Sets - JEE Main Previous Year Question with Solutions

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 Download eSaral app for free study material and video tutorials. [esquestion] 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 #tag# [AIEEE- 2009] #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 $6 .$ [/esquestion] [esquestion] 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) $\mathrm{B} \subset \mathrm{A}$ #tag# [JEE-MAINS-2018] #sol# (1) [/esquestion] [esquestion] 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. #tag# [JEE-MAINS-2018] #sol# (2) [/esquestion]

This is one chapter within the larger Maths syllabus, so students can continue with the JEE Mains PYQ chapter wise collection.

To revise Sets alongside every other chapter in one sitting, switch to our JEE Main last year question paper, which has complete, session-wise papers.