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JEE MAIN 2023
02-04-2023-S2
Question
If $\int_{\frac{1}{3}}^3\left|\log _e x\right| d x=\frac{m}{n} \log _e\left(\frac{n^2}{e}\right)$, where $m$ and $n$ are coprime natural numbers, then $m^2+n^2-5$ is equal to
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Showing 18 questions
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If $\int_{\frac{1}{3}}^3\left|\log _e x\right| d x=\frac{m}{n} \log _e\left(\frac{n^2}{e}\right)$, where $m$ and $n$ are coprime natural numbers, then $m^2+n^2-5$ is equal...
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Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white...
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Let $a \in R$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{1 / 4} x+a=0$. If $\alpha^4+\beta^4=-30$,...
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Points $\mathrm{P}(-3,2), \mathrm{Q}(9,10)$ and $\mathrm{R}(\alpha, 4)$ lie on a circle C with PR as its diameter. The tangents to C...
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For the two positive numbers $a, b$, if $a, b$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{a}, 10$...
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QJEE MAIN 20232023
The foot of perpendicular of the point $(2,0,5)$ on the line $\frac{x+1}{2}=\frac{y-1}{5}=\frac{z+1}{-1}$ is $(\alpha, \beta, \gamma)$. Then. Which of the...
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Let $\vec{a}=-\hat{i}-\hat{j}+\hat{k}, \vec{a} \cdot \vec{b}=1$ and $\vec{a} \times \vec{b}=\hat{i}-\hat{j}$. Then $\vec{a}-6 \vec{b}$ is equal to
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