NDA/NA SOLVED PAPER 2016-I (MATHEMATICS)

Total Questions: 120

31. Let f(x) and g(x) be twice differentiable functions on [0, 2] satisfying f(x) =g(x), f'(1) = 4, g'(1) = 6 , f(2) = 3 and g(2) = 9. Then what is f(x) - g(x) at x = 4 equal to ?

Correct Answer: (a) -10
Solution:


32. What is/are the point(s) of intersection of the curves ?

Consider the curves y = |x - 1| and |x| = 2

Correct Answer: (c) (-2, 3) and (2, 1)
Solution:

33. What is the area of the region bounded by the curves and x-axis ?

Consider the curves y = |x - 1| and |x| = 2

Correct Answer: (c) 5 square units
Solution:

34. What is the value of f'(0) ?

Correct Answer: (d) - 6p³
Solution:


35. What is the value of p for which f''(0) = 0 ?

Correct Answer: (a) - 1/6 or 0
Solution:

36. What is the value of sin(A/2) sin(B/2) sin(C/2) ?

Correct Answer: (c) 1/8
Solution:



37. What is the value of

Correct Answer: (d) None of the above
Solution:

38. What is tan(α + β) equal to?

Given that tan α and tan β are the roots of the equation x² + bx + c = 0 with b ≠ 0 .

Correct Answer: (d) b(c - 1)⁻¹
Solution:

39. What is sin(α + β) sec(α) sec(β) equal to?

Given that tan α and tan β are the roots of the equation x² + bx + c = 0 with b ≠ 0 .

Correct Answer: (b) -b
Solution:

40. What is the distance between the centres of the two circles?

Consider the two circles (x - 1)² + (y - 3)² = r² and x²+ y² - 8x + 2y + 8 = 0

Correct Answer: (a) 5 units
Solution: