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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

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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]**
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]**
Y only few questions want more number of questions

Wrong answer in 3

Please upload more questions

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

Not so hard question

Pls help me with the 2nd question

Maja aa gaya

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

Only few questions are there

Wrong answer

Right answer is 1 option

Not satisfied

Super ππ good job πππ

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

solutions are not correct plz correct them

Need more previous questions based on all chapters

Nise

We want more questions

it will benefit if some more questions are there

it will benefit if some more questions are there

It’s really helpful I like it

Very poor solutions

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Only three questions ,thank you so much

Only 3 questions.more questions ,more benefit.