(Mathematics) NDA/NA SOLVED PAPER 2024 - I (51 to 100)

31. What is the value of α ?

(a) 7
(b) 13
(c) 17
(d) 26

Correct Answer: (d) 26

Solution:

(d) α = 26

32. What is the value of β?

(a) 7
(b) 13
(c) 17
(d) 26

Correct Answer: (a) 7

Solution:

β = 7

33. Consider the following statements:

(A) f(x) is increasing in the interval (e, ∞)
(B) f(x) is decreasing in the interval (1, e)
(C) 9 ln(7) > 7 ln(9)
Which of the statements given above are correct?

(a) (A) and (B) only
(b) (B) and (C) only
(c) (A) and (C) only
(d) (A), (B) and (C)

Correct Answer: (d) (A), (B) and (C)

Solution:

34. Consider the following statements:

(A) f "(e) = 1/e

(B) f(x) attain local minimum value at x = e

Which of the statements given above are correct?

(a) (A) and (B) only
(b) (B) and (C) only
(c) (A) and (C) only
(d) (A), (B), and (C)

Correct Answer: (d) (A), (B), and (C)

Solution:

35. What is g[f(x) - 3x] equal to?

Correct Answer: (a)

Solution:

36. What is f "(x) equal to?

(a) -2/x³
(b) 2x + 2/x³
(c) 6x + 3
(d) 6x

Correct Answer: (d) 6x

Solution:

37. Consider the following statements:

(A) f(x) is differentiable for all x < 0
(B) g(x) is continuous at x = 0.0001
(C) The derivative of g(x) at x = 2.5 is 1
Which of the statements given above are correct?