Mathematics (NDA/NA SOLVED PAPER 2023-I) (51 to 100)

Total Questions: 50

41. Consider the following statements:

Which of the statements given above is/are correct?

Correct Answer: (a) I only
Solution:

42. What is the derivative of sin² x with respect to cos²x?

Correct Answer: (a) -1
Solution:

43. For what value of m with m < 0, is the area bounded by the lines y = x, y = mx and x = 2 equal to 3?

Correct Answer: (a) - 1/2
Solution:O (0, 0) is the origin
A = A (2, 2), B = B(2, 2m)
Area (Δ OAB) = 3

44. What the derivative of cosec(x°)?

Correct Answer: (b)
Solution:

45. Find the value?

Correct Answer: (d) y = (x²- 2)/2
Solution:

46. If f(x) = x² + 2 and g(x) = 2x - 3, then what is (fg)(1) equal to?

Correct Answer: (d) -3
Solution:f(x) = x² + 2
g(x) = 2x - 3
(fg)(1) = f(1) × g(1) = (1 + 2)(2 - 3) = - 3.

47. What is the range of the function f(x) = x + |x| if the domain is the set of real numbers?

Correct Answer: (b) [0, ∞)
Solution:f(x) = x + |x|
when x < 0, f(x) = x - x = 0
when x > = 0 , f(x) = x + x = 2x
f(x) ∈ in (0, ∞)

48. If f(x) = x(4x² - 3), then what is f(sinθ) equal to?

Correct Answer: (a) - sin 3θ
Solution:f(x) = x(4x² - 3)
f(sinθ) = sinθ (4sin²θ - 3)
= - (3sinθ - 4sin³θ) = - sin 3θ

49. equal to?

Correct Answer: (d) Limit does not exist
Solution:

50. equal to?

Correct Answer: (c) 3
Solution: