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

Total Questions: 50

11. Consider the following statements in respect of the function f(x) = x + 1/x :

1. The maximum value of f(x) is less thar its local minimum value.
2. The local maximum value of f (x) occurs at x = 1
Which of the above statements is/are correct?

Correct Answer: (a) 1 only
Solution:We have x + 1/x < - 2 or x + 1/x > = 2
Hence Local minimum value of f (x) is 2 and Local maximum value g(x) is
-2 Hence statement 1 is correct.

12. What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?

Correct Answer: (c) 8 square units
Solution:We known that a rectangle inscriped in a circle having maximum area is a square.
Here r = 2 (given)
Hence diagonal of the square is 2r = 4 unit
Area will be (4)²/2 = 8 sq. units

13. equal to?

Correct Answer: (a)
Solution:

14. What is the derivative of with respect to eˣ?

Correct Answer: (a)
Solution:

15. What is the condition tha f(x) = x³ + x² + kx has no local extremum?

Correct Answer: (b) 3k > 1
Solution:

16. equal to?

Correct Answer: (d) 8 ln 2
Solution:

17. Find the value?

Correct Answer: (d) greater than or equal to k
Solution:

18. If the function f(x) = x² - kx is monotonically increasing in the interval (1, ∞) then which one of the following is correct?

Correct Answer: (a) k < 2
Solution:

19. What is the area bounded by y = [x], where [ . ] is the greatest integer function, the x-axis and the lines x = - 1.5 and x = - 1.8?

Correct Answer: (c) 0.6 square unit
Solution:

20. The tangent to the curve x² = y at (1, 1) makes an angle θ with the positive direction of x-axis. Which one of the following is correct?

Correct Answer: (d)
Solution: