MATHEMATICS (NDA/NA SOLVED PAPER 2022-I) (01 to 50)

Total Questions: 50

41. Consider all the subsets of the set A = {1, 2, 3, 4}. How many of them are supersets of the set {4}?

Correct Answer: (c) 8
Solution:

42. Consider the following statements in respect of two non-empty sets A and B :

1. x ∉ A ∪ B) ⇒ x ∉ A or x ∉ B
2. x ∉ (A ∩ B) ⇒ x ∉ A and x ∉ B
Which of the above statements is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:

43. Consider the following statements in respect of two non-empty sets A and B :

1. A ∪ B=A ∩ B iff A = B
2 A Δ B = φ iff A = B
Which of the above statements is/are correct?

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

44. Consider the following statements in respect of the relation R in the set IN of natural numbers defined by xRy if x² - 5xy + 4y² = 0:

1. R is reflexive
2 R is symmetric
3. R is transitive
Which of the above statements is/are correct?

Correct Answer: (a) I only
Solution:

45. Consider the following statements in respect of any relation R on a set A:

1. If R is reflexive, then R⁻¹ is also reflexive
2. If R is symmetric, then R⁻¹ is also symmetric
3. If R is transitive, then R⁻¹ is also transitive
Which of the above statements are correct?

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

46. What is the principal argument of 1/1 + i where i = √-1?

Correct Answer: (b) -π/4
Solution:

47. Find the value?

Correct Answer: (c) 1
Solution:

48. Consider the following statements:

1. (n!)/(3!) is divisible by 6, where n > 3
2. (n!)/(3!) + 3 is divisible by 7, where n > 3
Which of the above statements is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:

49. In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players?

Correct Answer: (b) 21
Solution:

50. Find the value?

Correct Answer: (c) C(2n, n)
Solution: