Relations and Functions MCQ: Video Solutions – NCERT Class 12 Maths

Relations and Functions MCQ with answers and solutions from NCERT Class 12 Maths. Revise all 6 important questions step by step with clear explanations. You can also watch the video solutions for better understanding. This is in continuation of the previous topic on Determinants MCQs.

Ready? Okay, let’s begin with the first question!

Table of Contents show

Relations and Functions MCQ#1 (NCERT Exercise 1.1 – Question 15)

📍Let $R$ be the relation in the set $\{1, 2, 3, 4\}$ given by
$R = \{(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)\}$ .
Choose the correct answer.

Options:

(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.

Answer:
✅ Correct option: (B)

Explanation:
– $R$ is reflexive because $(1,1), (2,2), (3,3), (4,4)$ are all in $R$ .
– $R$ is transitive: for all $(a,b),(b,c) \in R$ , we have $(a,c) \in R$ .
– $R$ is *not symmetric* because $(1,2) \in R$ but $(2,1) \notin R$ .
Hence, $R$ is reflexive and transitive but not symmetric.

Watch Video Solution on YouTube

Let me tell you all of these 6 Relations and Functions MCQ are so simple and easy to understand and therefore scoring too. But then as they say, Math requires practice.

So, my suggestion to you is to practice these NCERT Relations and Functions MCQ a good number of times and feel confident. And if you ever need any clarification, just drop a comment — I’ll be more than happy to help.

Relations and Functions MCQ#2 (NCERT Exercise 1.1 – Question 16)

📍Let $R$ be the relation in the set $\mathbb{N}$ given by
$R = \{(a, b) : a = b - 2, b > 6\}$ .
Choose the correct answer.

Options:

(A) $(2, 4) \in R$
(B) $(3, 8) \in R$
(C) $(6, 8) \in R$
(D) $(8, 7) \in R$

Answer:
✅ Correct Option: (C)

Explanation:

We are given $R = \{(a, b) : a = b - 2, b > 6\}$ .

For $(2, 4)$ : $2 = 4 - 2 \Rightarrow 2 = 2$ ✅ but $b = 4 \ngtr 6$ ❌ → Not in $R$

For $(3, 8)$ : $3 = 8 - 2 \Rightarrow 3 = 6$ ❌ → Not in $R$

For $(6, 8)$ : $6 = 8 - 2 \Rightarrow 6 = 6$ ✅ and $b = 8 > 6$ ✅ → ✅ This is in $R$

For $(8, 7)$ : $8 = 7 - 2 \Rightarrow 8 = 5$ ❌ → Not in $R$

Hence, the correct answer is (C) $(6, 8) \in R$ .

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Relations and Functions MCQ#3 (NCERT Exercise 1.2 – Question 11)

📍Let $f : \mathbb{R} \to \mathbb{R}$ be defined as $f(x) = x^4$ . Choose the correct answer.

Options:

(A) $f$ is one-one onto
(B) $f$ is many-one onto
(C) $f$ is one-one but not onto
(D) $f$ is neither one-one nor onto

Answer:
✅ Correct Option: (D)

Explanation:

One-one check: $f(x_1) = f(x_2) \Rightarrow x_1^4 = x_2^4 \Rightarrow x_1 = x_2 \text{ or } x_1 = -x_2$
→ Since $x_1 \neq x_2$ can give the same output, $f$ is not one-one.

Onto check: Range of $f(x)$ is $[0, \infty)$ , but codomain is $\mathbb{R}$ .
→ Not all real numbers are covered, so $f$ is not onto.

✅ Hence, the correct answer is (D) $f$ is neither one-one nor onto.

Watch Video Solution on YouTube

Did you know, there are about 100 MCQs in NCERT textbooks for Class 12 (both Part 1 and Part 2)? I shall be taking one Chapter at a time and show you the explanations for each of the questions.

Moreover, I have also covered these solutions in the video form and they are freely available on my YouTube channel, @Mathsbetter. And here also, in each of the 6 Relations and Functions MCQ on this page, I have provided the direct links to each and every MCQ for you to understand the solutions in a very simple and easy manner.

Relations and Functions MCQ#4 (NCERT Exercise 1.2 – Question 12)

📍Let $f : \mathbb{R} \to \mathbb{R}$ be defined as $f(x) = 3x$ . Choose the correct answer.

Options:

(A) $f$ is one-one onto
(B) $f$ is many-one onto
(C) $f$ is one-one but not onto
(D) $f$ is neither one-one nor onto

Answer:
✅ Correct Option: (A)

Explanation:

One-one check: Suppose $f(x_1) = f(x_2)$ , then $3x_1 = 3x_2 \Rightarrow x_1 = x_2$ .
→ So $f$ is one-one.

Onto check: For any $y \in \mathbb{R}$ , $x = y/3 \in \mathbb{R}$ satisfies $f(x) = y$ .
→ So $f$ is onto.

✅ Hence, the correct answer is (A) $f$ is one-one onto.

Watch Video Solution on YouTube

Relations and Functions MCQ#5 (NCERT Miscellaneous Exercise Ch. 1 – Question 6)

📍Let $A = \{1,2,3\}$ .
Then number of relations containing $(1,2)$ and $(1,3)$ which are reflexive and symmetric but not transitive is

Options:

(A) $1$
(B) $2$
(C) $3$
(D) $4$

Answer:
✅ Correct Option: (A)

Explanation:

A reflexive relation must contain $(1,1),(2,2),(3,3)$ . Symmetry forces that $(1,2)\in R \Rightarrow (2,1)\in R$ and $(1,3)\in R \Rightarrow (3,1)\in R$ . The remaining 2 ordered pairs are $(2,3)$ and $(3,2)$ — we may either include them or not.

If we do not include $(2,3)$ , but the relation contains $(2,1)$ and $(1,3).$ So transitivity would require $(2,3)$ (which is absent) therefore it is not transitive, so it is one required relation.

Now, if we do include $(2,3)$ , then we will have to include $(3, 2)$ also to make the relation symmetric. But after doing so, all the possible pairs would be present and the relation becomes equivalence and so transitive, and that is not required.

So exactly one relation meets all the three requirements as per the question (reflexive, symmetric, contains (1,2) and (1,3), and not transitive).

Watch Video Solution on YouTube

If you have been following this website as a resource for some of the important questions. For example, how to Integrate Square Root of tan x, or may be a complete guide to look at using Matrix Method in solving a system of linear equations.

Trust me, similarly, this series on NCERT Class 12 MCQs is going to help you in many ways.

Moving onto the next Relations and Functions MCQ in this part of the series.

Relations and Functions MCQ#6 (NCERT Miscellaneous Exercise Ch. 1 – Question 7)

📍Let $A = \{1,2,3\}$ .
Then number of equivalence relations containing $(1,2)$ is

Options:

(A) $1$
(B) $2$
(C) $3$
(D) $4$

Answer:
✅ Correct option: (B)

Explanation:

If we start with the smallest equivalence relation (i.e. the identity relation) on the given set,
we have $R = \{(1,1), (2,2), (3,3)\}$

Now, as per the question, $(1,2)$ must be in $R$ .
So we add it, therefore,
$R = \{(1,1), (2,2), (3,3), (1,2)\}$

But this relation is not symmetric (since $(2,1)$ is missing),
so we need to add $(2,1)$ to make it symmetric. Therefore,
$R = \{(1,1), (2,2), (3,3), (1,2), (2,1)\}$

Now, this relation is reflexive, symmetric, and transitive.
Hence, it is an equivalence relation. (You can see the detailed explanation in the video)

Next, let’s check if any other equivalence relation can be formed.
If we add one more pair (out of the remaining 4 possible ordered pairs), say $(1,3)$ , we must also add $(3,1)$ for symmetry.
Then for transitivity, $(2,3)$ must also be included.
To make it symmetric again, we add $(3,2)$ .

Now $R$ becomes the universal relation, i.e.
$R = A \times A$

which is also an equivalence relation.

So we can form 2 equivalence relations containing $(1, 2)$

Watch Video Solution on YouTube

Quick Answer Key

Q1 → (B)
Q2 → (C)
Q3 → (D)
Q4 → (A)
Q5 → (A)
Q6 → (B)

Closing Note

That completes all the important NCERT Class 12 Maths Relations and Functions MCQ from chapter 1.
I hope the explanations and video solutions made things clearer and gave you more confidence. Stay tuned for the next chapter, where we’ll cover all the important Inverse Trigonometric Functions MCQ (Chapter 2 from NCERT) with the same clarity and video support.

👉 Make sure to practice these questions again to strengthen your concepts.
👉 Watch the video solutions for a clearer and faster revision.

Keep practicing, and you’ll master relations and functions easily! 🚀

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Relations and Functions MCQ: Video Solutions – NCERT Class 12 Maths

Relations and Functions MCQ#1 (NCERT Exercise 1.1 – Question 15)

Relations and Functions MCQ#2 (NCERT Exercise 1.1 – Question 16)

Relations and Functions MCQ#3 (NCERT Exercise 1.2 – Question 11)

Relations and Functions MCQ#4 (NCERT Exercise 1.2 – Question 12)

Relations and Functions MCQ#5 (NCERT Miscellaneous Exercise Ch. 1 – Question 6)

Relations and Functions MCQ#6 (NCERT Miscellaneous Exercise Ch. 1 – Question 7)

Quick Answer Key

Closing Note

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Relations and Functions MCQ#1 (NCERT Exercise 1.1 – Question 15)

Relations and Functions MCQ#2 (NCERT Exercise 1.1 – Question 16)

Relations and Functions MCQ#3 (NCERT Exercise 1.2 – Question 11)

Relations and Functions MCQ#4 (NCERT Exercise 1.2 – Question 12)

Relations and Functions MCQ#5 (NCERT Miscellaneous Exercise Ch. 1 – Question 6)

Relations and Functions MCQ#6 (NCERT Miscellaneous Exercise Ch. 1 – Question 7)

Quick Answer Key

Closing Note

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