SOLVED PAPER 2024 (CDS) (I) (Mathematics)

Total Questions: 100

51. If tan(3A) = cot(A - 22°) where 3A is an acute angle, then what is the value of A?

Correct Answer: (c) 28°
Solution:

52. Find the value

Correct Answer: (c) 2
Solution:

53. The angles of elevation of the top of a tower from two points A and B at a distance of x m and (x + 5) m from the base of the tower of height 6 m and in the same straight line with it are complementary. What is the value of x ?

Correct Answer: (a) 4 m
Solution:

54. Consider the following statements

1. In a triangle ABC, if sin A + sin B + sin C = (3√3)/2 then the triangle can be equilateral.

2. In a triangle ABC, if cos A + cos B + cos C = 3/2 then the triangle can be equilateral.

Which of the statements given above is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:

55. Two trains A and B leave Delhi for Hyderabad at 7:00 am and 7:50 am on the same day and travel at 80 km/h and 100km / h respectively. After how many kilometers from Delhi will the two trains be together?

Correct Answer: (d) 1000/3 km
Solution:

56. The length, breadth and height of a cuboid are increased by 10%, 20% and 50%, respectively. What is the percentage increase in volume of the cuboid ?

Correct Answer: (c) 98%
Solution:

57. ₹ 9400 is distributed among P, Q, R in such a way that if ₹ 93, ₹ 24, ₹ 55 are deducted from their respective shares, then they have money in the ratio 3 : 4 : 5. What is the share of P?

Correct Answer: (a) ₹ 2307
Solution:

58. If P² varies as R and Q² varies as R, (P ≠ Q ), then which of the following are correct?

1. P² + Q² varies as R.

2. PQ varies as R.

3. P² - Q² varies as R.

Select the correct answer using the code given below:

Correct Answer: (d) 1, 2 and 3
Solution:

59. p number of men can finish a piece of work in q days. If there are 50% more men, then the work will be finished 12 days earlier. What is the value of q?

Correct Answer: (c) 36
Solution:According to question,
pq = 1.5p(q - 12)
⇒ pq = 1.5pq - 18p
⇒ 18p = 0.5pq
⇒ q = 18/0.5
⇒ q = 36

60. Read the statement.

Correct Answer: (d) 25
Solution: