SOLVED PAPER 2024 (CDS) (II) (Mathematics)

51. Consider the following for the next three (03) items that follow

Let ABC be a triangle right-angled at B.
Let P be the point on BC such that
BP = PC If AB = 10 cm, ∠BAP = 45° and ∠CAP = θ

use tan(α + β) = (tan α + tan β)/(1 - tan α tan β)

What is tan theta equal to

(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/5

Correct Answer: (b) 1/3

52. Read the statement

If ∠ACP = Ƴ, then what is tan Ƴ equal to

(a) 1/2
(b) 1/3
(c) 2/3
(d) 1

Correct Answer: (a) 1/2

Solution:∠ACP = gamma
In ΔABC
tan Ƴ = 10/20
tan Ƴ = 1/2
∴ (a) is the correct option.

53. Read the statement

Consider the following statements.

I. The line segment AP divides the area of the triangle ABC into two equal parts.
II. The perimeter of the triangle APC is more than 46 cm.
III. The area of the triangle APC is 50 square cm.

Which of the statements given above are correct?

(a) Both I and II
(b) Both II and III
(c) Both I and III
(d) All I, II and III

Correct Answer: (d) All I, II and III

54. Consider the following for the next two (02) items that follow

A frequency distribution is as follows

Marks	Number of students
18-26	5
27-35	7
36-44	10
45-53	15
54-62	8
63-71	3
72-80	2

(a) 44.9
(b) 45.5
(c) 45.9
(d) 46.3

Correct Answer: (d) 46.3

Solution:

Class	Frequency	C₁	X
18-26	5	5	(18+26)/2=22
27-35	7	12	31
36-44	10	22	40
45-53	15	37	49
54-62	8	45	58
63-71	3	48	67
72-80	2	50	76

55. Read the statement

What is the mode of the distribution?

(a) 47.25
(b) 47.75
(c) 48.25
(d) 48.75

Correct Answer: (c) 48.25

56. Consider the following for the next two (02) items that follow

ABC is a triangle right-angled at B.
Given that AC - AB = 2 cm and BC = 16 cm.

If ∠BAC =θ then what is
sin θ + cos θ equal to

(a) 1
(b) 71/65
(c) 73/65
(d) 79/65

Correct Answer: (d) 79/65

57. Read the statement

If BD is the perpendicular on the side AC, then what is the length of BD?

(a) 1008/65 cm
(b) 756/65 cm
(c) 168/7 cm
(d) 165/7 cm

Correct Answer: (a) 1008/65 cm

Solution:BD = (BC × AB)/AC
= (16 × 63)/65
⇒ = 1008/65 cm
∴ (a) is the correct option.

58. Consider the following for the next three (03) items that follow.

Let MN be a chord of length 16 cm of a circle with centre at O and radius 10 cm. The tangents at M and N intersect at a point P. Further, OP intersect MN perpendicularly at Q.

What is OQ equal to