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]

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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
  • December 29, 2020 at 8:23 pm

    Y only few questions want more number of questions

    22
  • December 1, 2020 at 1:51 pm

    Wrong answer in 3

    5
    • April 24, 2021 at 7:49 pm

      Why

      0
  • November 27, 2020 at 8:11 pm

    Please upload more questions

    8
  • November 24, 2020 at 11:34 am

    Not giving sol correct that problem rather than that no problem good

    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

    1
  • September 29, 2020 at 6:04 pm

    Maja aa gaya

    0
  • September 14, 2020 at 10:52 am

    What is this..?😢😢……only a few questions are present here…it would be better for students if some more highly skilled questions are present here…

    1
  • September 10, 2020 at 5:28 pm

    Only few questions are there

    1
  • September 4, 2020 at 8:41 pm

    Wrong answer

    Right answer is 1 option

    0
  • September 2, 2020 at 9:06 am

    Not satisfied

    0
  • August 28, 2020 at 4:56 pm

    Super πŸ‘ŒπŸ‘Œ good job πŸ™πŸ™πŸ™

    0
  • August 27, 2020 at 8:20 pm

    Not satisfied..with these qns ..want more to perfect

    0
  • August 27, 2020 at 6:14 am

    solutions are not correct plz correct them

    0
  • August 23, 2020 at 10:54 am

    Need more previous questions based on all chapters

    0
  • August 20, 2020 at 6:03 pm

    Nise

    0
  • August 12, 2020 at 9:05 pm

    We want more questions

    0
  • July 16, 2020 at 9:36 pm

    it will benefit if some more questions are there

    0
  • July 16, 2020 at 9:35 pm

    it will benefit if some more questions are there

    0
  • July 10, 2020 at 8:03 pm

    It’s really helpful I like it

    0
  • July 4, 2020 at 1:20 pm

    Very poor solutions

    0
  • May 23, 2020 at 10:30 pm

    your site is very useful thanks

    0
  • May 22, 2020 at 9:44 am

    Only three questions ,thank you so much

    0
  • May 16, 2020 at 7:15 pm

    Only 3 questions.more questions ,more benefit.

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

      What is πŸ‘†there…….
      few questions (about 3)……set is the important topic in JEE mains,,,,,but you showed only 2 qstπŸ€·β€β™€…1st thng ,,,2 qst i cnt read ……plzzz update it

      0