These Relations And Functions Class 12 MCQ And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Relations And Functions Class 12 MCQ And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.
Relations And Functions Class 12 MCQ And Answers
1. A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings: a loves A} is-
(A) reflexive
(B) symmetric and transitive
(C) equivalence
(D) None of these
Answer: equivalence
2. If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?
(A) Many-one onto
(B) Constant function
(C) one-one onto
(D) into
Answer: one-one onto
3. If the function f(x) = x³ + ex/2 and g (x) = fn(x), then the value of g'(1) is
(A) 1
(B) 2
(C) 3
(D) 4
Answer: 2
4. If A = [1, 2, 3}, B = {5, 6, 7} and f: A → B is a function such that f(x) = x + 4 then what type of function is f?
(A) into
(B) one-one onto
(C) many-onto
(D) constant function
Answer: one-one onto
5. If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
(A) reflexive
(B) transitive
(C) symmetric
(D) None of these
Answer: transitive
6. Let A = {1, 2,3,…. n} and B = { a, b}. Then the number of surjections from A into B is
(A) nP2
(B) 2n – 2
(C) 2n – 1
(D) None of these
Answer: 2n – 2
7. Let f: R → R be the function defined by f(x) = x³ + 5. Then f-1 (x) is
(A) (x + 5)1/3
(B) (x -5)1/3
(C) (5 – x)1/3
(D) 5 – x
Answer: (x -5)1/3
8. Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
(A) 31
(B) 40
(C) 43
(D) None of these
Answer: 31
9. If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is
(A) many one
(B) one-one onto
(C) onto
(D) one-one
Answer: one-one
10. What type of relation is ‘less than’ in the set of real numbers?
(A) only symmetric
(B) only transitive
(C) only reflexive
(D) equivalence
Answer: only transitive
11. Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
(A) 14
(B) 16
(C) 12
(D) 8
Answer: 14
12. Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is
(A) Reflexive and symmetric
(B) Transitive and symmetric
(C) Equivalence
(D) Reflexive, transitive but not symmetric
Answer: Reflexive, transitive but not symmetric
13. The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
(A) {(2, 1), (4, 2), (6, 3),….}
(B) {(1, 2), (2, 4), (3, 6),….}
(C) R-1 is not defined
(D) None of these
Answer: {(1, 2), (2, 4), (3, 6),….}
15. Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is
(A) Reflexive
(B) Symmetric
(C) Transitive
(D) Anti-symmetric
Answer: Symmetric
16. Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is
(A) Reflexive
(B) Symmetric
(C) Transitive
(D) None of these
Answer: None of these
17. If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =
(A) x² – 2
(B) 1
(C) 1/3 (x – 2)²
(D) None of these
Answer: 1/3 (x – 2)²
19. The domain of sin-1 (log (x/3)] is. .
(A) [1, 9]
(B) [-1, 9]
(C) [-9, 1]
(D) [-9, -1]
Answer: [1, 9]
20. Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a congruent to b ∀ a, b ∈ T. Then R is
(A) reflexive but-not transitive
(B) transitive but not symmetric
(C) equivalence
(D) None of these
Answer: equivalence