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Relations and Functions Practice Questions

Class 12 · Mathematics · 1660 free MCQs with instant results and detailed explanations.

1660
Total
574
Easy
781
Medium
305
Hard

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Topics in Relations and Functions

Inverse Functions 474
Types of Functions 520
Composition of Functions 107
Types of Relations 559

Sample Questions from Relations and Functions

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
Which of the following relations is an example of a reflexive relation?
A. {(1, 1), (2, 2), (3, 3)}
B. {(1, 2), (2, 3), (1, 3)}
C. {(1, 2), (2, 2), (2, 3)}
D. {(1, 2), (2, 3), (3, 1)}
Show Answer & Explanation
Correct Answer: A
A reflexive relation means every element is related to itself. Option A fulfills this criterion.
Q2
Easy
If A = {1, 2, 3} and B = {2, 3, 4}, which of the following represents the relation R from A to B where each element in A is related to the elements in B that are greater than it?
A. {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}
B. {(1, 2), (1, 3), (2, 3), (2, 4)}
C. {(1, 3), (2, 4)}
D. {(2, 3), (3, 4)}
Show Answer & Explanation
Correct Answer: A
Each element in A is paired with all elements in B that are greater than it. Option A includes all valid pairs.
Q3
Easy
Which of the following statements is true regarding a symmetric relation?
A. If (a, b) is in R, then (b, a) must also be in R.
B. If (a, b) is in R, then (a, a) must be in R.
C. If (a, b) is in R, then (a, c) must be in R for any c.
D. All pairs (a, b) must be distinct for R to be symmetric.
Show Answer & Explanation
Correct Answer: A
A symmetric relation requires that if one pair exists, the reverse pair must also exist.
Q4
Medium
Which of the following is an example of a reflexive relation?
A. {(1,1), (2,2), (3,3)}
B. {(1,2), (1,3)}
C. {(2,3), (3,2)}
D. {(1,2), (2,1)}
Show Answer & Explanation
Correct Answer: A
A reflexive relation must have every element related to itself, which is satisfied by option A.
Q5
Medium
In a relation R on set A = {a, b, c}, how many elements can R have at most?
A. 3
B. 6
C. 9
D. 12
Show Answer & Explanation
Correct Answer: B
The maximum number of elements in a relation is given by n^2 where n is the number of elements in set A.
Q6
Medium
Which of the following relations is symmetric?
A. {(1,2), (2,1)}
B. {(1,2), (2,3)}
C. {(3,3), (2,3)}
D. {(1,3), (2,3)}
Show Answer & Explanation
Correct Answer: A
A symmetric relation must have pairs such that if (a,b) is included, then (b,a) must also be included, satisfied only by option A.
Q7
Medium
What is the domain of the relation R = {(1,2), (3,4), (5,6)}?
A. {1, 3, 5}
B. {2, 4, 6}
C. {1, 2, 3}
D. {4, 5, 6}
Show Answer & Explanation
Correct Answer: A
The domain of a relation is the set of the first elements of the ordered pairs, which are 1, 3, and 5 here.
Q8
Hard
If R is a relation on the set A = {1, 2, 3, 4} defined by R = {(1, 2), (2, 3), (3, 4)}, which property does R not satisfy?
A. Reflexivity
B. Symmetry
C. Transitivity
D. Antisymmetry
Show Answer & Explanation
Correct Answer: A
Reflexivity requires every element to relate to itself. Here, (1,1), (2,2), (3,3), and (4,4) are missing.
Q9
Hard
Consider the sets X = {a, b} and Y = {1, 2}. If relation S is defined as S = {(a, 1), (b, 2)}, what type of function is S?
A. One-to-One
B. Onto
C. Neither One-to-One nor Onto
D. One-to-One and Onto
Show Answer & Explanation
Correct Answer: D
S covers all elements in Y uniquely with elements from X, thus it is both one-to-one and onto.
Q10
Hard
What is the maximum number of elements in the Cartesian product of sets P = {x, y} and Q = {1, 2, 3}?
A. 5
B. 4
C. 6
D. 3
Show Answer & Explanation
Correct Answer: C
The Cartesian product P × Q will have |P| * |Q| elements, which is 2 * 3 = 6.

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Relations and Functions — Class 12 Mathematics Practice Questions Online

This page contains 1660 practice MCQs for the chapter Relations and Functions in Class 12 Mathematics. The questions are organized by difficulty — 574 easy, 781 medium, 305 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.