NDA/NA SOLVED PAPER 2016-I (MATHEMATICS)

Total Questions: 120

21. What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1/2 and x = 1 ?

Consider the function f(x) = |x - 1| + x², where x ∈ R.

Correct Answer: (a) square unit 5/12
Solution:

22. What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1 and x = 3/2 ?

Consider the function f(x) = |x - 1| + x², where x ∈ R.

Correct Answer: (d) 11/12 square unit
Solution:

23. Consider the following statements:


1. The sequence {a₂ₙ is in AP with common difference zero.
2. The sequence {a₂ₙ₊₁} is in AP with common difference zero.

Which of the above statements is/are correct?

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

24. What is aₙ₋₁ - aₙ₋₄ equal to ?

Correct Answer: (b) 0
Solution:∵ given sequence aₙ also AP with no difference. Thus aₙ₋₁ - aₙ₋₄ = 0

25. Which of the following statements are not correct?

Consider the equation x + |y| = 2y

1. y as a function of x is not defined for all real x.
2. y as a function of x is not continuous at x = 0 .
3. y as a function of x is differentiable for all x.

Select the correct answer using the code given below.

Correct Answer: (d) 1, 2 and 3
Solution:


26. What is the derivative of y as a function of x with respect to x for x < 0 ?

Consider the equation x + |y| = 2y

Correct Answer: (d) 1/3
Solution:

27. What is the area of the triangle formed by these lines?

Consider the lines y = 3x y = 6x and y = 9

Correct Answer: (a) square units 27/4
Solution:


28. The centroid of the triangle is at which one of the following points?

Correct Answer: (b) (3/2, 6)
Solution:

29. What is the number of points of local minima of the function f(x)?

Consider the function f(x) = (x - 1)² (x + 1) (x - 2)³

Correct Answer: (c) Two
Solution:


30. What is the number of points of local maxima of the function f(x) ?

Correct Answer: (b) One
Solution:Local Maxima is [x= 1]