JEE (Main) Mathematics - Sets, Relations, and Functions - MCQs

61. Which of the following is the correct representation of the set of natural numbers less than 10?
    • a) { 1, 2, 3, 4, 5, 6, 7, 8, 9 }
    • b) { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
    • c) { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
    • d) { 0, 1, 2, 3, 4, 5, 6, 7, 8 }
    Answer: a) { 1, 2, 3, 4, 5, 6, 7, 8, 9 }
62. If A = { 1, 2, 3 } and B = { 2, 3, 4 }, then A ∪ B is:
    • a) { 1, 2, 3, 4 }
    • b) { 1, 2, 3 }
    • c) { 2, 3 }
    • d) { 1, 4 }
    Answer: a) { 1, 2, 3, 4 }
63. The complement of the set A = { 1, 2, 3, 4 } with respect to the universal set U = { 1, 2, 3, 4, 5, 6 } is:
    • a) { 5, 6 }
    • b) { 4, 5, 6 }
    • c) { 1, 2, 3 }
    • d) { 1, 2, 3, 4 }
    Answer: a) { 5, 6 }
64. If A = { 1, 2, 3 } and B = { 3, 4, 5 }, then A ∩ B is:
    • a) { 1, 2 }
    • b) { 3 }
    • c) { 3, 4 }
    • d) { 5 }
    Answer: b) { 3 }
65. The power set of A = { a, b } is:
    • a) { ∅, { a }, { b }, { a, b } }
    • b) { { a }, { b }, { a, b } }
    • c) { ∅, { a, b } }
    • d) { ∅, { a }, { b } }
    Answer: a) { ∅, { a }, { b }, { a, b } }
66. Which of the following is an equivalence relation on the set of real numbers ℝ?
    • a) x < y
    • b) x ≤ y
    • c) x = y
    • d) x ≠ y
    Answer: c) x = y
67. If the function f(x) = 2x + 1 is defined for x ∈ ℝ, then it is:
    • a) One-to-one and onto
    • b) One-to-one but not onto
    • c) Onto but not one-to-one
    • d) Neither one-to-one nor onto
    Answer: a) One-to-one and onto
68. If A = { 1, 2, 3 } and B = { a, b, c }, then the number of functions from A to B is:
    • a) 6
    • b) 9
    • c) 27
    • d) 81
    Answer: b) 9
69. If f(x) = x², then the function f(x) is:
    • a) One-to-one
    • b) Onto
    • c) Many-to-one
    • d) One-to-one and onto
    Answer: c) Many-to-one
70. If A = { 1, 2, 3 }, then the number of subsets of A is:
    • a) 3
    • b) 6
    • c) 8
    • d) 16
    Answer: c) 8
71. The inverse of a function f(x) = 2x + 3 is:
    • a) f⁻¹(x) = (x-3)/2
    • b) f⁻¹(x) = 2x - 3
    • c) f⁻¹(x) = (x+3)/2
    • d) f⁻¹(x) = x + 3
    Answer: a) f⁻¹(x) = (x-3)/2
72. If f(x) = x³ and g(x) = x², then the composition (g ∘ f)(x) is:
    • a) x⁵
    • b) x⁶
    • c) x⁴
    • d) x³
    Answer: b) x⁶
73. If f(x) = 3x - 1, then f(2) is:
    • a) 5
    • b) 6
    • c) 7
    • d) 4
    Answer: a) 5
74. Which of the following is a function from the set {1, 2, 3} to the set {a, b}?
    • a) f = { (1, a), (2, b), (3, a) }
    • b) f = { (1, a), (2, a), (1, b) }
    • c) f = { (1, a), (2, a), (3, b) }
    • d) f = { (1, a), (2, b), (2, a) }
    Answer: a) f = { (1, a), (2, b), (3, a) }
75. The composition of two functions f(x) and g(x) is denoted as:
    • a) f(x) + g(x)
    • b) f(g(x))
    • c) g(f(x))
    • d) Both b) and c)
    Answer: d) Both b) and c)

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