Q JEE MAIN 2022

$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$ is equal to :

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Q JEE-Main_2026

Let $\mathrm{S}=\{x \in[-\pi, \pi]: \sin x(\sin x+\cos x)=\mathrm{a}, \mathrm{a} \in Z\}$. Then $\mathrm{n}(\mathrm{S})$ is equal to :

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Q JEE-Main 2024

If $\sin \left(\frac{\pi}{18}\right) \sin \left(\frac{5 \pi}{18}\right) \sin \left(\frac{7 \pi}{18}\right)=K$, then the value of $\sin \left(\frac{10 K \pi}{3}\right)$ is

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Q JEE MAIN 2026

If $S=\left\{\theta \in[-\pi, \pi]: \cos \theta \cos \frac{5 \theta}{2}=\cos 7 \theta \cos \frac{7 \theta}{2}\right\}$, then $n(S)$ is equal to $\_\_\_\_$...

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Q JEE MAIN 2026

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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Q JEE MAIN 2026

The sum of all the integral values of $p$ such that the equation $...

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Q Jee Main 2026

If $\mathrm{A}=\frac{\sin 3^{\circ}}{\cos 9^{\circ}}+\frac{\sin 9^{\circ}}{\cos 27^{\circ}}+\frac{\sin 27^{\circ}}{\cos 81^{\circ}}$ and $\mathrm{B}=\tan 81^{\circ}-\tan 3^{\circ}$, then $\frac{\mathrm{B}}{\mathrm{A}}$ is equal to $\_\_\_\_$ .

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Q Jee Main 2026

Let $P=\left\{\theta \in[0,4 \pi]: \tan ^2 \theta \neq 1\right\}$ and $...

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Q JEE Main 2024

The number of solutions of $\sin ^2 x+\left(2+2 x-x^2\right) \sin x-3(x-1)^2=0$, where $-\pi \leq \mathrm{x} \leq \pi$, is $\_\_\_\_$ .

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Q JEE MAIN 2024

For $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$, let $3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)$ and a real number k be such that $...

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Q JEE Main 2026

The number of elements in the set $\left\{x \in\left[0,180^{\circ}\right]: \tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan x \tan \left(x-50^{\circ}\right)\right\}$ is $\_\_\_\_$ .

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Q JEE MAIN 2026

The least value of $\left(\cos ^2 \theta-6 \sin \theta \cos \theta+3 \sin ^2 \theta+2\right)$ is

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Q JEE MAIN 2026

Let $\frac{\pi}{2}

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Q JEE MAIN 2026

If $\cot x=\frac{5}{12}$ for some $x \in\left(\pi, \frac{3 \pi}{2}\right)$, then $...

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Q JEE MAIN 2026

The value of $\frac{\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ} \cos 40^{\circ} \cos 60^{\circ} \cos 80^{\circ}}$ is equal to

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Q JEE MAIN 2026

Let $\cos (\alpha+\beta)=-\frac{1}{10}$ and $\sin (\alpha-\beta)=\frac{3}{8}$, where $0

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Q JEE MAIN 2026

The value of $\operatorname{cosec} 10^{\circ}-\sqrt{3} \sec 10^{\circ}$ is equal to :

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Q JEE MAIN 2019

The value of $\cos ^2 10^{\circ}-\cos 10^{\circ} \cos 50^{\circ}+\cos ^2 50^{\circ}$ is:

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Q JEE MAIN 2019

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be...

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Q JEE MAIN 2020

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the...

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Q JEE MAIN 2019

If the angle of elevation of a cloud from a point P which is 25 m above a lake be...

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Q JEE MAIN 2020

The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing...

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Q JEE MAIN 2020

If $L=\sin ^2\left(\frac{\pi}{16}\right)-\sin ^2\left(\frac{\pi}{8}\right)$ and $M=\cos ^2\left(\frac{\pi}{16}\right)-\sin ^2\left(\frac{\pi}{8}\right)$, then

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Q JEE MAIN 2020

The angle of elevation of a cloud $C$ from a point $P, 200 \mathrm{~m}$ above a still lake is $30^{\circ}$....

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Q JEE MAIN 2020

Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with...

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Q JEE MAIN 2019

The value of sin10° sin30° sin50° sin70° is

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Q JEE MAIN 2019

Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their...

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Q JEE MAIN 2020

Let $\alpha$ and $\beta$ be two real roots of the equation $(\mathrm{k}+1) \tan ^2 \mathrm{x}-\sqrt{2} \cdot \lambda \tan \mathrm{x}=(1-\mathrm{k})$, where...

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Q JEE MAIN 2019

The value of $\cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \ldots \ldots \cos \frac{\pi}{2^{10}} \cdot \sin \frac{\pi}{2^{10}}$ is

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Q JEE MAIN 2021

cosec18º is a root of the equation :

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Q JEE MAIN 2021

Let $\frac{\sin A}{\sin B}=\frac{\sin (A-C)}{\sin (C-B)}$, where $A, B, C$ are angles of a triangle $A B C$. If the...

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Q JEE Main 2021

The sum of solutions of the equation $\frac{\cos x}{1+\sin x}=|\tan 2 x|, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4}-\frac{\pi}{4}\right\}$ is :

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Q JEE MAIN 2019

If $\cos (\alpha+\beta)=\frac{3}{5}, \sin (\alpha-\beta)=\frac{5}{13}$ and $0

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Q JEE MAIN 2021

A 10 inches long pencil $A B$ with mid point $C$ and a small eraser $P$ are placed on the...

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Q JEE MAIN 2019

If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0

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Q JEE MAIN 2021

The value of $...

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Q JEE Main 2019

For any $\theta \in\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$, the expression $3(\sin \theta-\cos \theta)^4+6(\sin \theta+\cos \theta)^2+4 \sin ^6 \theta$ equals :

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Q JEE MAIN 2021 S2

Let $\alpha=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$ and $...

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Q JEE MAIN 2021 S2

If $\tan \left(\frac{\pi}{9}\right), x, \tan \left(\frac{7 \pi}{18}\right)$ are in arithmetic progression and $\tan \left(\frac{\pi}{9}\right), y, \tan \left(\frac{5 \pi}{18}\right)$ are also...

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Q JEE MAIN 2019

Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters)...

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Q JEE MAIN 2021

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Q JEE MAIN 2021

The number of integral values of ' k ' for which the equation $3 \sin x+4 \cos x=k+1$ has a...

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Q JEE-Main 2023

The value of $36\left(4 \cos ^2 9^{\circ}-1\right)\left(4 \cos ^2 27^{\circ}-1\right)\left(4 \cos ^2 81^{\circ}-1\right)\left(4 \cos ^2 243^{\circ}-1\right)$ is

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Q JEE MAIN 2023

The value of tan 9° – tan 27° – tan 63° + tan 81° is _________.

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Q JEE MAIN 2025

The number of solutions of the equation $(4-\sqrt{3}) \sin x-2 \sqrt{3} \cos ^2 x=-\frac{4}{1+\sqrt{3}}, x \in\left[-2 \pi, \frac{5 \pi}{2}\right]$ is

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Q JEE MAIN 2023

If the line $x=y=z$ intersects the line $...

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Q JEE MAIN 2023

$96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$ is equal to

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Q JEE-Main 2024

If $\tan \mathrm{A}=\frac{1}{\sqrt{x\left(x^2+x+1\right)}}, \tan B=\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$ and $\tan C=\left(x^{-3}+x^{-2}+x^{-1}\right)^{\frac{1}{2}}, 0

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Q JEE MAIN 2025

If $\sin x+\sin ^{2} x=1, x \in\left(0, \frac{\pi}{2}\right)$, then $...

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Q JEE MAIN 2025

Let the range of the function $...

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Q JEE MAIN 2025

The value of $\left( {\sin {{{70}}^{{}^\circ }}} \right)\left( {\cot {{{10}}^{{}^\circ }}\cot {{{70}}^{{}^\circ }}-1} \right)$ is

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Q JEE MAIN 2025

The sum of all values of $\theta \in[0,2 \pi]$ satisfying $2 \sin ^2 \theta=\cos 2 \theta$ and $...

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