MATHEMATICS (NDA/NA SOLVED PAPER 2022-I) (51 to 100)

Total Questions: 50

21. Let y = [x + 1], - 4 < x < - 3 where [.] is the greatest integer function. What is the derivative of y with respect to x at x = - 3.5?

Correct Answer: (d) 0
Solution:

22. If dy/dx = (l n 5) y with y(0) = ln(5), then what is y(1) equal to?

Correct Answer: (d) 5 ln 5
Solution:

23. Consider the following in respect of the function f(x) = 10ˣ:

1. Its domain is (- ∞, ∞)
2. It is a continuous function
3. It is differentiable at x = 0
Which of the above statements are correct?

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

24. equal to?

Correct Answer: (a) 0
Solution:

25. equal to?

Correct Answer: (c) 6
Solution:

26. In which one of the following intervals is the function

Correct Answer: (b) (1, 6)
Solution:

27. If the derivative of the function f(x) = m/x + 2nx + 1 vanishes at x = 2, then what is the value of m + 8n?

Correct Answer: (d) Cannot be determined due to insufficient data
Solution:

28. What is the area included in the first quadrant between the curves y = x and y = x³?

Correct Answer: (b) 1/4 square unit
Solution:

29. If xy = 4225 where x, y are natural numbers, then what is the minimum value of x + y?

Correct Answer: (a) 130
Solution:

30. What does the equation xdy/dx - 2y = 0 represent?

Correct Answer: (c) A family of parabolas
Solution: