Types of Relations and Functions Quiz - CBSE Class 12 Mathematics

Free practice quiz: Types of Relations and Functions (CBSE Class 12 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 12 Mathematics practice quiz has 17 multiple-choice questions on Types of Relations and Functions, and 17 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. Which of the following is a function?

   1. y = x^2
   2. y^2 = x
   3. x = y^2
   4. y^3 = x
   Show answer

   Answer: A. y = x^2

   A function is a relation in which each input from the domain has exactly one output in the range. y = x^2 is a function as every x corresponds to exactly one y.

2. Determine the identity function from the options below.

   1. f(x) = x + 1
   2. f(x) = 2x
   3. f(x) = x
   4. f(x) = -x
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   Answer: C. f(x) = x

   The identity function is of the form f(x) = x. Here, f(x) = x represents the identity function where the output is the same as the input.

3. Which of the following sets of ordered pairs is a function?

   1. {(1, 2), (2, 3), (1, 4)}
   2. {(1, 2), (2, 3), (3, 4)}
   3. {(1, 2), (2, 3), (2, 4)}
   4. {(1, 2), (3, 4), (5, 6)}
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   Answer: B. {(1, 2), (2, 3), (3, 4)}

   In a function, each input should map to exactly one output. The set {(1, 2), (2, 3), (3, 4)} ensures each input has one unique output.

4. Identify the bijective function among the options.

   1. f(x) = x^2
   2. f(x) = x^3
   3. f(x) = |x|
   4. f(x) = sin(x)
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   Answer: B. f(x) = x^3

   A bijective function is both injective and surjective. f(x) = x^3 is bijective as it is one-one (each y has a unique x) and onto (covers all reals).

5. If a function f: A → B is defined such that it is surjective but not injective, what can you infer about the cardinality of A and B?

   1. |A| < |B|
   2. |A| = |B|
   3. |A| > |B|
   4. Cannot determine
   Show answer

   Answer: C. |A| > |B|

   If f is surjective, every element in B is mapped to by some element in A. If not injective, some elements in A map to the same element in B, implying |A| > |B|.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Consider the relation R on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3), (3, 3)}. What is the type of this relation?
2. Which of the following is NOT a one-one function?
3. Which of the following relations on set A = {1, 2, 3} is reflexive?
4. In terms of functions, what does it mean when f: A → B is a bijection?
5. Identify the non-equivalence relation in the following.
6. Which relation on set A = {a, b, c} is symmetric but not transitive?
7. Among the following, which function is the inverse of f(x) = 3x + 2?
8. Which function is an example of a non-injective, surjective function?
9. Find the complexity of the relation R = {(x, y) | x ≥ y} on set of real numbers.
10. What can be deduced from the inverse of a bijection?
11. What distinguishes an equivalence relation from other types of relations?
12. Let R be a relation on set A defined as R = {(a, b) | a, b ∈ A, a divides b}. Is R an equivalence relation?

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