Mathematics (NDA/NA SOLVED PAPER 2021-I) (51 to 100)

Total Questions: 50

31. What is the area bounded by y = √16 - x²

y >= 0 and the x-axis?

Correct Answer: (b) 8π square units
Solution:

32. The curve y = - x³ + 3x² + 2x - 27 has the maximum slope at

Correct Answer: (c) x = 1
Solution:

33. A 24 cm long wire is bent to form a triangle with one of the angles as 60°. What is the altitude of the triangle having the greatest possible area?

Correct Answer: (a) 4√3 cm
Solution:

34. If f(x) = e|ˣ|, then which one of the following is correct?

Correct Answer: (d) f' (0) does not exist
Solution:

35. equal to?

Correct Answer: (d) ln | sec x + tan x | - ln | sec x | + c
Solution:

36. equal to?

Correct Answer: (b) tan⁻¹ x + c
Solution:

37. If x + y = 20 and P = xy, then what is the maximum value of P?

Correct Answer: (a) 100
Solution:

38. What is the derivative of sin (ln x) + cos (ln x) with respect to x at x = e ?

Correct Answer: (a)
Solution:

39. x = eᵗ cos t and y = eᵗ sin t, then what is dx/dy at t = 0 equal to?

Correct Answer: (b) 1
Solution:

40. What is the maximum value of sin 2x . cos 2x?

Correct Answer: (a) 1/2
Solution: