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

Total Questions: 100

41. In a right angled triangle ABC, AB = 15cm BC = 20cm and AC = 25cm Further, BP is the perpendicular on AC. What is the difference in the area of triangles PAB and PCB?

Correct Answer: (b) 42cm²
Solution:
Hence required difference = 1/2 × 16 × 12 - 1/2 × 9 × 12 = 42 cm²

42. Let the positive numbers a₁ a₂ , a₃, ....... a₃ₙ be in GP. If P is the GM of a₁ a₂ , a₃, ....... aₙ, and Q is the GM of aₙ₊₁, aₙ₊₂, aₙ₊₃, ...... a₃ₙ, then what is the GM of 3n numbers?

Correct Answer: (d)
Solution:

43. The cost price of y articles is equal to selling price of z articles. If y : z = 5 : 4, what is the profit percentage ?

Correct Answer: (b) 25%
Solution:

44. A sum of money invested at simple interest triples itself in 8 yr and becomes n times in 20 yr. What is the value of n?

Correct Answer: (b) 6
Solution:

45. If the work done by x men in (x + 1) days is equal to the work done by (x + 5) men in (x - 2) days, then what is the value of x?

Correct Answer: (a) 5
Solution:

46. If (a + b) : (b + c) : (c + a) = 5 : 7 : 6 , then what is the value of (a - b + c) : (a + b - c)?

Correct Answer: (c) 3 : 1
Solution:

47. Let x be the compound interest at the end of 3 yr on a sum of ₹1000 at the rate of 10% compounded annually and y be the simple interest at the end of 3 yr on a sum of ₹1000 at the annual rate of 11%. What is the difference between x and y?

Correct Answer: (d) ₹1
Solution:

48. In a quadrilateral ABCD, AB = 6 cm, BC = 18cm CD = 6cm and DA = 10cm If the diagonal BD = x, then which one of the following is correct?

Correct Answer: (b) 12 < x < 16
Solution:

49. In a quarter circle of radius R, a circle of radius r is inscribed. What is the ratio of R tor?

Correct Answer: (a) (√2+1) : 1
Solution:On making the circle whose center O and O', as per the given information,
∵ OP = OO' + O'P (By figure)

50. In a quadrilateral ABCD, AB = BC and CD = DA ; AC and BD are diagonals such that AC = 6cm and BD = 12cm What is the area of the quadrilateral?

Correct Answer: (c) 36cm²
Solution: