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Equal Sets — JEE Main Mathematics MCQs with Solutions
Free JEE Main Mathematics Equal Sets MCQs with step-by-step solutions (9 questions). Part of Sets. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Equal Sets · medium · theory
The sets $A = \{x : x^2 = 4\}$ and $B = \{2, -2\}$ are:
A. not equal but equivalent
B. such that $A \subset B$ strictly
C. disjoint
D. equal ✓ Correct
Solution: $x^2=4 \Rightarrow x=\pm2$, so $A=\{2,-2\}=B$: the sets are equal.
Q2 — Equal Sets · medium · theory
Two sets $A$ and $B$ are said to be equivalent if:
A. they have exactly the same elements
B. they are both empty
C. one is a subset of the other
D. they have the same number of elements (same cardinality) ✓ Correct
Solution: Equivalent sets have equal cardinality; equal sets have identical elements. Equal $\Rightarrow$ equivalent, but not conversely.
Q3 — Equal Sets · medium · theory
Which pair is equivalent but NOT equal?
A. $\{a, b, c\}$ and $\{1, 2, 3\}$ ✓ Correct
B. $\{x : x^2 = 1\}$ and $\{-1, 1\}$
C. $\{1, 2\}$ and $\{1, 2, 3\}$
D. $\{1, 2, 3\}$ and $\{3, 1, 2\}$
Solution: Both have three elements (equivalent) but different members (not equal).
Q4 — Equal Sets · medium · theory
If $A = \{x \in \mathbb{N} : x^2 - 3x + 2 = 0\}$, then $A$ equals:
A. $\{2, 3\}$
B. $\{-1, -2\}$
C. $\{1, 2\}$ ✓ Correct
D. $\{1, 2, 3\}$
Solution: $x^2-3x+2=(x-1)(x-2)=0 \Rightarrow x=1,2$, both natural.
Q5 — Equal Sets · hard · theory
If $\{a, b\} = \{2, 3\}$ and $a < b$, then $2a + b$ equals:
A. $5$
B. $7$ ✓ Correct
C. $8$
D. $6$
Solution: From $a<b$: $a=2, b=3$, so $2a+b = 4+3 = 7$.
Q6 — Equal Sets · hard · theory
If the ordered-pair equality $(x + y,\ x - y) = (5,\ 1)$ holds, then the set $\{x, y\}$ is:
A. $\{2, 3\}$ is wrong since order matters
B. $\{3, 2\}$ ✓ Correct
C. $\{5, 1\}$
D. $\{4, 1\}$
Solution: $x+y=5,\ x-y=1 \Rightarrow x=3,\ y=2$, so $\{x,y\}=\{3,2\}$ (as a set, $\{3,2\}=\{2,3\}$).
Q7 — Equal Sets · hard · theory
If $\{2a + b,\ a - b\} = \{5,\ 1\}$ with $a - b = 1$, then the value of $a$ is:
A. $4$
B. $3$
C. $1$
D. $2$ ✓ Correct
Solution: From the pairing $a-b=1$ and $2a+b=5$: adding, $3a=6 \Rightarrow a=2$ (then $b=1$).
Q8 — Equal Sets · medium · theory
Two finite sets $A$ and $B$ have $n(A) = n(B)$. Then $A$ and $B$ are necessarily:
A. disjoint
B. equal
C. subsets of each other
D. equivalent, but not necessarily equal ✓ Correct
Solution: Same cardinality means equivalent; they need not have the same elements, so not necessarily equal.
Q9 — Equal Sets · hard · theory
If $A = \{x : x = 6n,\ n \in \mathbb{N}\}$ and $B = \{x : x \text{ is a common multiple of } 2 \text{ and } 3\} \cap \mathbb{N}$, then:
A. $A = B$ ✓ Correct
B. $A \cap B = \emptyset$
C. $A \subset B$ strictly
D. $B \subset A$ strictly
Solution: Common multiples of 2 and 3 are exactly the multiples of 6, so $A = B$.