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Sets - JEE Main Previous Year Question with Solutions

Practice JEE Main Sets previous year questions with detailed solutions, covering set operations, subsets, intersections, unions, and problem-solving techniques frequently asked in the exam.

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Sets - JEE Main Previous Year Question with Solutions

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Q. If $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are three sets such that $\mathrm{A} \cap \mathrm{B}=\mathrm{A} \cap \mathrm{C}$ and $\mathrm{A} \cup \mathrm{B}=\mathrm{A} \cup \mathrm{C},$ then :- (1) B = C $(2) \mathrm{A} \cap \mathrm{B}=\phi$ (3) A = B (4) A = C [AIEEE- 2009]
Ans. (1) $\mathrm{n}(\mathrm{A})=3, \mathrm{n}(\mathrm{B})=6, \mathrm{n}(\mathrm{A} \cap \mathrm{B})=3(\text { maximum })$ so $\mathrm{n}(\mathrm{A} \cup \mathrm{B})=\mathrm{n}(\mathrm{A})+\mathrm{n}(\mathrm{B})-\mathrm{n}(\mathrm{A} \cap \mathrm{B})$ $3+6-3$ $\mathrm{n}(\mathrm{A} \cup \mathrm{B})=6$ so minimum no of elements in $\mathrm{A} \cup \mathrm{B}$ is $6 .$
Q. Two sets A and B are as under $\mathrm{A}=\{(\mathrm{a}, \mathrm{b}) \in \mathrm{R} \times \mathrm{R}:|\mathrm{a}-5|<1 \text { and }|\mathrm{b}-5|<1\}$ $\mathrm{B}=\left\{(\mathrm{a}, \mathrm{b}) \in \mathrm{R} \times \mathrm{R}: 4(\mathrm{a}-6)^{2}+9(\mathrm{b}-5)^{2} \leq 36\right\} .$ Then (1) $\mathrm{A} \subset \mathrm{B}$ (2) $\mathrm{A} \cap \mathrm{B}=\phi$ (an empty set) (3) neither $\mathrm{A} \subset \mathrm{B}$ nor $\mathrm{B} \subset \mathrm{A}$ (4) $\mathrm{B} \subset \mathrm{A}$ [JEE-MAINS-2018]
Ans. (1)
Q. Let $\mathrm{S}=\{\mathrm{x} \in \mathrm{R}: \mathrm{x} \geq 0 \text { and } 2|\sqrt{\mathrm{x}}-3|+\sqrt{\mathrm{x}}(\sqrt{\mathrm{x}}-6)+6=0\} .$ Then $\mathrm{S}:$ (1) contains exactly one element. (2) contains exactly two elements. (3) contains exactly four elements. (4) is an empty set. [JEE-MAINS-2018]
Ans. (2)

Frequently Asked Questions

Find answers to common questions.

Are Sets important for JEE Main?

Yes, Sets is one of the fundamental topics in Mathematics and forms the base for Relations, Functions, Probability, and Logic. JEE Main regularly includes direct and concept-based questions from Sets.

What are the most important concepts in Sets for JEE Main?

The most important concepts include union of sets, intersection of sets, complement of a set, difference of sets, Venn diagrams, subsets, power sets, and set identities.

How many questions from Sets are usually asked in JEE Main?

Generally, 1–2 questions are asked from Sets and related topics in JEE Main. These questions are often straightforward and scoring.

Why should I solve JEE Main previous year questions on Sets?

Previous year questions help you understand the exam pattern, identify frequently tested concepts, and improve your speed and accuracy in solving problems.

Are Venn diagrams useful for solving Sets questions?

Yes, Venn diagrams are extremely useful for visualizing relationships between sets and solving problems involving unions, intersections, and complements.

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Comments

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March 29, 2025, 6:35 a.m.
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May 1, 2024, 6:35 a.m.
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User ID 676758
Dec. 15, 2021, 7:12 a.m.
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Sept. 23, 2021, 8:09 p.m.
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Aug. 14, 2021, 8:30 a.m.
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May 25, 2021, 11:31 p.m.
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Dec. 29, 2020, 8:23 p.m.
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Monu
Dec. 1, 2020, 1:51 p.m.
Wrong answer in 3
Abidh zain
Nov. 27, 2020, 8:11 p.m.
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Manas
Nov. 24, 2020, 11:34 a.m.
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Nov. 22, 2020, 8:23 p.m.
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Anonymous
Oct. 2, 2020, 9:52 a.m.
Pls help me with the 2nd question
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Sept. 29, 2020, 6:04 p.m.
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Sept. 14, 2020, 10:52 a.m.
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Ikshan
Sept. 10, 2020, 5:28 p.m.
Only few questions are there
Peeyush shukla
Sept. 4, 2020, 8:41 p.m.
Wrong answer Right answer is 1 option
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Sept. 2, 2020, 9:06 a.m.
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Aug. 28, 2020, 4:56 p.m.
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Aug. 27, 2020, 8:20 p.m.
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derek
Aug. 27, 2020, 6:14 a.m.
solutions are not correct plz correct them
Airin ali
Aug. 23, 2020, 10:54 a.m.
Need more previous questions based on all chapters
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Aug. 20, 2020, 6:03 p.m.
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Aug. 12, 2020, 9:05 p.m.
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July 16, 2020, 9:36 p.m.
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July 16, 2020, 9:35 p.m.
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July 10, 2020, 8:03 p.m.
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July 4, 2020, 1:20 p.m.
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May 23, 2020, 10:30 p.m.
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Pavithra
May 22, 2020, 9:44 a.m.
Only three questions ,thank you so much
Pavithra
May 16, 2020, 7:15 p.m.
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