Class XI Maths Sets and Functions MCQs (Difficulty-wise) — Answers & Explanations
If you’re revising Sets and Functions for Class XI, doing questions in the right order helps a lot. Start with basic language of sets, then move to operations and complements, and finally practise relations and functions.
This difficulty-wise page is arranged as Easy → Medium → Hard. Each MCQ has the correct answer and a short explanation. If you want a quick mixed test, use the mixed page linked at the end.
Easy (Build the Basics)
1) Which symbol means “is an element of”?
A. $\subseteq$
B. $\in$
C. $\cup$
D. $\times$
Correct Answer: B
Explanation: $a\in A$ means $a$ belongs to set $A$.
2) Which of the following is a null (empty) set?
A. Even prime numbers
B. Odd natural numbers divisible by 2
C. Natural numbers less than 10
D. Integers between 1 and 5
Correct Answer: B
Explanation: No odd natural number is divisible by 2.
3) If $A={1,2,3}$, then $2$ is
A. an element of $A$
B. a subset of $A$
C. equal to $A$
D. not related to $A$
Correct Answer: A
Explanation: Elements are individual members; subsets are sets.
4) A set with a definite number of elements is called
A. infinite
B. finite
C. universal
D. empty
Correct Answer: B
Explanation: Finite means “countable with an end”.
5) If $A={a,e,i,o,u}$ then
A. $b\in A$
B. $a\notin A$
C. $a\in A$
D. $A$ has 6 elements
Correct Answer: C
Explanation: $A$ is the set of vowels.
6) The number of elements in ${\varnothing}$ is
A. 0
B. 1
C. 2
D. cannot be defined
Correct Answer: B
Explanation: ${\varnothing}$ is a set that contains one element (the empty set).
Revision Tip: Most confusion happens between $\varnothing$ and ${\varnothing}$. The first has 0 elements; the second has 1.
Medium (Operations + Properties)
7) If $A\subseteq B$, then $A\cap B$ equals
A. $B$
B. $A$
C. $\varnothing$
D. $A\cup B$
Correct Answer: B
Explanation: Common part is all of $A$.
8) The identity element for union is
A. $U$
B. $\varnothing$
C. $A$
D. $A'$
Correct Answer: B
Explanation: $A\cup\varnothing=A$.
9) Which is correct?
A. $(A\cup B)'=A'\cup B'$
B. $(A\cup B)'=A'\cap B'$
C. $(A\cap B)'=A'\cap B'$
D. $(A\cap B)'=A\cap B$
Correct Answer: B
Explanation: This is De Morgan’s law.
10) If $A={1,2}$ and $B={3,4,5}$, then $|A\times B|$ equals
A. 5
B. 6
C. 7
D. 8
Correct Answer: B
Explanation: $|A\times B|=|A||B|=2\cdot 3$.
11) If $U$ is universal set and $A\subseteq U$, then $A\cap A'$ is
A. $A$
B. $U$
C. $\varnothing$
D. $A'$
Correct Answer: C
Explanation: A set and its complement have no common elements.
12) If $A={2,3}$ and $B={x: x^2+5x+6=0}$, then
A. $A=B$
B. $A\subseteq B$
C. $A$ and $B$ are disjoint
D. $B\subseteq A$
Correct Answer: C
Explanation: $x^2+5x+6=0\Rightarrow (x+2)(x+3)=0$, so $B={-2,-3}$, which has no common element with ${2,3}$.
Hard (Relations + Functions)
13) A relation from $A$ to $B$ is a subset of
A. $A\cup B$
B. $A\times B$
C. $B\times A$
D. $A\cap B$
Correct Answer: B
Explanation: By definition, $R\subseteq A\times B$.
14) Which statement correctly describes a function $f:A\to B$?
A. Each element of $B$ must be related to exactly one element of $A$
B. Each element of $A$ must be related to exactly one element of $B$
C. An element of $A$ may have two images in $B$
D. No two elements of $A$ can have the same image
Correct Answer: B
Explanation: Exactly one output for each input.
15) For $f(x)=x^2$ from $\mathbb{R}$ to $\mathbb{R}$, the function 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: D
Explanation: Not one-one because $f(1)=f(-1)$; not onto $\mathbb{R}$ because negative values aren’t in the range.
16) If $A={1,2,3}$, then number of relations from $A$ to $A$ is
A. $2^3$
B. $2^6$
C. $2^9$
D. $3^3$
Correct Answer: C
Explanation: $|A\times A|=9$, so relations = number of subsets of $A\times A$ = $2^9$.
17) The empty set is the identity element for
A. union only
B. intersection only
C. both union and intersection
D. neither
Correct Answer: A
Explanation: $A\cup\varnothing=A$ but $A\cap\varnothing=\varnothing$.
18) Which collection is not well-defined (so not a set)?
A. Prime numbers less than 30
B. Students of Class XI in your school
C. The most intelligent students in Class XI
D. Multiples of 6
Correct Answer: C
Explanation: “Most intelligent” is subjective.
Quick Mixed Test
After finishing this page, do a quick mixed run: