Question

If for $x\in \left(0,\frac{\pi }{2}\right),{\log }_{10}\sin x+{\log }_{10}\cos x=-1$ and ${\log }_{10}\left(\sin x+\cos x\right)=\frac{1}{2}\left({\log }_{10}n-1\right),n>0$, then the value of $n$ is equal to : 

JEE Main 2021 (16 Mar Shift 1)

Options

• A: $20$
• B: $12$
• C: $9$
• D: $16$

Question

If $A=\{x\in R:|x-2|>1\},B=\left\{x\in R:\sqrt{x^2-3}>1\right\},C=\{x\in R:|x-4|⩾2\}$ and $Z$ is the set of all integers, then the number of subsets of the set $(A\cap B\cap C{)}^c\cap Z$ is _________.

JEE Main 2021 (27 Aug Shift 1)

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Question

Let $S=\left\{x\in \left[-6,3\right]-\left\{-2,2\right\}:\frac{\left|x+3\right|-1}{\left|x\right|-2}\ge 0\right\}$ and $T=\left\{x\in Z:x^2-7\left|x\right|+9\le 0\right\}$. Then the number of elements in $S\cap T$ is

JEE Main 2022 (28 Jul Shift 2)

Options

• A: $7$
• B: $5$
• C: $4$
• D: $3$