Let $P(S)$ denote the power set of $S=\{1,2,3,\ldots,10\}$. Define the relations $R_{1}$ and $R_{2}$ on $P(S)$ as $A\,R_{1}\,B \iff (A\cap B^{c})\cup(B\cap A^{c})=\varnothing$ and $A\,R_{2}\,B \iff A\cup B^{c}=B\cup A^{c}$, for all $A,B\in P(S)$. Then:

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Let $9=x_{1} < x_{2} < \ldots < x_{7}$ be in an A.P. with common difference d. If the standard deviation of $x_{1}, x_{…

Topic: JEE Main 2023 (1 February Evening Shift)

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The sum of the absolute maximum and minimum values of the function $f(x)=\lvert x^{2}-5x+6\rvert-3x+2$ in the interval …

Topic: JEE Main 2023 (1 February Evening Shift)

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Let $\vec a=5\hat{\imath}-\hat{\jmath}-3\hat{k}$ and $\vec b=\hat{\imath}+3\hat{\jmath}+5\hat{k}$ be two vectors. Then …

Topic: JEE Main 2023 (1 February Evening Shift)

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For the system of linear equations $\alpha x+y+z=1,\quad x+\alpha y+z=1,\quad x+y+\alpha z=\beta$, which one of the fol…

Topic: JEE Main 2023 (1 February Evening Shift)

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The value of the integral $\displaystyle \int_{-\pi/4}^{\pi/4}\frac{x+\pi/4}{\,2-\cos 2x\,}\,dx$ is:

Topic: JEE Main 2023 (1 February Evening Shift)

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If $y(x)=x^{x},\ x>0$, then $y''(2)-2y'(2)$ is equal to:

Topic: JEE Main 2023 (1 February Evening Shift)

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The area of the region given by $\{(x,y):\, xy\le 8,\ 1\le y\le x^{2}\}$ is:

Topic: JEE Main 2023 (1 February Evening Shift)

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The number of integral values of $k$ for which one root of the equation $2x^{2}-8x+k=0$ lies in the interval $(1,2)$ an…

Topic: JEE Main 2023 (1 February Evening Shift)

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Let $a,b$ be two real numbers such that $ab

Topic: JEE Main 2023 (1 February Evening Shift)

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If $A=\dfrac12\begin{bmatrix}1 & \sqrt{3}\\ -\sqrt{3} & 1\end{bmatrix}$, then:

Topic: JEE Main 2023 (1 February Evening Shift)

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Two dice are thrown independently. Let \(A\) be the event that the number on the \(1^{\text{st}}\) die is less than t…

Topic: JEE Main 2023 (1 February Evening Shift)