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1. If f(x) = x + 1 and g(x) = x², then (g∘f)(x) is

A. x² + 2x + 1 B. x² + x + 1 C. x² - 1 D. x² + 1

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2. The complement of a set A in the universal set U is

A. A - U B. U ∪ A C. U ∩ A D. U - A

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3. Let A = {1, 2, 3, ..., 20}. Let R₁ and R₂ be two relations on A such that R₁ = {(a, b) : b is divisible by a} and R₂ = {(a, b) : a is an integral multiple of b}. Then, the number of elements in R₁ - R₂ is

A. 190 B. 210 C. 220 D. 200

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4. If A = {x : x is an integer and -1 < x < 5}, then A is

A. {1, 2, 3, 4} B. {-1, 0, 1, 2, 3} C. {-1, 0, 1, 2} D. {0, 1, 2, 3, 4}

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5. If f(x) = x² and g(x) = 2x + 1, then (f∘g)(x) is

A. 4x² + 4x + 1 B. (2x + 1)² C. 2x² + 2 D. 4x² + 2x + 1

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6. The number of symmetric relations defined on the set {1, 2, 3, 4} which are not reflexive is

A. 192 B. 64 C. 256 D. 128

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7. A function f: A → B is called bijective if it is

A. both one-one and onto B. one-one C. onto D. neither one-one nor onto

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8. If f(x) = 3x + 5, what is f^−1(x)?

A. (x + 5)/3 B. (x - 5)/3 C. 3/x - 5 D. x/3 - 5

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9. The universal set U = {1, 2, 3, ..., 10} and A = {2, 4, 6, 8, 10},The complement of A is

A. {2, 4, 6, 8} B. {1, 3, 5, 7, 9} C. {1, 2, 3, 4} D. {3, 5, 7, 9}

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10. The total number of subsets of a set with n elements is

A. 2ⁿ B. n² C. n! D. n² + n

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11. If A = {1, 2, 3} and B = {3, 4},then A ∪ B is

A. {1, 2, 3, 4} B. {1, 2, 3} C. {1, 3, 4} D. {3, 4}

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12. If R is a relation on a set A = {1, 2, 3} defined as R = {(1, 2), (2, 3)}, then R is

A. Neither reflexive nor symmetric B. Symmetric but not reflexive C. Reflexive but not symmetric D. Reflexive and transitive

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13. The intersection of A = {1, 2, 3} and B = {3, 4, 5} is

A. {1, 3} B. {2, 3} C. {1, 2} D. {3}

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14. If A = {1, 2, 3} and R = {(1, 2), (2, 3)}, then the number of ordered pairs in R is

A. 2 B. 3 C. 1 D. 4

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15. If A = {1, 2, 3} and B = {4, 5}, then the Cartesian product A × B has

A. 3 elements B. 5 elements C. 6 elements D. 2 elements

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16. If A = {1, 2, 3} and B = {4, 5}, then the total number of relations from A to B is

A. 25 B. 10 C. 15 D. 20

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17. Which of the following is an example of an equivalence relation?

A. < B. = C. ≠ D. <=

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18. The total number of reflexive relations on a set with 4 elements is

A. 8 B. 16 C. 2¹² D. 2⁴

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19. If n(A) = 10 and n(B) = 5, then the total number of subsets of A × B is

A. 2¹⁵ B. 2⁵⁰ C. 2²⁰ D. 2¹⁰

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20. Let f: A → B be defined as f(x) = 2x + 1,If A = {1, 2, 3}, then the range of f is

A. {2, 4, 6} B. {1, 3, 5} C. {3, 5, 7} D. {3, 5, 7, 9}