Relations and Functions - ISC Class 12 Mathematics Questions with Answers, Page 2

58 past-paper questions on Relations and Functions from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 21-40 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.

2025 · 1 mark · MCQOpen: Consider the following graph of , : Statement 1: The function is one-one…

Consider the following graph of $f(x)$, $f: \mathbb{R} \to \mathbb{R}$: Statement 1: The function is one-one function. Statement 2: The function is onto function.

(a)Statement 1 is true and Statement 2 is false.
(b)Statement 2 is true and Statement 1 is false.
(c)Both the statements are true.
(d)Both the statements are false.

No answer yet.

2025 · 1 mark · Assertion-reasonOpen: If Set has elements, Set has elements and , then the number of one-one…

Assertion: If Set $A$ has $m$ elements, Set $B$ has $n$ elements and $n < m$, then the number of one-one function(s) from $A \to B$ is zero.

Reason: A function $f: A \to B$ is defined only if all elements in Set $A$ have an image in Set $B$.

(a)Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
(b)Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
(c)Assertion is true and Reason is false.
(d)Assertion is false and Reason is true.

No answer yet.

2025 · 4 marks · Long answerOpen: A part of the graph of the function is shown below: Answer the following…

A part of the graph of the function $f(x) = 2x^3 - 3x^2 - 12x + 8, x \in \mathbb{R}$ is shown below: Answer the following questions.

(a)

Explain why ‘f’ does not have an inverse.

(b)

The domain of ‘f’ is now restricted to $a \le x \le b$ where $a < 0$ and $b > 0$. $a$ and $b$ are chosen so that f has an inverse and the interval $[a, b]$ is as large as possible. Find the domain and range of $f^{-1}$.

No answer yet.

2025 · 1 mark · MCQOpen: Statement I: given by , is neither injective nor surjective. Statement II…

Statement I: $f: \mathbb{R} \to \mathbb{R}$ given by $f(x) = \frac{1}{x} - 2$, is neither injective nor surjective. Statement II: $f: \mathbb{Z} \to \mathbb{Z}$ given by $f(x) = \sqrt[3]{x^9}$, is neither injective nor surjective.

(a)Both the statements are true.
(b)Both the statements are false.
(c)Statement I is true, and Statement II is false.
(d)Statement I is false, and Statement II is true.

No answer yet.

2025 · 1 mark · One wordOpen: If is a relation from to defined by , find the range of .

If $R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$, find the range of $R^{-1}$.

No answer yet.

2025 · 1 mark · Assertion-reasonOpen: The relation defined by is a bijective function. Assertion (A): The relation…

Assertion: The relation $f: \{m, n, p, q\} \to \{11, 12, 13, 14\}$ defined by $f = \{(m, 11), (n, 12), (p, 13)\}$ is a bijective function.

Reason: The function $f: \{m, n, p\} \to \{11, 12, 13, 14\}$ such that $f = \{(m, 11), (n, 12), (p, 13)\}$ is one-one.

Assertion (A): The relation $f: \{m, n, p, q\} \to \{11, 12, 13, 14\}$ defined by $f = \{(m, 11), (n, 12), (p, 13)\}$ is a bijective function. Reason (R): The function $f: \{m, n, p\} \to \{11, 12, 13, 14\}$ such that $f = \{(m, 11), (n, 12), (p, 13)\}$ is one-one.

(a)Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b)Both Assertion (A) and Reason (R) are true, and Reason (R) is not the correct explanation of Assertion (A).
(c)Assertion (A) is true; Reason (R) is false.
(d)Assertion (A) is false; Reason (R) is true.

No answer yet.

2025 · 1 mark · One wordOpen: Write the smallest equivalence relation from the set to , where .

Write the smallest equivalence relation from the set $A$ to $A$, where $A = \{1, 2, 3\}$.

No answer yet.

2024 · 1 mark · MCQOpen: Let be a set of all straight lines in a plane. The relation on defined as…

Let $L$ be a set of all straight lines in a plane. The relation $R$ on $L$ defined as 'perpendicular to' is:

(a)Symmetric and Transitive
(b)Transitive
(c)Symmetric
(d)Equivalence

No answer yet.

2024 · 1 mark · Short answerOpen: Which one of the following graphs is a function of ? Graph A Graph B

Which one of the following graphs is a function of $x$? Graph A Graph B

No answer yet.

2024 · 2 marks · Short answerOpen: Let be defined as is invertible. Find .

Let $f: \mathbb{R} - \left\{-\frac{1}{3}\right\} \to \mathbb{R} - \{0\}$ be defined as $f(x) = \frac{5}{3x + 1}$ is invertible. Find $f^{-1}(x)$.

No answer yet.

2024 · 1 mark · MCQOpen: Let be a non-empty set. Statement 1: Identity relation on is Reflexive…

Let $A$ be a non-empty set. Statement 1: Identity relation on $A$ is Reflexive. Statement 2: Every Reflexive relation on $A$ is an Identity relation.

(a)Both the statements are true.
(b)Both the statements are false.
(c)Statement 1 is true and Statement 2 is false.
(d)Statement 1 is false and Statement 2 is true.

No answer yet.

2024 · 2 marks · DerivationOpen: If is defined by , show that is one - one and onto.

If $f: \mathbb{R} \to \mathbb{R}$ is defined by $f(x) = \frac{2x - 7}{4}$, show that $f(x)$ is one - one and onto.

Given: $f(x) = \frac{2x - 7}{4}$

To show: $f(x)$ is one - one and onto

No answer yet.

2023 · 1 mark · Short answerOpen: Write the smallest equivalence relation on the set

Write the smallest equivalence relation on the set $A = \\{a, b, c\\}$

No answer yet.

2023 · 1 mark · MCQOpen: Let be the set of all cards numbered from to . Let be a function defined by…

Let $A$ be the set of all $50$ cards numbered from $1$ to $50$. Let $f: A \to \mathbb{N}$ be a function defined by $f(x) =$ card number of the card ‘$x$’. Then the function ‘$f$’ is:

(a)one to one but not onto.
(b)onto but not one to one.
(c)neither one to one nor onto.
(d)one to one and onto.

No answer yet.

2023 · 2 marks · Short answerOpen: If is a real invertible function, then find .

If $f(x) = [4 - (x - 7)^3]^{\frac{1}{5}}$ is a real invertible function, then find $f^{-1}(x)$.

No answer yet.

2023 · 1 mark · MCQOpen: A relation on is given by . Then the relation is:

A relation $R$ on $\{1, 2, 3\}$ is given by $R = \{(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)\}$. Then the relation $R$ is:

(a)Reflexive.
(b)Symmetric.
(c)Transitive.
(d)Symmetric and Transitive.

No answer yet.

2023 · 1 mark · MCQOpen: Which of the following is NOT an equivalence relation on ?

Which of the following is NOT an equivalence relation on $\mathbb{Z}$?

(a)$aRb \iff a + b$ is an even integer
(b)$aRb \iff a - b$ is an even integer
(c)$aRb \iff a < b$
(d)$aRb \iff a = b$

No answer yet.

2023 · 1 mark · MCQOpen: Let be a function with domain . Then domain of is:

Let $f(x) = x^3$ be a function with domain $\{0, 1, 2, 3\}$. Then domain of $f^{-1}$ is:

(a)$\{3, 2, 1, 0\}$
(b)$\{0, -1, -2, -3\}$
(c)$\{0, 1, 8, 27\}$
(d)$\{0, -1, -8, -27\}$

No answer yet.

2023 · 2 marks · DerivationOpen: Let and . If is a function defined by then show that is a one-one and an onto…

Let $A = \mathbb{R} - \{2\}$ and $B = \mathbb{R} - \{1\}$. If $f : A \to B$ is a function defined by $f(x) = \frac{x - 1}{x - 2}$ then show that $f$ is a one-one and an onto function.

Given: $f : A \to B \text{ defined by } f(x) = \frac{x - 1}{x - 2}$

To show: $f \text{ is a one-one and an onto function}$

No answer yet.

2023 · 2 marks · Short answerOpen: Let defined as . Find domain and range of

Let $f: \mathbb{R} \to \mathbb{R}$ defined as $f(x) = 2x - 3$. Find

(i)

$f^{-1}(x)$

(ii)

domain and range of $f^{-1}(x)$

No answer yet.

Relations and Functions - ISC Class 12 Mathematics Questions with Answers, Page 2

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