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

Total Questions: 100

31. A 4-digit number N has exactly 15 distinct divisors. What is the total number of distinct divisors of N² ?

Correct Answer: (c) 45
Solution:

32. If p, q and r are the lengths (in cm) of the sides of a right-angled triangle, then (p - q - r)(q - r - p)(r - p - q) is always

Correct Answer: (b) Negative only
Solution:

33. .

Correct Answer: (c) 9
Solution:

34. In a class containing 200 students, n students prefer both tea and coffee, 2n students prefer coffee, 3n students prefer tea; 4n students prefer neither tea nor coffee. What is the value of n?

Correct Answer: (b) 25
Solution:

35. Let ABC be a triangle with area 36cm². If AB = 9cm, BC = 12cm and ∠ABC = θ, then what is cos theta equal to

Correct Answer: (a) √5/3
Solution:Area of triangle = 1/2
(AB × BC) sinθ

36. Let n be a natural number. The HCF of n, n + 10 is 10. If the LCM is x (a 2-digit number), then how many values of x are possible ?

Correct Answer: (b) Only two
Solution:HCF of (n, n + 10) is 10.
⇒ n = 10a and n + 10 = 10a + 10
(a is any constant)
We know that, N₁ × N₂ = LCM × HCF
⇒ (10a) (10a + 10) = x ⋅ 10
⇒ x = 10a(a + 1)
If a = 1 then

37. What is HCF of a⁴ + 2a³ + 3a²+ 2a + 1 and a⁶ - 2a³+ 1 ?

Correct Answer: (c) (a² + a + 1)²
Solution:

38. If the roots of the equation x² - (k - 2) * x + (k + 1) = 0 are equal, then what are the values of k?

Correct Answer: (b) 0, 8
Solution:

39. .

Correct Answer: (a) -1
Solution:

40. What is (sinθ - 2sin³θ)/(2cos³θ - cosθ) equal to

Correct Answer: (d) tanθ
Solution: