(Mathematics) NDA/NA SOLVED PAPER 2023 – II (01 to 50)

Total Questions: 50

21. The Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/are correct?

1. It is possible to determine set A

2. A × A contains the element (3, 2).

Select the correct answer using the code given below:

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

22. Let A= {1, 2, 3 ,____20}. Define a relation R from A to A by R = {(x, y) : 4x - 3y = 1}, where x, y ∈ A. Which of the following statements is/are correct?

1. The domain of R is {1, 4, 7, 10, 13, 16}.
2. The range of R is {1, 5, 9, 13, 17}.
3. The range of R is equal to codomain of R.
Select the correct answer using the code given below:

Correct Answer: (b) 2 only
Solution:

23. Consider the following statements:

Which of the statements given above is/are correct?

Correct Answer: (a) 1 only
Solution:(a)

24. Consider the following statements:

1. A = (A ∪ B) ∪ (A - B)
2. A ∪ (B - A) = (A ∪ B)
3. B=(A ∪ B) - (A - B)
Which of the statements given above are correct?

Correct Answer: (b) 2 and 3 only
Solution:(b)

25. equal to?

Correct Answer: (d) 31/64
Solution:

26. equal to?

Correct Answer: (c) 3 + √5
Solution:

27. If sec⁻¹ p - cosec⁻¹ q = 0, where p > 0, q > 0; then what is the value of p⁻² + q⁻²?

Correct Answer: (a) 1
Solution:

28. equal to?

Correct Answer: (a) 25/17
Solution:

29. Find the value?

Correct Answer: (c) 1
Solution:

30. Find the value?

Correct Answer: (c) 1/√2
Solution: