Mathematics (NDA SOLVED PAPER 2020 – II) (51 to 100)

Total Questions: 50

41. Consider the following statements for f(x) = e⁻|ˣ| :

1. The function is continuous at x = 0.
2. The function is differentiable at x = 0.
Which of the above statements is/are correct?

Correct Answer: (a) 1 Only
Solution:

42. What is the maximum value of sin x . cos x?

Correct Answer: (c) 1/2
Solution:

43. Solve it?

Correct Answer: (a) 0
Solution:

44. What is the derivative of tan⁻¹ x with respect to cot⁻¹ x?

Correct Answer: (a)
Solution:

45. The function u(x, y) = c which satisfies the differential equation x (dx - dy) + y (dy - dx) = 0, is

Correct Answer: (b) x² + y² = 2xy + c
Solution:

46. What is the minimum value of 3 cos (A + π/3) where A ∈ R?

Correct Answer: (a) − 3
Solution:

47. Consider the following statements:

1. The function f(x) = ln x increases in the interval (0 , ∞).
2. The function f(x) = tan x increases in the interval
(-π/2,  π/2).
Which of the above statements is/are correct?

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

48. Which one of the following is correct in respect of the graph of y = 1/x - 1 ?

Correct Answer: (b) The domain is {x ∈ R| x ≠ 1} the range is { y ∈ R | y ≠ 0} and the graph intersects y-axis at (0 , -1)
Solution:

49. What is the solution of the differential equation ln (dy/dx) = x?

Correct Answer: (a) y = eˣ + c
Solution:

50. Let l be the length and b be the breadth of a rectangle such that l + b = k. What is the maximum area of the rectangle?

Correct Answer: (d) k²/4
Solution: