ) 2 a) b)
c) d)
18. The volume of two spheres are in the ratio 216 : 125. The difference of their surface areas, if the sum of their
radii is 11 units, is _____.
[1]
4 5 p sq. units 5 0 p sq. units 
4 4 p sq. units 3 8 p sq. units 
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 area of an equilateral triangle is  cm
2
, then the semi perimeter of triangle is 20 cm. 
Reason (R): Semi perimeter of a triangle is s = , where a, b, c are sides of triangle.
[1]
8 1 3 – v a + b + c 2 20. Assertion (A): There are infinite number of lines which passes through (2, 14). 
Reason (R): A linear equation in two variables has infinitely many solutions.
[1]
Page 4


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-
Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with sub-parts of the
values of 1,1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2 Questions of Section
C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks
questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take  wherever required if not stated.
11. Use of calculators is not allowed.
Section A
p = 2 2 / 7 a) b)
c) d)
1. An irrational number between 2 and 2.5 is [1]
2 2 . 5 - - - - v 1 2 . 5 - - - - v 5 – v 1 1 - - v a) y = 5x – 3 b) x = 5y – 3
c) y = 5x + 3 d) x = 5y + 3
2. The taxi fare in a city is as follows: For the first kilometer, the fare is ?8 and for the subsequent distance it is ?5
per kilometer. Taking the distance covered as x km and total fare as ?y, write a linear equation for this
information.
[1]
a) (4, 0) b) (1, 4)
3. The point whose ordinate is 4 and which lies on y-axis is [1]
c) (4, 2) d) (0, 4)
a) vertical axis only b) horizontal axis only
c) vertical axis and horizontal axis d) horizontal axis and vertical axis
4. A histogram is a pictorial representation of the grouped data in which class intervals and frequency are
respectively taken along
[1]
a) three b) many
c) only one d) two
5. How many linear equations can be satisfied by x = 2 and y = 3? [1]
a) lines and curves b) points
c) surfaces d) curves
6. The boundaries of surfaces are [1]
a) 12° b) 8°
c) 15° d) 18°
7. In Fig. if  and , then the value of x is [1] = 5 y x = 4 z x a) trapezium b) Parallelogram
c) rectangle d) square
8. The figure formed by joining the mid-points of the adjacent sides of a rhombus is a [1]
a) 2 b) 3
c) 1 d) 0
9. The value of x
3
 + y
3
 + 15xy - 125 when x + y = 5 is
[1]
a) (0, 3) b) (3, 2)
c) (3, 0) d) (2, 3)
10. The graph of the line x = 3 passes through the point. [1]
a) 35° b) 110°
c) 70° d) 55°
11. ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, BAD = 
[1]
? 12. The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD = 50
o
, then DPC =
[1]
? ? a)
70
o b)
100
o
c)
80
o d)
90
o
a) b)
c) d)
13. In the given figure, ABCD is a cyclic quadrilateral in which   and 
, AC and BD intersect at P. the measure of  is 
[1]
? B A D = , 7 5 o ? A B D = 5 8 o ? A D C = 7 7 o ? D P C 1 0 5 o 9 4 o 9 2 o 9 0 o a) non-terminating non-recurring b) non-terminating recurring
c) a finite decimal d) 1.41421
14. The decimal expansion of the number  is [1] 2 – v a) (x, y) b) (x, 0)
c) (0, y) d) (x, x)
15. Any point on the x-axis is of the form [1]
a) 55° b) 40°
c) 85° d) 90°
16. In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure
of the other interior angle is
[1]
a) 0 b) 2
c) 3 d) 1
17. If p(x) = x
3
 - x
2
 + x + 1, then the value of  is
[1]
p ( - 1 ) + p ( 1 ) 2 a) b)
c) d)
18. The volume of two spheres are in the ratio 216 : 125. The difference of their surface areas, if the sum of their
radii is 11 units, is _____.
[1]
4 5 p sq. units 5 0 p sq. units 
4 4 p sq. units 3 8 p sq. units 
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 area of an equilateral triangle is  cm
2
, then the semi perimeter of triangle is 20 cm. 
Reason (R): Semi perimeter of a triangle is s = , where a, b, c are sides of triangle.
[1]
8 1 3 – v a + b + c 2 20. Assertion (A): There are infinite number of lines which passes through (2, 14). 
Reason (R): A linear equation in two variables has infinitely many solutions.
[1]
Section B
Section C
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.
21. 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.
[2]
22. Find the area of a triangle whose perimeter is 180 cm and two of its sides are 80 cm and 18 cm. Hence calculate
the altitude of the triangle taking the longest sides as base.
[2]
23. If O is the centre of below circle, find the value of x in given figure: 
[2]
24. In the figure,
i. BAC = 70
o
 and DAC = 40
o
, then find BCD
ii. BAC = 60
o
 and BCA = 60
o
, then find ADC
[2]
OR
In the given figure, two circles intersect at two points A and B. AD and AC are diameters to the two circles. Prove
that B lies on the line segment DC. 
? ? ? ? ? ? 25. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a. [2]
OR
Find whether  is the solution of the equation x – 2y = 4 or not? ( , 4 ) 2 – v 2 – v 26. State whether the following statements are true or false. Give reasons for your answers. 
(i) Every natural number is a whole number. 
(ii) Every integer is a whole number. 
(iii) Every rational number is a whole number.
[3]
27. Show that p - 1 is a factor of p
10
 - 1 and also of p
11
 - 1.
[3]
28. A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the
rate of ? 5 per m
2
. Find the cost of painting.
[3]
Page 5


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-
Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with sub-parts of the
values of 1,1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2 Questions of Section
C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks
questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take  wherever required if not stated.
11. Use of calculators is not allowed.
Section A
p = 2 2 / 7 a) b)
c) d)
1. An irrational number between 2 and 2.5 is [1]
2 2 . 5 - - - - v 1 2 . 5 - - - - v 5 – v 1 1 - - v a) y = 5x – 3 b) x = 5y – 3
c) y = 5x + 3 d) x = 5y + 3
2. The taxi fare in a city is as follows: For the first kilometer, the fare is ?8 and for the subsequent distance it is ?5
per kilometer. Taking the distance covered as x km and total fare as ?y, write a linear equation for this
information.
[1]
a) (4, 0) b) (1, 4)
3. The point whose ordinate is 4 and which lies on y-axis is [1]
c) (4, 2) d) (0, 4)
a) vertical axis only b) horizontal axis only
c) vertical axis and horizontal axis d) horizontal axis and vertical axis
4. A histogram is a pictorial representation of the grouped data in which class intervals and frequency are
respectively taken along
[1]
a) three b) many
c) only one d) two
5. How many linear equations can be satisfied by x = 2 and y = 3? [1]
a) lines and curves b) points
c) surfaces d) curves
6. The boundaries of surfaces are [1]
a) 12° b) 8°
c) 15° d) 18°
7. In Fig. if  and , then the value of x is [1] = 5 y x = 4 z x a) trapezium b) Parallelogram
c) rectangle d) square
8. The figure formed by joining the mid-points of the adjacent sides of a rhombus is a [1]
a) 2 b) 3
c) 1 d) 0
9. The value of x
3
 + y
3
 + 15xy - 125 when x + y = 5 is
[1]
a) (0, 3) b) (3, 2)
c) (3, 0) d) (2, 3)
10. The graph of the line x = 3 passes through the point. [1]
a) 35° b) 110°
c) 70° d) 55°
11. ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, BAD = 
[1]
? 12. The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD = 50
o
, then DPC =
[1]
? ? a)
70
o b)
100
o
c)
80
o d)
90
o
a) b)
c) d)
13. In the given figure, ABCD is a cyclic quadrilateral in which   and 
, AC and BD intersect at P. the measure of  is 
[1]
? B A D = , 7 5 o ? A B D = 5 8 o ? A D C = 7 7 o ? D P C 1 0 5 o 9 4 o 9 2 o 9 0 o a) non-terminating non-recurring b) non-terminating recurring
c) a finite decimal d) 1.41421
14. The decimal expansion of the number  is [1] 2 – v a) (x, y) b) (x, 0)
c) (0, y) d) (x, x)
15. Any point on the x-axis is of the form [1]
a) 55° b) 40°
c) 85° d) 90°
16. In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure
of the other interior angle is
[1]
a) 0 b) 2
c) 3 d) 1
17. If p(x) = x
3
 - x
2
 + x + 1, then the value of  is
[1]
p ( - 1 ) + p ( 1 ) 2 a) b)
c) d)
18. The volume of two spheres are in the ratio 216 : 125. The difference of their surface areas, if the sum of their
radii is 11 units, is _____.
[1]
4 5 p sq. units 5 0 p sq. units 
4 4 p sq. units 3 8 p sq. units 
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 area of an equilateral triangle is  cm
2
, then the semi perimeter of triangle is 20 cm. 
Reason (R): Semi perimeter of a triangle is s = , where a, b, c are sides of triangle.
[1]
8 1 3 – v a + b + c 2 20. Assertion (A): There are infinite number of lines which passes through (2, 14). 
Reason (R): A linear equation in two variables has infinitely many solutions.
[1]
Section B
Section C
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.
21. 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.
[2]
22. Find the area of a triangle whose perimeter is 180 cm and two of its sides are 80 cm and 18 cm. Hence calculate
the altitude of the triangle taking the longest sides as base.
[2]
23. If O is the centre of below circle, find the value of x in given figure: 
[2]
24. In the figure,
i. BAC = 70
o
 and DAC = 40
o
, then find BCD
ii. BAC = 60
o
 and BCA = 60
o
, then find ADC
[2]
OR
In the given figure, two circles intersect at two points A and B. AD and AC are diameters to the two circles. Prove
that B lies on the line segment DC. 
? ? ? ? ? ? 25. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a. [2]
OR
Find whether  is the solution of the equation x – 2y = 4 or not? ( , 4 ) 2 – v 2 – v 26. State whether the following statements are true or false. Give reasons for your answers. 
(i) Every natural number is a whole number. 
(ii) Every integer is a whole number. 
(iii) Every rational number is a whole number.
[3]
27. Show that p - 1 is a factor of p
10
 - 1 and also of p
11
 - 1.
[3]
28. A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the
rate of ? 5 per m
2
. Find the cost of painting.
[3]
Section D
OR
In Fig., ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same
area as that of ABC is constructed. Find the height DF of the parallelogram. 
? ? 29. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap
is to be covered by canvas to protect it from rain. Find the area of the canvas required.
[3]
30. If AE = AD and BD = CE. Prove that AEB  ADC 
[3]
OR
In given figure, it is given that AB = CF, EF = BD and AFE = CBD. Prove that AFE  CBD. 
? ? ? ? ? ? ? ? 31. 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 intersect.
[3]
32. Simplify: .
[5]
OR
If a = 3 + 2 , then find the value of:
i. 
ii. 
- - 7 3 v + 1 0 v 3 v 2 5 v + 6 v 5 v 3 2 v + 3 1 5 v 2 v 2 – v + a 2 1 a 2 + a 3 1 a 3 33. i. AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.
[5]