Relations & Functions 50 MCQs | Class 11 Maths NCERT Chapter 2

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Maths — Relations And Functions

50 Questions Class 11 MCQs

Which of the following represents a relation from set \(A=\{1,2\}\) to \(B=\{3,4\}\)?
(Exam: NCERT Class XI)

a a. \(\{(1,3),(2,4)\}\) b b. \(\{(3,1),(4,2)\}\) c c. \(\{(1,2),(3,4)\}\) d d. \(\{(3,4)\}\)

The number of relations from a set with 2 elements to a set with 3 elements is:
(Exam: NCERT Class XI)

a a. \(6\) b b. \(8\) c c. \(2^6\) d d. \(3^2\)

Which of the following is a reflexive relation on \(A=\{1,2,3\}\)?
(Exam: NCERT Class XI)

a a. \(\{(1,1),(2,2)\}\) b b. \(\{(1,1),(2,2),(3,3)\}\) c c. \(\{(1,2),(2,3)\}\) d d. \(\{(2,2),(3,3)\}\)

A relation \(R\) on a set \(A\) is symmetric if:
(Exam: NCERT Class XI)

a a. \((a,b)\in R \Rightarrow (a,a)\in R\) b b. \((a,b)\in R \Rightarrow (b,a)\in R\) c c. \((a,a)\in R\) for all \(a\) d d. \((a,b),(b,c)\in R \Rightarrow (a,c)\in R\)

Which relation is transitive?
(Exam: NCERT Class XI)

a a. Equality b b. Inequality c c. “is friend of” d d. “is brother of”

If \(f(x)=x^2\), then \(f(-2)\) equals:
(Exam: NCERT Class XI)

a a. \(-4\) b b. \(0\) c c. \(2\) d d. \(4\)

The domain of the function \(f(x)=\sqrt{x-3}\) is:
(Exam: NCERT Class XI)

a a. \(\mathbb{R}\) b b. \(x>3\) c c. \(x\ge3\) d d. \(x\le3\)

Which of the following is not a function?
(Exam: NCERT Class XI)

a a. \(y=x^2\) b b. \(y=\sqrt{x}\) c c. \(x=y^2\) d d. \(y=|x|\)

A function having one-one and onto properties is called:
(Exam: NCERT Class XI)

a a. into b b. many-one c c. bijective d d. constant

The range of \(f(x)=x^2\), \(x\in\mathbb{R}\), is:
(Exam: NCERT Class XI)

a a. \(\mathbb{R}\) b b. \(x>0\) c c. \(x\ge0\) d d. \(x\le0\)

If \(f(x)=2x+1\), then \(f^{-1}(x)\) is:
(Exam: NCERT Class XI)

a a. \(\frac{x-1}{2}\) b b. \(\frac{x+1}{2}\) c c. \(2x-1\) d d. \(\frac{1-x}{2}\)

The composition \((f\circ g)(x)\) means:
(Exam: NCERT Class XI)

a a. \(f(x)+g(x)\) b b. \(f(g(x))\) c c. \(g(f(x))\) d d. \(f(x)g(x)\)

If \(f(x)=x+1\) and \(g(x)=x^2\), then \((f\circ g)(2)\) is:
(Exam: NCERT Class XI)

a a. \(5\) b b. \(6\) c c. \(9\) d d. \(10\)

A relation that is reflexive, symmetric, and transitive is called:
(Exam: NCERT Class XI)

a a. identity relation b b. equivalence relation c c. universal relation d d. empty relation

The identity function on \(\mathbb{R}\) is:
(Exam: NCERT Class XI)

a a. \(f(x)=1\) b b. \(f(x)=0\) c c. \(f(x)=x\) d d. \(f(x)=|x|\)

The number of equivalence relations on a set with one element is:
(Exam: NCERT Class XI)

a a. 0 b b. 1 c c. 2 d d. 3

Let \(R=\{(a,b)\in \mathbb{R}^2 : a-b=0\}\). Then \(R\) is:
(Exam: NCERT Class XI)

a a. reflexive only b b. symmetric only c c. transitive only d d. an equivalence relation

The range of \(f(x)=\frac{1}{x}\), \(x\in\mathbb{R}\setminus\{0\}\), is:
(Exam: NCERT Class XI)

a a. \(\mathbb{R}\) b b. \(\mathbb{R}^+\) c c. \(\mathbb{R}\setminus\{0\}\) d d. \((-\infty,0)\)

If \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=x^2+1\), then \(f\) is:
(Exam: NCERT Class XI)

a a. one-one b b. onto c c. bijective d d. neither one-one nor onto

The inverse of a function exists if and only if the function is:
(Exam: NCERT Class XI)

a a. one-one b b. onto c c. bijective d d. many-one

If \(f(x)=ax+b\) has an inverse, then:
(Exam: NCERT Class XI)

a a. \(a=0\) b b. \(a\neq0\) c c. \(b=0\) d d. \(a=b\)

Let \(A=\{1,2,3\}\). The number of symmetric relations on \(A\) is:
(Exam: JEE Main)

a a. \(2^3\) b b. \(2^6\) c c. \(2^9\) d d. \(2^{12}\)

The number of equivalence relations on a set with 3 elements equals:
(Exam: JEE Main)

a a. 3 b b. 4 c c. 5 d d. 6

If \(f(x)=|x|\), then \(f\) is:
(Exam: JEE Main)

a a. one-one b b. onto \(\mathbb{R}\) c c. many-one d d. bijective

Let \(f(x)=x^3\). Then \(f^{-1}(x)\) equals:
(Exam: JEE Main)

a a. \(x^{1/3}\) b b. \(3x^2\) c c. \(\sqrt{x}\) d d. does not exist

If \(f\circ g=g\circ f\), then \(f\) and \(g\) are said to be:
(Exam: JEE Main)

a a. associative b b. commutative c c. distributive d d. identity

Let \(f(x)=\frac{x-1}{x+1}\). Then domain of \(f^{-1}\) is:
(Exam: JEE Main)

a a. \(\mathbb{R}\) b b. \(\mathbb{R}\setminus\{-1\}\) c c. \(\mathbb{R}\setminus\{1\}\) d d. \(\mathbb{R}\setminus\{1,-1\}\)

The number of functions from a set of 3 elements to a set of 2 elements is:
(Exam: JEE Main)

a a. 6 b b. 8 c c. 9 d d. 12

The number of onto functions from a 3-element set to a 2-element set is:
(Exam: JEE Main)

a a. 2 b b. 4 c c. 6 d d. 8

If \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=x^2\), then \(f\) is invertible on:
(Exam: JEE Main)

a a. \(\mathbb{R}\) b b. \((-\infty,0]\) c c. \([0,\infty)\) d d. both b and c

Assertion (A): Every equivalence relation is reflexive. Reason (R): Every equivalence relation is symmetric.
(Exam: JEE Main – Assertion Reason)

a a. Both A and R true, R explains A b b. Both A and R true, R does not explain A c c. A true, R false d d. A false, R true

Assertion (A): If a function has an inverse, it must be bijective. Reason (R): Only one-one functions are invertible.
(Exam: JEE Main – Assertion Reason)

a a. Both true, R explains A b b. Both true, R does not explain A c c. A true, R false d d. A false, R true

If \(f(x)=\ln x\), then domain of \(f\circ f\) is:
(Exam: JEE Advanced)

a a. \(x>0\) b b. \(x>1\) c c. \(x\ge0\) d d. \(x\neq0\)

Let \(f(x)=x^2\) and \(g(x)=\sqrt{x}\). Then \((f\circ g)(x)\) equals:
(Exam: JEE Advanced)

a a. \(x\) b b. \(|x|\) c c. \(x^2\) d d. \(\sqrt{x}\)

The relation \(R=\{(x,y): x-y\in\mathbb{Z}\}\) on \(\mathbb{R}\) is:
(Exam: JEE Advanced)

a a. reflexive only b b. symmetric only c c. transitive only d d. equivalence relation

If \(f(x)=x^2+x\), then minimum value of \(f(x)\) is:
(Exam: JEE Main)

a a. \(-\frac14\) b b. \(0\) c c. \(\frac14\) d d. \(-1\)

Let \(f:\mathbb{N}\to\mathbb{N}\) be defined by \(f(x)=x+1\). Then \(f\) is:
(Exam: JEE Main)

a a. one-one but not onto b b. onto but not one-one c c. bijective d d. neither

The number of bijective functions from a set of 4 elements to itself is:
(Exam: JEE Main)

a a. 4 b b. 12 c c. 24 d d. 16

If \(f(x)=\frac{ax+b}{cx+d}\) is invertible, then:
(Exam: JEE Advanced)

a a. \(ad-bc=0\) b b. \(ad-bc\neq0\) c c. \(a=c\) d d. \(b=d\)

Let \(f(x)=\sin x\). The inverse of \(f\) exists on:
(Exam: JEE Main)

a a. \(\mathbb{R}\) b b. \([-\pi/2,\pi/2]\) c c. \([0,2\pi]\) d d. \([-\pi,\pi]\)

The range of \(f(x)=\frac{1}{1+x^2}\) is:
(Exam: JEE Main)

a a. \((0,1]\) b b. \([0,1)\) c c. \((-\infty,1]\) d d. \([1,\infty)\)

If \(f(x)=x^3+1\), then \(f^{-1}(2)\) equals:
(Exam: JEE Main)

a a. 0 b b. 1 c c. \(-1\) d d. 2

Let \(A=\{1,2\}\). Number of antisymmetric relations on \(A\) is:
(Exam: JEE Advanced)

a a. 4 b b. 6 c c. 8 d d. 12

If \(f(x)=x^2\) and domain is \(\mathbb{Z}\), then \(f\) is:
(Exam: JEE Main)

a a. one-one b b. onto c c. many-one d d. bijective

The relation “is parallel to” among straight lines is:
(Exam: JEE Main)

a a. reflexive only b b. symmetric only c c. transitive only d d. equivalence relation

If \(f(x)=e^x\), then \(f^{-1}(x)\) equals:
(Exam: JEE Main)

a a. \(\ln x\) b b. \(\log x\) c c. \(1/x\) d d. \(x^e\)

The number of equivalence classes induced by relation \(x\sim y\iff x-y\) is even, on \(\mathbb{Z}\), is:
(Exam: JEE Main)

a a. 1 b b. 2 c c. infinite d d. 4

If \(f(x)=x|x|\), then \(f\) is:
(Exam: JEE Advanced)

a a. one-one b b. onto c c. bijective d d. many-one

Let \(f(x)=\tan x\). Inverse exists on:
(Exam: JEE Advanced)

a a. \((-\pi/2,\pi/2)\) b b. \((0,\pi)\) c c. \((-\pi,\pi)\) d d. \(\mathbb{R}\)

Assertion (A): A many-one function cannot have an inverse. Reason (R): Inverse of a function must be unique.
(Exam: JEE Advanced – Assertion Reason)

a a. Both A and R true, R explains A b b. Both true, R does not explain A c c. A true, R false d d. A false, R true

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Relations & Functions 50 MCQs | Class 11 Maths NCERT Chapter 2

Relations & Functions 50 MCQs | Class 11 Maths NCERT Chapter 2 — Complete Notes & Solutions · academia-aeternum.com

Relations and Functions form the conceptual backbone of higher mathematics and play a decisive role in developing analytical thinking at the senior secondary level. For Class XI students, this chapter acts as a bridge between elementary set theory and advanced topics such as calculus, matrices, and real analysis. The following set of 50 carefully graded multiple-choice questions has been designed strictly in accordance with the NCERT syllabus for Chapter 2, Relations and Functions, while…

🎓 Class 11 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE

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Relations & Functions

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Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

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Maths — Relations And Functions

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Relations & Functions

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — Relations And Functions

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