ICSE Class 10 Competency Based Questions (CBQ) Mathematics

PREFACE
With a growing emphasis on competency-based education globally, the educational landscape in India
has also steered towards high-quality learning experiences that allow learners to incorporate critical
thinking and problem-solving approaches. This approach goes beyond rote memorisation and focuses
on developing the skills and knowledge that students need to apply in their real-world scenarios.
The Council for the Indian School Certificate Examinations (CISCE), as a national-level progressive
examination board, has taken several steps to infuse competency-based education in CISCE schools
through teacher capacity-building on item development for competency-based assessments and the
incorporation of competency-focused questions at the ICSE and ISC levels from the examination year
2024.
To further facilitate the adoption of competency-based assessment practices in schools and to support
teachers and students towards the preparation for attempting higher-order thinking questions in future
board examinations, Item Banks of Competency-Focused Practice Questions for selected subjects
at the ICSE and ISC levels have been developed. This Item Bank consists of a rich variety of questions,
both objective and subjective in categories, aimed at enhancing the subject-specific critical and
analytical thinking skills of the students.
In this Item Bank, each question is accompanied by the topic and cognitive learning domain/s that it
intends to capture. The cognitive domains reflected in these questions include understanding, analysis,
application, evaluation and creativity, along with some questions of the higher-order recall domain.
The Answer Key at the end presents the possible answers to a given question, but it is neither limiting
nor exhaustive.
These practice questions are also meant to serve as teacher resources for classroom assignments and
as samplers to develop their own repository of competency-focused questions. Apart from offering a
good practice of higher-order thinking skills, engaging with these questions would allow students to
gauge their own subject competencies and use these assessments for learning to develop individual
learning pathways.
During the development of this Item Bank, a large pool of questions was prepared by a team of
experienced CISCE teachers. The questions that were finalised by the internal and external reviewers
as being higher-order competency-focused questions have been collated in this item bank.
I acknowledge and appreciate all the ICSE and the ISC subject matter experts who have contributed
to the development and review of these high-quality competency-focused questions for CISCE
students.
We are hopeful that teachers and students will utilise these questions to support their teaching-learning
processes.
July 2024 Dr. Joseph Emmanuel
Chief Executive & Secretary
CISCE

Table of Contents

Pg. No

Questions

I. Multiple-Choice Questions Type 1

II. Short Answer Type-1 14

III. Short Answer Type-2 21

IV. Long Answer Type-1 (Graph-based) 29

V. Long Answer Type-2 31

Answer Key 36

COMPETENCY-FOCUSED PRACTICE QUESTIONS

FOR ICSE – CLASS X

Mathematics
I: Multiple Choice Questions Type (1 Mark Each)

S.No. Questions
1. [Commercial Mathematics]
A retailer buys an article at its listed price from a wholesaler and sells it to a
consumer in the same state after marking up the price by 20%. The list price of the
article is ₹ 2500, and the rate of GST is 12%. What is the tax liability of the retailer
to the central government?
(a) ₹0
(b) ₹15
(c) ₹30
(d) ₹60 [Analysis & Evaluate]

2. [Commercial Mathematics]
Dev bought an electrical fan which has a marked price of ₹800. If the GST on the
goods is 7%, then the SGST is:
(a) ₹ 24
(b) ₹ 28
(c) ₹ 56
(d) ₹ 80 [Evaluate]

3. [Commercial Mathematics]
₹ P is deposited for n number of months in a recurring deposit account which pays
interest at the rate of r % per annum. The nature and time of interest calculated is:
(a) compound interest for n number of months.
(b) simple interest for n number of months.
(c) compound interest for one month.
(d) simple interest for one month [Understanding & Application]

1

S.No. Questions
4. [Commercial Mathematics]
Anwesha intended to open a Recurring Deposit account of ₹1000 per month for 1
year in a Bank, paying a 5% per annum rate of simple interest. The bank reduced
the rate to 4% per annum. How much must Anwesha deposit monthly for 1 year so
that her interest remains the same?
(a) ₹12325
(b) ₹1250
(c) ₹1200
(d) ₹1000 [Analysis & Evaluate]

5. [Commercial Mathematics]
Mr. Das invests in ₹100, 12% shares of Company A available at ₹60 each. Mr. Singh
invests in ₹50, 16 % shares of Company B available at ₹40 each. Use this
information to state which of the following statements is true.
(a) The rate of return for Mr. Das is 12%
(b) The rate of return for Mr. Singh is 10%
(c) Both Mr. Das and Mr. Singh have the same rate of return of 10%
(d) Both Mr. Das and Mr. Singh have the same rate of return of 20%
[Application & Evaluate]

6. [Commercial Mathematics]
Amit invested a certain sum of money in ₹100 shares, paying a 7.5% dividend. The
rate of return on his investment is 10%. The money invested by Amit to purchase
10 shares is:
(a) ₹ 250
(b) ₹ 750
(c) ₹ 900
(d) ₹ 1100 [Application & Evaluate]

7. [Algebra]
If -3 ≤ -4x+5 and x ε W, then the solution set is.
(a) { ….-3,-2,-1,0,1,2,3…}
(b) { 1, 2 }
(c) { 0,1,2}
(d) { 2, 3 4,5} [Understanding & Application]

8. [Algebra]
If -4x > 8y, then
(a) x > 2y
(b) x > -2y
(c) x < -2y
(d) x < 2y [Understanding & Application]

2

S.No. Questions
9. [Algebra]
The value/s of ‘k’ for which the quadratic equation 2𝑥 2 − 𝑘𝑥 + 𝑘 = 0 has equal
roots is(are):
(a) 0 only
(b) 4,0
(c) 8 only
(d) 0,8 [Understanding & Application]

10. [Algebra]
If x = -2 is one of the solutions of the quadratic equation 𝑥 2 + 3𝑎-x = 0, then the
value of ‘a’ is
(a) -8
(b) -2
(c) -1/3
(d) 1/3 [Understanding & Application]

11. [Algebra]
In solving a quadratic equation, one of the values of the variable x is 233.356. The
solution rounded to two significant figures is:
(a) 233.36
(b) 233.35
(c) 233.3
(d) 230
[Understanding & Application]

12. [Algebra]
In the adjoining diagram, AB = x cm, BC=y cm and x – y = 7 cm. Area of ∆ABC
= 30 𝑐𝑚2. The length of AC is:
(a) 10 cm A
(b) 12 cm
(c) 13 cm 𝑥
(d) 15 cm
B 𝑦 C
[Analysis & Evaluate]

13. [Algebra]
If p, q, and r are in continued proportion, then:
(a) p : q = p: r
(b) q : r = 𝑝2 : 𝑞 2
(c) p : 𝑞 2 = r : 𝑝2
(d) p : r = 𝑝2 : 𝑞 2 [Understanding & Application]

3

S.No. Questions
14. [Mensuration]
The ratio of diameter to height of a Borosil cylindrical glass is 3:5. If the actual
diameter of the glass is 6cm, then the curved surface area of the glass is (in cm2):
(a) 120π
(b) 60π
(c) 30π
(d) 18π [Analysis & Evaluate]

15. [Algebra]
If the polynomial 2 𝑥 3 + 3 𝑥 2 − 2𝑥 − 3 is completely divisible by (2x + a), and the
quotient is equal to (𝑥 2 − 1), then one of the values of a is:
(a) -3
(b) -1
(c) 1
(d) 3 [Analysis]

16. [Algebra]
A polynomial in x is 𝑥 3 + 5𝑥 2 – kx -24. Which of the following is a factor of the
given polynomial so that the value of k is 2?
(a) (x + 2)
(b) (x – 3)
(c) (x + 4)
(d) (x – 4) [Analysis & Evaluate]

17. [Algebra]
𝑐
If 𝐴 = [𝑎 𝑏] 𝑎𝑛𝑑 𝐵 = [𝑑 ], then
(a) only matrix AB is possible.
(b) only matrix BA is possible.
(c) both matrices AB and BA are possible.
(d) both matrices AB and BA are possible, AB = BA.
[Understanding & Application]

18. [Algebra]
6 9 0 0
Matrix 𝐴 = [ ] such that 𝐴2 = [ ].Then k is:
−4 𝑘 0 0
(a) 6
(b) -6
(c) 36
(d) ±6 [Analysis & Evaluate]

4

S.No. Questions
19. [Algebra]
If the sum of n terms of an arithmetic progression Sn = n2 – n, then the third term
of the series is:
(a) 2
(b) 4
(c) 6
(d) 9 [Understanding & Application]

20. [Algebra]
Which of the following is not a geometric progression?
(a) 1/3, 1, 3, 9
(b) 1/5, 1/5,1/5,1/5
(c) -2, 4, -8, 16
(d) 2,0,4,0,8,0 [Understanding]

21. [Algebra]
In the adjoining diagram, G is the centroid of ∆ABC. A (3,-3), B (2,-6), C (x, y)
and G (5,-5). The coordinates of point D are:
(a) (2,- 6 )
(b) (3,- 6 ) A (3, -3)
(c) (6,- 6 )
(d) (10,- 6 )

G (5, -5)

B (2, -6) D C (x, y)

[Analysis & Application]

22. [Algebra]
In the given diagram, O is the origin, and P is the midpoint of AB. The equation of
OP is:
(a) y = x
(b) 2y = x
(c) y = 2x
(d) y = -x

[Analysis & Application]

5

S.No. Questions
23. [Algebra]
In the given figure Line l1 is a parallel to Line l2. If line l3 is perpendicular to Line
l1, then the slopes of lines l2 and l3 respectively are:
(a) 1, 1 Y-axis
(b) -1, -1 Line l3 Line l1
(c) 1, -1
(d) -1, 1

45 X-axis
0 °

Line l2

[Analysis & Application]

24. [Algebra]
Which of the following lines cut the positive x-axis and positive y-axis at equal
distances from the origin?
(a) 3x+3y=6
(b) 5x +10y = 10
(c) -x + y = 1
(d) 10x +5y = 5 [Understanding & Application]

25. [Geometry]
In the given diagram (not drawn to scale), railway stations A, B, C, P and Q are
connected by straight tracks. Track PQ is parallel to BC. The time taken by a train
travelling at 90km/hr to reach B from A by the shortest route is:
(a) 8 minutes A
(b) 12 minutes
(c) 16.8 minutes
(d) 20 minutes P 20 km Q

B C
50 km
[Analysis & Application]

6

S.No. Questions
26. [Geometry]

A D

B C E F

In the given diagram, Δ ABC and ΔDEF (not drawn to scale) are such that
𝐴𝐵 𝐵𝐶
∠𝐶 = ∠ F and 𝐷𝐸 = 𝐸𝐹 , then
(a) Δ ABC ~ Δ DEF
(b) Δ BCA ~ Δ DEF
(c) Δ CAB ~ Δ DEF
(d) the similarity of given triangles cannot be determined. [Analysis]

27. [Geometry]
In the adjoining diagram, ST is not parallel to PQ. T Q
R
The necessary and sufficient conditions
for ∆PQR ~∆TSR is:
(a) ∠PQR=∠STR S
(b) ∠QPR=∠TSR
(c) ∠PQR=∠TSR P
(d) ∠PRQ=∠RST [Understanding & Application]

28. [Geometry]
The scale factor of a picture and the actual height of Sonia is 20cm: 1.6m. If her
height in the picture is 18cm, then her actual height is,
(a) 14.4m
(b) 2.25m
(c) 1.78m
(d) 1.44m [Analysis & Application]

7

S.No. Questions
29. [Geometry]
In the adjoining figure, O is the centre of the circle, and a semicircle is drawn on
OA as the diameter. ∠APQ=20°.The degree measure of ∠OAQ is:
(a) 25°
(b) 40°
(c) 50°
(d) 65°

[Analysis & Application]

30. [Geometry]
In the given diagram, O is the centre of the circle, and PQ is a tangent at A. If
∠ABC=50°, then values of x,y and z respectively are:
(a) 500 , 1000 , 400
(b) 500 , 500 , 650
(c) 400 , 800 , 500
(d) 500 , 250 , 780

[Analysis & Evaluation]

8

S.No. Questions
31. [Geometry]
In the given figure PT and QT are tangents to a circle such that ∠TPS = 450 and
∠TQS = 300. Then the value of x is:

(a) 300
(b) 450
(c) 750
(d) 1050

[Analysis & Evaluation]

32. [Mensuration]
A cylindrical metallic wire is stretched to double its length. Which of the following
will NOT change for the wire after stretching?
(a) Its curved surface area.
(b) Its total surface area.
(c) Its volume.
(d) Its radius. [Understanding]

33. [Mensuration]
A right circular cone has the radius of the base equal to the height of the cone. If
the volume of the cone is 9702 cu cm, then the diameter of the base of the cone is:

(a) 21cm
(b) 42cm
(c) 21√7 cm
(d) 2√7 cm.

[Use π = 22/7] [Understanding & Application]

9

S.No. Questions
34. [Mensuration]
A solid sphere with a radius of 4cm is cut into 4 identical pieces by two mutually
perpendicular planes passing through its centre. Find the total surface area of one-
quarter piece.
(a) 24π
(b) 32π
(c) 48π
(d) 64π

[Understanding & Application]

35. [Mensuration]
Two identical solid hemispheres are kept in contact to form a sphere. The ratio of
the total surface areas of the two hemispheres to the surface area of the sphere
formed is:
(a) 1 : 1
(b) 3 : 2 + =
(c) 2 : 3
(d) 2 : 1
[Analysis & Application]

36. [Trigonometry]
𝑐𝑜𝑠𝑒𝑐 2 𝜃 + 𝑠𝑒𝑐 2 𝜃 is equal to:
(a) 𝑡𝑎𝑛2 𝜃 + 𝑐𝑜𝑡 2 𝜃
(b) 𝑐𝑜𝑡𝜃 + 𝑡𝑎𝑛𝜃
(c) (𝑐𝑜𝑡𝜃 + 𝑡𝑎𝑛𝜃)2
(d) 1 [Application]

37. [Trigonometry]
Given 𝑎 = 3 𝑠𝑒𝑐 2 𝜃 and 𝑏 = 3 𝑡𝑎𝑛2 𝜃 − 2. The value of (a – b) is:
(a) 1
(b) 2
(c) 3
(d) 5 [Application]

10

S.No. Questions
38. [Trigonometry]
At a certain time of day, the ratio of the height of the pole to the length of its shadow
is 1 : √3, then the angle of elevation of the sun at that time of the day is:
(a) 30°
(b) 45°
(c) 60°
(d) 90° [Understanding & Application]

39. [Trigonometry]
A man standing on a ship approaching the port towards the lighthouse is observing
the top of the lighthouse. In 10 minutes, the angle of elevation of the top of the
lighthouse changes from α to β. Then:
(a) α > β
(b) α < β
(c) α = β
(d) α ≤ β [Analysis & Evaluation]

40. [Statistics]
Assertion (A): The difference in class marks of the modal class and the median
class of the following frequency distribution table is 0.
Class 20 – 30 30 – 40 40 – 50 50 – 60 60 -70
interval
Frequency 1 3 2 6 4
Reason (R): Modal class and median class are always the same for a given
frequency distribution.
(a) Both A and R are correct, and R is the correct explanation for A.
(b) Both A and R are correct, and R is not the correct explanation for A.
(c) A is true, but R is false.
(d) Both A and R are true. [Analysis]

41. [Statistics]
Assertion(A): For a collection of 11 arrayed data, the median is the middle number.
Reason (R): For the data 5, 9,7, 13,10,11,10, the median is 13.
(a) Both A and R are correct, and R is the correct explanation for A.
(b) Both A and R are correct, and R is not the correct explanation for A.
(c) A is true, but R is false.
(d) Both A and R are true. [Analysis]

11

S.No. Questions
42. [Commercial Mathematics]
Ankit had the option of investing in company A, where 7%, ₹ 100 shares are
available at ₹ 120 or in company B, where 8%, ₹ 1000 shares are available at ₹
1620.
Assertion (A): Investment in Company A is better than Company B.
Reason (R): The rate of income in Company A is better than in Company B.
(a) Both A and R are true, and R is the correct explanation.
(b) Both A and R are true, but R is not the correct explanation.
(c) A is false, but R is true.
(d) Both A & R are false. [Analysis]

43. [Algebra]
Assertion (A): 𝑥 3 + 2𝑥 2 − 𝑥 − 2is a polynomial of degree 3.
Reason (R): x + 2 is a factor of the polynomial.
(a) Both A and R are correct, and R is the correct explanation for A.
(b) Both A and R are incorrect.
(c) A is true, but R is false.
(d) Both A and R both are true. [Analysis]

44. [Algebra]
Assertion(A): The point ( -2, 8) is invariant under reflection in line x = - 2
Reason (R): If a point has its x-coordinate 0, it is invariant under reflection in
both axes.
(a) Both A and R are correct, and R is the correct explanation for A.
(b) Both A and R are correct, and R is not the correct explanation for A.
(c) A is true, but R is false.
(d) Both A and R are true. [Analysis]

45. [Probability]

When a die is cast with numbering on its faces, as shown, the ratio of the probability
of getting a composite number to the probability of getting a prime number is
_______.
(a) 2:3
(b) 3:2
(c) 1:3
(d) 1:2 [Analysis]

12

S.No. Questions
46. [Algebra]
1 −2 2
The product of A = [ ] and matrix M is AM = B where B = [ ], then the
−3 4 24
order of matrix M is ____________.
(a) 2x2
(b) 2x1
(c) 1x2
(d) 4x1 [Understanding & Application]

47. [Algebra]
Given, 𝑎1 , 𝑎2 , 𝑎3 ,…….and 𝑏1 , 𝑏2 , 𝑏3 ,……. are real numbers such that
𝑎1 − 𝑏1 = 𝑎2 − 𝑏2 = 𝑎3 − 𝑏3 =⋯………. are all equal.
𝑎1 − 𝑏1 , 𝑎2 − 𝑏2 , 𝑎3 − 𝑏3………. forms a ______________ progression.
(a) Geometric (r=1)
(b) Arithmetic (d=1)
(c) Geometric (r<1)
(d) Arithmetic (d=0) [Analysis & Application]

48. [Geometry]
Locus of a moving point is _______________ if it moves such that it keeps a
fixed distance from a fixed point.
(a) Circle
(b) Line
(c) Angle
(d) Line segment [Recall & Understanding]

49. [Geometry]
The point of concurrence of the angle bisectors of a triangle is called the _________
of the triangle.
(a) centroid
(b) incentre
(c) circumcentre
(d) orthocentre [Recall & Understanding]

13

II. Short Answer Type-1 (3 Marks)

S.No. Questions
50. [Commercial Mathematics]
A shopkeeper marked a pressure cooker at Rs 1800.The rate of GST on pressure
cooker is 12% . The customer has only Rs. 1792 with him and he requests the
shopkeeper to reduce the price so that he can buy the cooker in Rs. 1792. What
percent discount must the shopkeeper give? [Application & Evaluation]

51. [Commercial Mathematics]
A man opened a recurring deposit account in a branch of PNB. The man deposits
certain amount of money per month such that after 2 years , the interest accumulated
is equal to his monthly deposits. Find the rate of interest per annum that the bank
was paying for the recurring deposit account.
[Application & Evaluation]

52. [Commercial Mathematics]
Akshay buys 350 shares of ₹50 par value of a company. The dividend declared by
the company is 14%. If his return percent from the shares is 10%, find the market
value of each share. [Application & Evaluation]

53. [Algebra]
Solve the following inequation:
1 1 1
(2𝑥 − 1) ≤ 2x + ≤ 52 + 𝑥
2 2

(a) Write the maximum and minimum values of x for x ∈ R.
(b) What will be the change in maximum and minimum values of x if x ∈ W.
[Evaluate & Analysis]

54. [Algebra]
5 2√3
Solve for x, if 𝑥 + 4√3 = 𝑥 2 , x ≠0 [Application & Evaluate]

55. [Algebra]
The marked price of a toy is same as the percentage of GST that is charged. The
price of the toy is ₹ 24 including GST. Taking the marked price as x, form an
equation and solve it to find x. [Application & Evaluate]

56. [Algebra]
The mean proportion between two numbers is 6 and their third proportional is 48.
Find the two numbers. [Application & Evaluate]

14

S.No. Questions
57. [Algebra]
Pamela factorized the following polynomial:
2𝑥 3 + 3𝑥 2 − 3𝑥 − 2
She found the result as (x+2)(x-1)(x-2). Using remainder and factor theorem, verify
whether her result is correct. If incorrect, give the correct result.
[Analysis & Application]

58. [Algebra]
−6 0 1 0
A=[ ] and B = [ ] .
4 2 1 3
1
Find matrix M, if M = A -2B + 5l, where l is the identity matrix.
2

[Application & Evaluate]

59. [Algebra]
(a) Write the nth term (Tn) of an Arithmetic Progression (A.P.) consisting of all
whole numbers which are divisible by 3 and 7.
(b) How many of these are two-digit numbers? Write them.
(c) Find the sum of first 10 terms of this A.P. [Application & Evaluate]

60. [Algebra]
𝒏
Write the first five terms of the sequence given by (√𝟑) , n ∈ N.
(a) Is the sequence an A.P. or G.P?
(b) If the sum of its first ten terms is p(3+√3),find the value of p.
[Application & Evaluate]

15

S.No. Questions
61. [Algebra]
ABC is a triangle as shown in the figure below.

(a) Write down the coordinates of A, B, and C on reflecting through the origin.
(b) Write down the coordinates of the point/s which remain invariant on reflecting
the triangle ABC on the x-axis and y-axis respectively.
[Analysis & Evaluate]

62. [Algebra]
Determine the ratio in which the line y = 2 + 3x divides the line segment AB
joining the points A (-3, 9) and B (4 ,2 ). [Understanding & Application]

63. [Algebra]
Square ABCD lies in the third quadrant of a XY plane such that its vertex A is at
(-3,-1) and the diagonal DB produced is equally inclined to both the axes.The
diagonals AC and BD meets at P (-2,-2). Find the:
(a) slope of BD
(b) equation of AC [Analysis, Create & Evaluate]

64. [Geometry]
ABCD is a rectangle where side BC is twice side AB. If ∆ACQ~∆BAP, find area
of ∆BAP: area of ∆ACQ

[Analysis & Evaluate]

16

S.No. Questions
65. [Geometry]

Given a triangle ABC, and D is a point on BC such that BD = 4cm and DC = x cm.
If ∠BAD = ∠C, and AB = 8cm, then,
(a) Prove that triangle ABD is similar to triangle CBA.
(b) Find the value of ‘x’. [Understanding, Application & Evaluate]

66. [Geometry]
In the extract of Survey of India map G43S7, prepared on a scale of 2cm to 1 km,a
child finds the length of the cart track between two settlements is 7.6 cm. Find:
(a) the actual length of the cart track on the ground.
(b) actual area of a grid square,if each has an area of 4 𝑐𝑚2 .
[Understanding & Evaluate]

67. [Geometry]
Construct a triangle ABC such that AB = 7cm, BC = 6cm and CA = 5cm. (use ruler
and compass to do so).
(a) Draw the locus of the points such that
i) it is equidistant from BC and BA.
ii) it is equidistant from points A and B.
(b) Mark P where the loci i) and ii) meet , measure and write length of PA.
[Analysis & Create]

17

S.No. Questions
68. [Geometry]
In the given figure O is the centre of the circle. ABCD is a quadrilateral where sides
AB, BC, CD and DA touch the circle at E, F, G and H respectively. If AB = 15 cm,
BC= 18 cm and AD=24 cm , find the length of CD.

[Application & Evaluate]

69. [Geometry]
In the given diagram ABCDEF is a regular hexagon inscribed in a circle with centre
O. PQ is a tangent to the circle at D. Find the value of:
(a) ∠FAG
P
(b) ∠BCD
(c) ∠PDE
E D

F O C Q

G
A B
[Application & Evaluate]

70. [Geometry]

AB and CD intersect at the centre O of the circle
given in the above diagram. If ∠EBA=33° and
∠EAC=82 °, find
(a) ∠BAE
(b) ∠BOC
(c) ∠ODB

[Application & Evaluate]

18

S.No. Questions
71. [Mensuration]
A famous sweet shop “Madanlal Sweets” sells tinned rasgullas. The tin container is
cylindrical in shape with diameter 14cm, height 16cm, and it can hold 20 spherical
rasgullas of diameter 6cm and sweetened liquid such that the can is filled and then
sealed. Find out how much sweetened liquid the can contains. Take π=3.14.
[Analysis, Application & Evaluate]

72. [Mensuration]
The ratio of the radius and the height of a solid metallic right circular cylinder is
7 : 27. This is melted and made into a cone of diameter 14 cm and slant height 25
cm. Find the height of the:
(a) cone
(b) cylinder [Analysis, Application & Evaluate]

73. [Trigonometry]
An inclined plane AC is prepared with its base AB which is √3 times its vertical
height BC.The length of the inclined plane is 15 m.Find:
(a) value of θ
(b) length of its base AB,in nearest metre.

C
15m

𝜃
A B
[Analysis, Application & Evaluate]

74. [Trigonometry]
Prove that
𝑡𝑎𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 − 1 = 𝑡𝑎𝑛2 𝜃 . 𝑠𝑖𝑛2 𝜃
[Analysis & Application]

19

S.No. Questions
75. [Statistics]
The class mark and frequency of a data is given in the graph. From the graph, Find:
(a) The table showing the class interval and frequency.
(b) Calculate the mean.

[Analysis, Application & Evaluate]

76. [Statistics]
The mean of 5,7, 8 , 4 and m is n and the mean of 5, 7 , 8 , 4 , m and n is m. Find
the values of m and n. [Understanding & Application]

77. [Probability]
The probability of selecting a blue marble and a red marble from a bag containing
red,blue and green marbles is 1/3 and 1/5 respectively. If the bag contains 14
green marbles,then find:
(a) number of red marbles.
(b) total number of marbles in the bag. [Analysis & Evaluate]

20

III. Short Answer Type -2 (4 Marks)

S.No. Questions
78. [Commercial Mathematics]
The following bill shows the GST rate and the marked price of items:
𝐆𝐫𝐨𝐰 𝐒𝐡𝐫𝐞𝐞 𝐆𝐫𝐨𝐜𝐞𝐫𝐢𝐞𝐬
S. No. 𝐈𝐭𝐞𝐦 𝐌𝐚𝐫𝐤𝐞𝐝 𝐏𝐫𝐢𝐜𝐞 𝐐𝐮𝐚𝐧𝐭𝐢𝐭𝐲 𝐑𝐚𝐭𝐞 𝐨𝐟 𝐆𝐒𝐓
(₹)
1. Wheat Flour 35.00 5 𝑘𝑔 𝑥%
(unpacked)
2. Basmati Rice 180.00 5 𝑘𝑔 5%
(Branded &
Packed)
3. Surf Excel Quick 220.00 𝑦 𝑘𝑔 18 %
Wash Detergent

Find:
(a) the value of x if the total GST on wheat flour and basmati rice is ₹45.
(b) the value of y, if CGST paid for detergent powder is ₹39.60.
(c) total amount to be paid (including GST) for the above bill.
[Understanding, Analysis & Evaluate]

79. [Commercial Mathematics]
Amit deposited ₹ 600 per month in a recurring deposit account. The bank pays a
simple interest of 12% p.a. Calculate the:
(a) number of monthly instalments Amit deposits to get a maturity amount of
₹11826?
(b) total interest paid by the bank.
(c) total amount deposited by him. [Application & Evaluate]

80. [Commercial Mathematics]
Aman has 500, ₹100 shares of a company quoted at ₹ 120, paying a 10% dividend.
When the share price rises to ₹ 200 each, he sells all his shares. He invests half of
the sale proceeds in ₹10, 12% shares at ₹25, and the remaining sale proceeds in ₹
400, 9% shares at ₹ 500.
Find his:
(a) sales proceeds.
(b) investment in ₹10, 12% shares at ₹ 25.
(c) original income.
(d) change in income. [Application & Evaluate]

21

S.No. Questions
81. [Algebra]
Solve the following inequation:

11 + 3𝑥 3
≥ 3 −𝑥 > − ,𝑥 ∈ R
5 2

(a) Write the solution set.
(b) Represent the solution on the number line. [Application & Create]

82. [Algebra]
Determine whether the following quadratic equation has real roots.
5𝑥 2 − 9𝑥 + 4 = 0
(a) Give reasons for your answer.
(b) If the equation has real roots, identify them. [Analysis & Application]

83. [Algebra]
The profit in rupees in a local restaurant and the number of customers who visited
the restaurant are tabulated below for each week for one month.
Week number Week 1 Week 2 Week 3 Week 4
Number of customers 1400 5600 x 3212
Profit in ₹ 28000 112000 32140 y
Find:
(a) if the number of customers and profit per week in continued proportion or
not? Justify your answer.
(b) the value of x and y. [Analysis & Evaluation]

84. [Algebra]
Given, 9𝑥 2 – 4 is a factor of 9𝑥 3 − 𝑚𝑥 2 − 𝑛𝑥 + 8:
(a) find the value of m and n using the remainder and factor theorem.
(b) factorise the given polynomial completely.
[Understanding & Application]

22

S.No. Questions
85. [Probability]
The marks scored by 100 students are given below:
Marks scored No. of students
0-10 4
10- 20 5
20-30 9
30-40 7
40-50 13
50-60 12
60-70 15
70-80 11
80-90 14
90-100 10
A student in the class is selected at random. Find the probability that the student
has scored:
(a) less than 20.
(b) below 60 but 30 or more.
(c) more than or equal to 70.
(d) above 89. [Analysis & Evaluation]

86. [Algebra]
𝑥 1 𝑥
Given, matrix A = [ ] and B = [ ] such that AB is a null matrix. Find:
𝑦 2 𝑥−2
(a) order of the null matrix.
(b) possible values of x and y. [Understanding & Application]

87. [Algebra]
The sum of a certain number of terms of the Arithmetic Progression (A.P.) 20, 17,
14, …. is 65. Find the:
(a) number of terms.
(b) last term. [Understanding & Application]

88. [Algebra]
(a) Point P (2, -3) on reflection becomes P’(2,3). Name the line of reflection (say
𝐿1 ).
(b) Point P’ is reflected to P’’ along the line (𝐿2 ), which is perpendicular to the
line 𝐿1 and passes through the point, which is invariant along both axes. Write
the coordinates of P’’.
(c) Name and write the coordinates of the point of intersection of the lines 𝐿1 and
𝐿2 .
(d) Point P is reflected to P’’’ on reflection through the point named in the answer
of above part of this question. Write the coordinates of P’’’. Comment on the
location of the points P’’ and P’’’. [Analysis & Create]

23

S.No. Questions
89. [Algebra]
In the given figure, If the line segment AB is intercepted by the y-axis and x-axis at
C and D, respectively, such that AC: AD = 1: 4 and D is the midpoint of CB. Find
the coordinates of D, C and B.

[Understanding & Application]

90. [Algebra]
Find the equation of the straight line perpendicular to the line x+2y=4, which cuts
an intercept of 2 units from the positive y-axis. Hence, find the intersection point
of the two lines. [Analysis & Application]

91. [Geometry]
While preparing a PowerPoint presentation, ∆ABC is enlarged along the side BC
to ∆AB’C’, as shown in the diagram, such that BC∶ B’C’ is 3∶5. Find:
(a) AB∶BB’ C’
(b) length AB, if BB’ = 4 cm.
(c) Is ∆ABC ~∆AB’C’? Justify your answer.
(d) ar (∆ABC): ar (quad. BB’C’C). C

A B B’

[Understanding & Evaluate]

24

S.No. Questions
92. [Geometry]

The approximate volume of a human eye is 6.5 cm3. The volume of a laboratory
model (excluding base and stand) of the human eye is 1404 cm3.
(a) State whether the scale factor k is less than, equals to or greater than 1.
(b) Calculate the:
i. value of k
ii. diameter of the human eye if the radius of the model is 7.2 cm.
iii. the external surface area of the human eye if the surface area of the model
is 651.6 cm2. [Analysis & Evaluate]

93. [Geometry] P
In the adjoining diagram PQ, PR and ST are the
tangents to the circle with centre O and radius
7 cm. Given OP=25 cm. 𝜃
25 cm
Find:
S T
(a) length of ST
(b) value of ∠OPQ, i.e. θ R
(c) ∠QUR, in nearest degree Q 7 cm
(use mathematical tables) O

U

[Application & Evaluate]

94. [Geometry]
Use ruler and compass to answer this question. Construct a triangle ABC where
AB=5.5 cm, BC= 4.5 cm and angle ABC=135o.
Construct the circumcircle to the triangle ABC. Measure and write down the length
of AC. [Create & Evaluate]

25

S.No. Questions
95. [Mensuration]
The curved surface area of a right circular cone is half of another right circular cone.
If the ratio of their slant heights is 2:1 and that of their volumes is 3:1, find ratio of
their:
(a) radii
(b) heights [Understanding & Application]

96. [Trigonometry]
A cylindrical drum is unloaded from a truck by rolling it down along a wooden
plank. The length of the plank is 10 m and it is making an angle of 10o with the
horizontal ground. Find the height from which the cylindrical drum was rolled
down. Give your answer correct to 3 significant figures.

[Analysis & Evaluate]

97. [Statistics]
The data given below shows the marks of 12 students in a test, arranged in
ascending order:
2, 3, 3, 3,4, x, x+2, 8, p, q,8, 9
If the given value of the median and mode is 6 and 8 respectively, then find the
values of x, p, q. [Understanding & Evaluate]

98. [Algebra]
Solve the linear inequation, write down the solution set and represent it on the real
number line:
5(2 - 4x) > 18 - 16x > 22 - 20x , x ∈ R
[Application & Create]

99. [Algebra]
If a polynomial x3 + 2x2 – ax + b leaves a remainder -6 when divided by x +1 and
the same polynomial has x – 2 as a factor, then find the values of a and b.
[Application & Evaluate]

26

S.No. Questions
100. [Algebra]
−1 3 1 −2 4
If A= [ ], B= [ ], C= [1 −4] and D = [ ].
2 0 0 3 1
(a) Is the product AC possible? Justify your answer.
(b) Find the matrix X,such that X=AB+𝐵 2 −DC
[Analysis & Evaluate]

101. [Geometry]

In the given figure(not drawn to scale), BC is parallel to EF , CD is parallel to FG,
AE : EB = 2:3, ∠BAD= 70°,∠ACB = 105°, ∠ADC = 40° and AC is bisector of
∠BAD.
(a) Prove Δ AEF ~ ΔAGF
(b) Find:
i. AG: AD
ii. area of ΔACB: area Δ ACD
iii. area of quadrilateral ABCD: area of Δ ACB.
[Analysis, Application & Evaluate]

27

S.No. Questions
102. [Geometry]
In the given figure angle ABC = 70° and
angle ACB = 50°. Given O is the centre
of the circle and PT is the tangent to the
circle. Then calculate the following
angles
(a) ∠CBT
(b) ∠BAT
(c) ∠PBT
(d) ∠APT
[Application & Evaluate]

103. [Geometry]
(Use a ruler and a compass for this question.)
(a) Construct a triangle ABC such that BC = 8cm , AC = 10 cm and ∠ABC = 90°.
(b) Construct an incircle to this triangle. Mark the centre as I.
(c) Measure and write the length of the in-radius.
(d) Measure and write the length of the tangents from vertex C to the incircle.
(e) Mark points P, Q and R where the incircle touches the sides AB, BC, and AC
of the triangle respectively. Write the relationship between ∠RIQ and ∠QCR.
[Analysis & Create]

104. [Statistics]
The daily wages of workers in a constuction unit were recorded as follows:
Class Marks (Wages) 425 475 525 575 625 675
No. of workers 6 12 15 17 7 13

Form a frequency distribution table with class intervals and find modal wage by
plotting a histogram. [Analysis & Create]

105. [Probability]
A bag contains 13 red cards , 13 black cards and 13 green cards. Each set of cards
are numbered 1 to 13. From these cards, a card is drawn at random. What is the
probability that the card drawn is a:
(a) green card?
(b) a card with an even number?
(c) a red or black card with a number which is a multiple of three?
[Understanding & Evaluate]

28

IV. Long Answer Type-1 (Graph-based) (5 Marks)

S.No. Questions
106. [Algebra]
(For this question, use a graph paper. Scale: 2cm = 1unit along both x and y-axis.)
Plot the points A(2,2), and B (6, -2) in the graph and answer the following:
(a) Reflect points A in origin to point D and write the co-ordinates of point D.
(b) Reflect points A in line y = - 2 to point C and write the co-ordinates of points
C.
(c) Find a point P on CD which is invariant under reflection in x = 0, write its co-
ordinates.
(d) Write the geometrical name of the closed figure ABCD.
(e) Write the co-ordinates of the point of intersection of the diagonals of ABCD.
[Understanding & Create]

107. [Algebra]
(For this question, use a graph paper. Scale: 1cm = 1unit along both x and y-axis.)
Plot points A ( 0,3 ) , B ( 4,0 ) , C ( 6,2 ) and D ( 5,0 ). Reflect the points as given
below and write their coordinates:
(a) Reflect A on x-axis to A’.
(b) Reflect B on y- axis to B’.
(c) Reflect C on x-axis to C’.
(d) D remain invariant when reflected on the line whose equation is _______.
(e) Join the points A, B, C, D,C’,B,A’ , B’ and A to form a closed figure. Name
the closed figure BCDC’. [Understanding & Create]

108. [Statistics]
The following data represents the daily wages in rupees of a certain number of
employees of a company:
Daily wages 30 – 40 -50 50 – 60 60 -70 70-80 80-90 90-100 100-110
(in ₹) 40
No. of 8 14 12 17 20 26 13 10
Employees
Use a graph to answer the following questions:
(a) Represent the above distribution by an ogive.
(b) Find the following on the graph drawn:
i) Median wage.
ii) Percentage of employees who earn more than ₹ 84 per day.
iii) Number of employees who earn ₹56 and below
[Create & Evaluate]

29

109. [Statistics]
Study the graph and answer the questions that follow∶

(a) Make a frequency table for the information provided in the graph.
(b) The number of students whose height is less than 150 cm.
(c) The total number of students.
(d) The modal height
(e) The difference in the modal height and the mean height, if the average height
of the students is 145.5 cm
[Analysis & Application]

30

V. Long Answer Type 2 (5 Marks)

S.No. Questions
110. [Commercial Mathematics]

On seeing the above display board outside Pearl Stationary Shop, Chetan enters the
shop to buy the following items:
Pen Pencil Rainbow Cover Notebook
Price ₹5 each ₹7 each ₹200 each
Discount 5% on a 10% on 20 --
dozen pens pencils
Premium - - ₹50 on each notebook
Items purchased 1 dozen 20 pencils 5
GST 18% 12% 12%

The shopkeeper handed over the bill to Chetan saying that he has given further
discount of 2% on total bill. Chetan became so happy hearing about the discount that
he did not check the bill until he reached home. He later found out that though
shopkeeper has given 2% discount as promised, he had also charged uniform 18%
GST on all the items.
(a) Calculate :
i. total selling price of all the items as per the offers displayed on the board.
ii. total amount to be paid by Chetan including GST with correct rates.
iii. actual amount charged by the shopkeeper.
(b) Did the shopkeeper overcharge Chetan? Justify your answer.
[Application & Evaluate]

31

S.No. Questions
111. [Algebra]
Using remainder and factor theorem,show that (2x+3) is a factor of the polynomial
2𝑥 2 +11x+12. Hence,factorise it completely. What must be multiplied to the given
polynomial so that 𝑥 2 + 3𝑥 − 4 is a factor of the resulting polynomial?Also,write
the resulting polynomial. [Understanding, Application & Evaluate]

112. [Algebra]
The sequence 2,9,16,……is given.
(a) Identify if the given sequence is an AP or a GP. Give reasons to support your
answer.
(b) Find the 20th term of the sequence.
(c) Find the difference between the sum of its first 22 and 25 terms.
(d) Is the term 102 belong to this sequence?
(e) If ‘k’ is added to each of the above terms, will the new sequence be in A.P. or
G.P.? [Analysis & Evaluate]

113. [Algebra]
Given the equations of two straight lines, L1 and L2 are x – y = 1 and x + y = 5
respectively . If L1 and L2 intersects at point Q ( 3, 2).Find :
(a) the equation of line L3 which is parallel to L1 and has y-intercept 3.
(b) the value of k, if the line L3 meets the line L2 at a point P (k,4).
(c) the coordinate of R and the ratio PQ: QR, if line L2 meets x-axis at point R.
[Analysis & Evaluate]

114. [Geometry]

D
E
C
F

A G B

In the figure given above( not drawn to scale), AD ∥ GE ∥ BC,DE = 18 cm, EC =
3cm, AD = 35 cm. Find :
(a) AF:FC
(b) length of EF
(c) area(trapezium ADEF ) : area(ΔEFC)
(d) BC∶ GF [Application & Evaluate]

32

S.No. Questions
115. [Geometry]
(Use a ruler and a compass for this question.)
(a) Construct the locus of a moving point which moves such that it keeps a fixed
distance of 4.5 cm from a fixed-point O.
(b) Draw line segment AB of 6 cm where A and B are two points on the locus (a).
(c) Construct the locus of all points equidistant from A and B. Name the points of
intersection of the loci (a) and (c) as P and Q respectively.
(d) Join PA. Find the locus of all points equidistant from AP and AB.
Mark the point of intersection of the locus (a) and (d) as R. Measure and write
down the length of AR. [Create & Analysis]

116. [Constructions]
(Use a ruler and a compass for this question.)
Construct a regular hexagon ABCDEF of side 4.3 cm and construct its circumscribed
circle.
Also, construct tangents to the circumscribed circle at points B and C which meets
each other at point P. Measure and record ∠BPC.
[Create & Analysis]

117. [Mensuration]
A mathematics teacher uses certain amount of terracotta clay to form different
shaped solids. First, she turned it into a sphere of radius 7cm and then she made a
right circular cone with base radius 14 cm. Find the height of the cone so formed. If
the same clay is turned to make a right circular cylinder of height 7/3 cm then find
the radius of the cylinder so formed. Also,compare the total surface areas of sphere
and cylinder so formed .
[Understanding, Application & Evaluate]

33

S.No. Questions
118. [Trigonometry]

A tree (TS) of height 30 m stands in front of a tall building (AB). Two friends Rohit
and Neha are standing at R and N respectively, along the same straight line joining
the tree and the building (as shown in the diagram). Rohit, standing at a distance of
150 m from the foot of the building, observes the angle of elevation of the top of the
building as 30o. Neha from her position observes that the top of the building and the
tree has the same elevation of 60o.
Find the:
(a) height of the building
(b) distance between
i. Neha and the foot of the building
ii. Rohit and Neha
iii. Neha and the tree
iv. building and the tree. [Analysis, Application & Evaluate]

34

S.No. Questions
119. [Statistics]
A life insurance agent found the following data of age distribution of 100 policy
holders where f is an unknown frequency.
Age in years No. of Policy Holders
15-20 7
20-25 12
25-30 15
30-35 22
35-40 𝑓
40-45 14
45-50 8
50-55 4
(a) If the mean age of the policy holders is 35.65 years, find the unknown frequency
f.
(b) Find the median class of the distribution. [Application & Evaluate]

35

Answer Key

S.No Expected Answer
1. (c) ₹30

2. (b) ₹ 28

3. (d) simple interest for one month

4. (b) ₹1250

5. (d) Both Mr. Das and Mr. Singh have same rate of return of 20%.

6. (b) ₹ 750

7. (c) { 0,1,2}

8. (c) x < - 2y

9. (d) 0 , 8

10. (b) – 2

11. (d) 230

12. (c) 13 cm

13. (d) p : r = 𝑝2 : 𝑞 2

14. (b) 60π

15. (d) 3

16. (c) (x+4)

17. (c) both matrices AB and BA are possible.

18. (b) -6

19. (b) 4

20. (d) 2, 0, 4, 0, 8, 0

21. (c) (6, -6)

22. (b) 2y = x

36

S.No Expected Answer
23. (c) 1, -1

24. (a) 3x + 3y = 6

25. (d) 20 minutes

26. (d) The similarity of given triangles cannot be determined.

27. (c) ∠𝑃𝑄𝑅 = ∠𝑇𝑆𝑅

28. (d) 1.44m

29. (c) 50°

30. (a) 500 , 1000 , 400

31. (d) 105°

32. (c) Its volume

33. (b) 42cm

34. (b) 32π

35. (b) 3 : 2

36. (c) (𝑐𝑜𝑡𝜃 + 𝑡𝑎𝑛𝜃)2

37. (d) 5

38. (a) 30°

39. (b) α < β

40. (c) A is true but R is false.

41. (c) A is true but R is false.

42. (a) Both A and R are True, and R is the correct explanation.

43. (d) A and R both are true.

44. (c) A is true but R is false.

45. (a) 2:3

46. (b) 2 x 1

47. (d) Arithmetic (d=0)

37

S.No Expected Answer
48. (a) circle

49. (b) Incentre

50. 11.11%

51. 4%

52. ₹70

53. -1 ≤ x ≤ 5
(a) 5, -1
(b) No change in maximum value, minimum value will change to 0.

54. 2 √3
𝑥=− ,𝑥 =
√3 4

55. x = 20 and GST rate = 20%

56. 3 and 12

57. (x+2) (x-1) (2x+1)

58. [
0 0
]
0 0
59. (a) Tn = 21+ (n-1)21 or 21n
(b) Four are two-digit numbers. 21, 42,63,84
(c) 1155

60. √3 , 3 , 3√3 , 9, 9√3
(a) G.P.
(b) p=121

61. (a) (- 4, -5), (0, -3), (-3, 0)
(b) For x-axis C (3,0); for y-axis B (0,3)

62. 4:3

63. (a) m=1
(b) x+y+4=0

64. 1:5

38

S.No Expected Answer
(a) In ∆ ABD and ∆CBA,
65.
∠B is common to both triangles,
∠BAD = ∠BCA (given)
∴ ∆ ABD ~ ∆CBA (by A.A.A. postulate)
(b) Since the triangles are similar, their corresponding sides are proportional.

𝐴𝐶 𝐴𝐵 𝐵𝐶
∴ 𝐴𝐷 = 𝐷𝐵 = 𝐵𝐴
𝐴𝐶 8 4+𝑥
∴ 𝐴𝐷 = 4 = 8
∴ 2x8=4+x
∴ 16 = 4 + x
∴ x = 16 - 4
∴ x = 12cm
66. (a) 3.8 km
(b) 1 𝑘𝑚2

67.

68. 27 cm

69. (a) 60°
(b) 120°
(c) 30°

39

S.No Expected Answer
70. (a) 57 °
(b) 50 °
(c) 17 °

71. 200.96 cm3

72. 24 cm, 18 cm

73. (a) 30°
(b) 13 m
L.H.S. = 𝑡𝑎𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 − 1
74.
= 𝑡𝑎𝑛2 𝜃 − (1 − 𝑐𝑜𝑠 2 𝜃)
𝑠𝑖𝑛2 𝜃
= − 𝑠𝑖𝑛2 𝜃
𝑐𝑜𝑠 2 𝜃
𝑠𝑖𝑛2 𝜃(1−𝑐𝑜𝑠 2 𝜃)
=
𝑐𝑜𝑠 2 𝜃
𝑠𝑖𝑛2 𝜃
= x 𝑠𝑖𝑛2 𝜃
𝑐𝑜𝑠 2 𝜃
= 𝑡𝑎𝑛2 𝜃 . 𝑠𝑖𝑛2 𝜃 = 𝑅. 𝐻. 𝑆

75. (a)
Class frequency
interval
12-14 8
14-16 2
16-18 3
18-20 4
20-22 5
22-24 6
(b) Mean = 18

76. m= 6; n= 6

77. (a) 6
(b) 30

78. (a) 0%
(b) y = 2 kg
(c) ₹1639.20

79. (a) 18 instalments
(b) ₹1026
(c) ₹10800

40

S.No Expected Answer
80. (a) ₹1,00,000
(b) ₹ 50,000
(c) ₹5000
(d) ₹1000 (gain)

81. 1 9
(a) {x: 2 ≤ x < 2 , x ∈ R}

(b)

82. (a) Since, D > 0
(b) 1 and 4/5

83. (a) No, they are in direct proportion.
(b) x = 1607, y = 64,240

84. (a) m = 18, n = 4
(b) (3x - 2) (3x + 2) (x - 2)

85. (a) 9/100
(b) 32/100 = 8/25
(c) 35/100 = 7/20
(d) 10/100 = 1/10

86. (a) Order of the null matrix is 2 x 1.
(b) x = 1, y = 2 and x = -2, y = -4

87. (a) 10
(b) -7

88. (a) x-axis
(b) P'' (-2, 3)
(c) Origin (0,0)
(d) P'''(-2,3); P'' & P''' are coincident points.

89. D (6,0),
C (0,9/2)
B (12, - 9/2)

41

S.No Expected Answer
90. 2x – y + 2 = 0
(0, 2)

91. (a) 𝐴𝐵: 𝐵𝐵 ′ =3:2
(b) 𝐴𝐵 = 6 𝑐𝑚
(c) 𝑌𝑒𝑠, ∵ 𝐵𝐶 ∥ 𝐵 ′ 𝐶 ′
(d) 9: 16

92. (a) k>1
(b) i. k=6
ii. 2.4 cm
iii. 18.1cm2

93. (a) 10.5 cm
(b) θ=16°16'
(c) 73°44' = 74°

94. AC = 9.1 cm (approx.)
Radius = 6.5 cm

95. (a) 1:4
(b) 48:1

96. 1.74 m

97. x = 5 and p = 8, q = 8

98. {x : x<-2 or x >1, x ∈ R}

99. a = 3, b = -10

100. No, number of columns in A is not equal to number of rows in C.
−4 19
b) [ ]
1 9
101. b)
i. 2:5
ii. 1:1
iii. 2:1

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S.No Expected Answer
102. (a) 900
(b) 300
(c) 200
(d) 100

103. (c) 2cm
(d) 5.8cm
(e) ∠RIQ +∠QCR=180°

104. Frequency table
Wages in ₹ f
400-450 6
450-500 12
500-550 15
550-600 17
600-650 7
650-700 13

Mode = ₹557.50

105. 1/3, 6/13, 8/39

106. (a) D (-2, -2)
(b) C (2, -6)
(c) P (0, -4)
(d) square
(e) (2, -2)

107. (a) (0, -3)
(b) (-4,0)
(c) (6, -2)
(d) y = 0
(e) Concave quadrilateral

108. (b) i) ₹74
ii) 32.5%
iii) 30

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S.No Expected Answer
109. (a)
Class f cf
120-130 6 6
130-140 29 35
140-150 34 69
150-160 22 91
160-170 12 103
(b) 69
(c) 103
(d) 143 cm
(e) 2.5 cm

110. a) i) ₹1433
ii) ₹1608.38
iii)₹1657.12
b) Yes, the shopkeeper overcharged an amount of ₹48.78

111. (x + 4) (2x + 3) to multiplied by (x - 1)
2x 3 + 9x 2 + x - 12

112. (a) AP as d = 7
(b) 135
(c) 489
(d) No
(e) A.P.

113. (a) x – y + 3 = 0
(b) k = 1
(c) R (5,0); 1:1

114. (a) 6:1
(b) 5 cm
(c) 48:1
(d) 7:6

115. AR ≈ 4.8cm

116. ∠BPC=120°

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S.No Expected Answer
117. hcone=7 cm
rcylinder =14 cm

TSA sphere 3
=
TSA cylinder 7

118. (a) 86.6 m
(b)
i. 50 m
ii. 100 m
iii. 17.32 m
iv. 32.68 m.

119. (a) 18
(b) 30-35

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