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]

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Sol. (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]

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Sol. (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]

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Sol. (2)

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Comments
  • September 23, 2021 at 8:09 pm

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    1
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    10
  • August 9, 2021 at 3:29 pm

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    121
  • July 23, 2021 at 6:06 pm

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    18
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    May 25, 2021 at 11:31 pm

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    17
  • December 29, 2020 at 8:23 pm

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    68
  • December 1, 2020 at 1:51 pm

    Wrong answer in 3

    6
    • April 24, 2021 at 7:49 pm

      Why

      6
  • November 27, 2020 at 8:11 pm

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    11
  • November 24, 2020 at 11:34 am

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    0
  • November 22, 2020 at 8:23 pm

    Not so hard question

    53
  • October 2, 2020 at 9:52 am

    Pls help me with the 2nd question

    2
  • September 29, 2020 at 6:04 pm

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    0
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    2
    • May 15, 2021 at 12:27 pm

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      1
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    1
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    Wrong answer

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    0
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    0
  • August 27, 2020 at 6:14 am

    solutions are not correct plz correct them

    0
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    Need more previous questions based on all chapters

    0
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    0
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    1
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    1
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    1
  • May 22, 2020 at 9:44 am

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    1
  • May 16, 2020 at 7:15 pm

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    0
    • sai
      March 15, 2021 at 11:13 pm

      What is πŸ‘†there…….
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      1