Sets - JEE Main Previous Year Question with Solutions

JEE Main Previous Year Question of Math with Solutions are available at eSaral. Practicing JEE Main Previous Year Papers Questions of mathematics will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas. eSaral helps the students in clearing and understanding each topic in a better way. eSaral is providing complete chapter-wise notes of Class 11th and 12th both for all subjects. Besides this, eSaral also offers NCERT Solutions, Previous year questions for JEE Main and Advance, Practice questions, Test Series for JEE Main, JEE Advanced and NEET, Important questions of Physics, Chemistry, Math, and Biology and many more. Download eSaral app for free study material and video tutorials.
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)

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User ID 676758
Dec. 15, 2021, 7:12 a.m.
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Nikhil Kumar
Sept. 23, 2021, 8:09 p.m.
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Aug. 14, 2021, 8:30 a.m.
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Aug. 9, 2021, 3:29 p.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.
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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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HIGGS bosons
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
Rahul shArma
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
Manoj
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.
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Aug. 20, 2020, 6:03 p.m.
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Khushi
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.
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Pavithra
May 16, 2020, 7:15 p.m.
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