Relations and Functions Class 12 Mcq Test

The function f: R → R defined by f(x) = x² + 1 is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

The relation R in the set of real numbers R defined as R = {(a, b) : a ≤ b²} is:
A) Reflexive
B) Symmetric
C) Transitive
D) None of the above

A relation R on the set of integers Z is defined by (x, y) ∈ R if |x - y| ≤ 1. The relation R is:
A) Reflexive and Symmetric
B) Reflexive and Transitive
C) Symmetric and Transitive
D) An Equivalence Relation

The relation R on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)} is:
A) Reflexive and Symmetric but not Transitive
B) Reflexive and Transitive but not Symmetric
C) Symmetric and Transitive but not Reflexive
D) An Equivalence Relation

Let A = R - {3} and B = R - {1}. The function f: A → B defined by f(x)=(x-2)/(x-3) is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

Let R be the relation on set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Which statement is correct?
A) R is reflexive and symmetric but not transitive.
B) R is reflexive and transitive but not symmetric.
C) R is symmetric and transitive but not reflexive.
D) R is an equivalence relation.

A function f: A → B is said to be onto (surjective) if:
A) The range of f is a proper subset of B
B) The range of f is equal to B
C) For every y ∈ B, there exists at most one x ∈ A such that f(x) = y
D) The domain of f is equal to A

The function f: Z → Z defined by f(x) = x³ is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

If A = {1, 2, 3} and B = {x, y}, then the total number of functions from A to B is:
A) 6
B) 8
C) 9
D) 3

The universal relation on a non-empty set A is always:
A) Not Symmetric
B) Not Transitive
C) An Equivalence Relation
D) None of the above

The function f: R → R defined by f(x) = eˣ is:
A) One-to-one but not onto
B) Onto but not one-to-one
C) Both one-to-one and onto
D) Neither one-to-one nor onto

If a relation R on the set {1, 2, 3} is defined by R = {(1, 2)}, then R is:
A) Reflexive
B) Symmetric
C) Transitive
D) None of the above

Let R be a relation on a set A such that R = R⁻¹. Then the relation R is:
A) Reflexive
B) Symmetric
C) Transitive
D) Equivalence

The greatest integer function f: R → R, defined by f(x) = [x], is:
A) One-to-one
B) Onto
C) Both one-to-one and onto
D) Neither one-to-one nor onto

The smallest equivalence relation on the set A = {a, b, c} is:
A) {(a, a), (b, b), (c, c)}
B) {(a, a), (b, b), (c, c), (a, b), (b, a)}
C) A × A
D) {(a, b), (b, c)}