Class XI Maths Sets and Functions MCQs (Mixed) — Answers & Explanations
Sets and functions are topics where small mistakes (like mixing up subset vs element, or range vs codomain) can cost easy marks. The quickest way to get confident is to solve questions that look like school exams and then check why the answer works.
This page gives you a mixed set of Class XI MCQs from Sets and Functions. Each question includes the correct option and a short explanation, so you can revise concepts like union/intersection, complements and De Morgan’s laws, Cartesian product and relations, domain–codomain–range, and what makes a relation a function.
For level-wise practice, use the difficulty-wise page linked at the end.
MCQs (Mixed Practice)
1) If $A = {1,2,3}$, $B = {3,2,1,1}$ then
A. $A \ne B$ because $B$ repeats 1
B. $A = B$
C. $A \subset B$ but $A \ne B$
D. $B$ is not a set
Correct Answer: B
Explanation: In a set, repetition is ignored. Both contain exactly ${1,2,3}$.
2) If $U={1,2,3,4,5,6,7,8,9}$, $B={2,4,6,8}$ and $C={3,4,5,6}$, then $(B-C)'$ equals
A. ${1,3,5,7,9}$
B. ${1,3,4,5,6,7,9}$
C. ${1,2,3,5,7,9}$
D. ${1,2,3,4,5,7,9}$
Correct Answer: B
Explanation: $B-C={2,8}$. So $(B-C)'=U-{2,8}={1,3,4,5,6,7,9}$.
3) The number of subsets of a set with 5 elements is
A. 10
B. 25
C. 32
D. 64
Correct Answer: C
Explanation: A set with $n$ elements has $2^n$ subsets. Here $2^5=32$.
4) If $A={x\in \mathbb{Z}: x^2 \le 4}$, then $A$ is
A. ${-2,-1,0,1,2}$
B. ${-2,-1,1,2}$
C. ${-4,-2,0,2,4}$
D. ${0,1,2}$
Correct Answer: A
Explanation: $x^2\le 4 \Rightarrow -2\le x\le 2$ for integers.
5) If $A={1,2,3,4}$ and $B={3,4,5}$, then $A\cap B$ is
A. ${1,2,5}$
B. ${3,4}$
C. ${1,2,3,4,5}$
D. $\varnothing$
Correct Answer: B
Explanation: Intersection contains common elements.
Revision Tip: When you see $A-B$, read it as “elements in $A$ but not in $B$”. Do it in two steps: write $A$, cross out anything also in $B$.
6) De Morgan’s law for two sets $A,B$ is
A. $(A\cup B)'=A'\cup B'$
B. $(A\cup B)'=A'\cap B'$
C. $(A\cap B)'=A'\cap B'$
D. $(A\cap B)'=A\cup B$
Correct Answer: B
Explanation: De Morgan: $(A\cup B)'=A'\cap B'$ and $(A\cap B)'=A'\cup B'$.
7) If $A\subseteq B$, then which is always true?
A. $A\cup B = A$
B. $A\cap B = B$
C. $A\cap B = A$
D. $A-B = A$
Correct Answer: C
Explanation: If $A$ is inside $B$, common part is all of $A$.
8) If $A={1,2}$ and $B={a,b,c}$, then $|A\times B|$ equals
A. 5
B. 6
C. 8
D. 9
Correct Answer: B
Explanation: $|A\times B|=|A|\cdot |B|=2\cdot 3=6$.
9) A relation $R$ from $A$ to $B$ is a subset of
A. $A\cup B$
B. $A\cap B$
C. $A\times B$
D. $B\times A$
Correct Answer: C
Explanation: By definition, $R\subseteq A\times B$.
10) Let $A={1,2,3}$. The number of relations on $A$ is
A. $9$
B. $2^9$
C. $2^6$
D. $3^2$
Correct Answer: B
Explanation: A relation on $A$ is any subset of $A\times A$. Here $|A\times A|=3\cdot 3=9$, so number of relations is $2^9$.
11) A function $f: A\to B$ is a relation in which
A. every element of $B$ has exactly one image in $A$
B. every element of $A$ is related to exactly one element of $B$
C. some elements of $A$ may have two images in $B$
D. no two elements of $A$ can map to the same element of $B$
Correct Answer: B
Explanation: Each input in the domain has exactly one output in the codomain.
12) If $f: \mathbb{R}\to \mathbb{R}$ is defined by $f(x)=x^2$, then the range of $f$ is
A. $\mathbb{R}$
B. $(-\infty,0]$
C. $[0,\infty)$
D. $(0,\infty)$
Correct Answer: C
Explanation: Squares of real numbers are non-negative, and 0 is included.
13) If $f: \mathbb{R}\to \mathbb{R}$ is $f(x)=2x+1$, then $f$ is
A. one-one and onto
B. one-one but not onto
C. onto but not one-one
D. neither one-one nor onto
Correct Answer: A
Explanation: A non-constant linear function on $\mathbb{R}$ is bijective.
14) The identity element for union on any set $A$ is
A. $A$
B. $U$
C. $\varnothing$
D. $A'$
Correct Answer: C
Explanation: $A\cup\varnothing=A$.
15) Which collection is not a set (not well-defined)?
A. Natural numbers less than 50
B. Students of Class XI in your school
C. The 10 best songs of the year
D. Even integers
Correct Answer: C
Explanation: “Best” is subjective, so the collection is not well-defined.
Next: Practice Level-Wise
If you want an easier-to-harder path (so you build confidence step by step), use the difficulty-wise set:
When you finish, try re-solving the questions you got wrong without looking at the explanation.