As shown in the diagram..... | JEE Main 2026 21 Jan Shift 2

JEE MAIN 2026

21-01-2026 S2

Question

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.

Select the correct option:

60º

75º

90º

45º

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

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Physics

Medium

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Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\} \rightarrow\left\{1, e, e^2, e^3\right\}$ and $...

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\text { The area of the region }\left\{(x, y): 0 \leq y \leq 6-x, y^2 \geq 4 x-3, x \geq...

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QJEE MAIN_2026

The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32 \cos ^4 x}{1+e^{\sin x}}\right) d x$ is:

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QJEE MAIN 20262026

The area of the region $\left\{(x, y): 0 \leq y \leq 6-x, y^2 \geq 4 x-3, x \geq 0\right\}$ is:

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QJEE MAIN 20262026

Let $f:[1, \infty) \rightarrow \mathbf{R}$ be a differentiable function defined as $f(x)=\int_1^x f(\mathrm{t}) \mathrm{dt}+(1-x)\left(\log _0 x-1\right)+\mathrm{e}$. Then the value of...

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QJEE MAIN 20262026

The value of $\lim _{x \rightarrow 0}\left(\frac{x^2 \sin ^2 x}{x^2-\sin ^2 x}\right)$ is:

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QJEE MAIN_2026

Let a line L be perpendicular to both the lines $\mathrm{L}_1: \frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and $\mathrm{L}_2: \frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}$. If $\theta$ is the acute...

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QJEE MAIN 20262026

Let $\left(2^{1-a}+2^{1+a}\right), f(a),\left(3^a+3^{-a}\right)$ be in A.P. and $\alpha$ be the minimum value of $f(a)$. Then the value of the integral...

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QJEE MAIN_2026

$\mathrm{SF}_4$ is isostructural with: A. $\mathrm{BrF}_4{ }^{!}$ B. $\mathrm{CH}_4$ C. $\mathrm{IF}_4^{\oplus}$ D. $\mathrm{XeF}_4$ E. $\mathrm{XeO}_2 \mathrm{~F}_2$ Choose the correct answer...

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QJEE MAIN_2026

Let the image of the point $\mathrm{P}(1,6, a)$ in the line $\mathrm{L}: \frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}, b>0$, be $\left(\frac{a}{3}, 0, a+c\right)$. If $...

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QJEE MAIN 20262026

Let $f(x)=\lim _{y \rightarrow 0} \frac{(1-\cos (x y)) \tan (x y)}{y^3}$. Then the number of solutions of the equation $...

JEE MainMathematicsMedium

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QJEE MAIN 20262026

Let $S=\{\theta \in(-2 \pi, 2 \pi): \cos \theta+1=\sqrt{3} \sin \theta\}$. Then $\sum_{\theta \in S} \theta$ is equal to:

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QJEE MAIN 20262026

Let $O$ be the origin, $\overrightarrow{O P}=\vec{a}$ and $\overrightarrow{O Q}=\vec{b}$. If $R$ is the point on $\overrightarrow{O P}$ such that...

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QJEE MAIN_2026

The first and second ionization constants of a weak dibasic acid $\mathrm{H}_2 \mathrm{~A}$ are $8.1 \times 10^{-8}$ and $...

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\text { Let } 0<\alpha<1, \beta=\frac{1}{3 \alpha} \text { and } \tan ^{-1}(1-\alpha)+\tan ^{-1}(1-\beta)=\frac{\pi}{4} \text {. Then } 6(\alpha+\beta) \text { is equal to: }

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QJEE MAIN 20262026

If the distance of the point $(a, 2,5)$ from the image of the point $(1,2,7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is...

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