Q JEE MAIN_2026

Number of solutions of $\sqrt{3} \cos 2 \theta+8 \cos \theta+3 \sqrt{3}=0, \theta \in[-3 \pi, 2 \pi]$ is :

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Q JEE MAIN_2026

If $\frac{\cos ^2 48^{\circ}-\sin ^2 12^{\circ}}{\sin ^2 24^{\circ}-\sin ^2 6^{\circ}}=\frac{\alpha+\beta \sqrt{5}}{2}$, where $\alpha, \beta \in \mathbb{N}$, then $\alpha+\beta$ is equal...

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Q JEE MAIN 2026

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at...

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Q JEE MAIN_2019_

ABC is a triangular park with $\mathrm{AB}=\mathrm{AC}=100$ metres. A vertical tower is situated at the mid-point of $B C$. If...

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Q JEE MAIN 2020

If the equation $\cos ^4 \theta+\sin ^4 \theta+\lambda=0$ has real solutions for $\theta$, then $\lambda$ lies in the interval

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Q JEE MAIN 2019

Let S be the set of all α ∈ R such that the equation, cos2x + αsinx = 2α –...

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Q JEE MAIN 2020

The value of $\cos ^3\left(\frac{\pi}{8}\right) \cdot \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \cdot \sin \left(\frac{3 \pi}{8}\right)$ is

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Q JEE MAIN 2019

Let $f_x(x)=\frac{1}{k}\left(\sin ^k x+\cos ^k x\right)$ for $k=1,2,3, \ldots$. Then for all $x \in R$, the value of $f_4(x)-f_6(x)$ is...

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Q JEE Main 2019

The shortest distance between the point $\left(\frac{3}{2}, 0\right)$ and the curve $y=\sqrt{x},(x>0)$ is

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Q JEE MAIN 2019

If $0 \leq x

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Q JEE MAIN 2021

A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on...

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Q JEE Main 2021

The number of solutions of the equation $32^{\tan ^2 x}+32^{x c^2 x}=81,0 \leq x \leq \frac{\pi}{4}$ is :

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Q JEE MAIN 2021

If $n$ is the number of solutions of the equation $2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]$...

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Q JEE MAIN 2021

If $\sin \theta+\cos \theta=\frac{1}{2}$, then $16(\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta))$ is equal to :

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Q JEE MAIN 2021

The value of $\cot \frac{\pi}{24}$ is :

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Q JEE MAIN 2021

If $15 \sin ^4 \alpha+10 \cos ^4 \alpha=6$, for some $\alpha \in \mathrm{R}$, then then value of $...

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Q JEE MAIN_2021_

The sum of possible values of $x$ for $\tan ^{-1}(x+1)+\cot ^{-1}\left(\frac{1}{x-1}\right)=\tan ^{-1}\left(\frac{8}{31}\right)$ is :

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Q _JEE MAIN_2021_

If $\cot ^{-1}(\alpha)=\cot ^{-1} 2+\cot ^{-1} 8+\cot ^{-1} 18+\cot ^{-1} 32+$ sum Upto 100 terms, then $\alpha$ is is

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Q JEE MAIN 2021

The number of solutions of the equation $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2 \pi]$ is

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Q JEE MAIN 2021

If $\sqrt{3}\left(\cos ^2 x\right)=(\sqrt{3}-1) \cos x+1$, the number of solutions of the given equation when $\mathrm{x} \in\left[0, \frac{\pi}{2}\right]$ is

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Q JEE MAIN 2021

All possible values of $\theta \in[0,2 \pi]$ for which $\sin 2 \theta+\tan 2 \theta>0$ lie in :

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Q JEE MAIN_2022

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

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Q JEE MAIN_2022

Let $S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^2 \theta}+8^{20 \cos ^2 \theta}=16\right\}$. Then $n(S)+\sum_{\theta \in S}\left(\sec \left(\frac{\pi}{4}+2 \theta\right) \operatorname{cosec}\left(\frac{\pi}{4}+2 \theta\right)\right)$ is...

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Q JEE MAIN 2022

A tower $P Q$ stands on a horizontal ground with base $Q$ on the ground. The point $R$ divides the...

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Q JEE MAIN 2022

The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is in

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Q Memory Based Question 2026

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

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Q JEE MAIN 2022

$\alpha=\sin 36^{\circ}$ is a root of which of the following equation

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Q JEE MAIN 2022

The number of solutions of the equation $\sin x=\cos ^2 x$ in the interval $(0,10)$ is $\_\_\_\_$ .

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Q JEE MAIN 2022

If $\cot \alpha=1$ and $\sec \beta=-\frac{5}{3}$, where $\pi

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Q JEE MAIN 2022

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower...

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Q JEE MAIN 2022

$16 \sin \left(20^{\circ}\right) \sin \left(40^{\circ}\right) \sin \left(80^{\circ}\right)$ is equal to :

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

The number of solutions of the equation $2 \theta-\cos ^2 \theta+\sqrt{2}=0$ is $R$ is equal to $\_\_\_\_$ .

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Q JEE MAIN 2022

The number of elements in the set $...

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Q JEE MAIN 2022

The value of $2 \sin \left(12^{\circ}\right)-\sin \left(72^{\circ}\right)$ is :

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Q JEE MAIN 2022

Let $A B$ and $P Q$ be two vertical poles, 160 m apart from each other. Let $C$ be the...

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Q JEE MAIN 2022

The value of $\cos \left(\frac{2 \pi}{7}\right)+\cos \left(\frac{4 \pi}{7}\right)+\cos \left(\frac{6 \pi}{7}\right)$ is equal to:

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Q JEE MAIN 2022

If $\sin ^2\left(10^{\circ}\right) \sin \left(20^{\circ}\right) \sin \left(40^{\circ}\right) \sin \left(50^{\circ}\right) \sin \left(70^{\circ}\right)=\alpha-\frac{1}{16} \sin \left(10^{\circ}\right)$, then $16+\alpha^{-1}$ is equal to $\_\_\_\_$

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Q JEE MAIN 2022

The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $...

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Q JEE MAIN 2022

Let $\mathrm{S}\left\{\theta \in[-\pi, \pi]-\left\{ \pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\}$ If $T=\sum_{\theta \in S} \cos 2 \theta$,...

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Q JEE MAIN 2025

If $\theta \in\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]$, then the number of solutions of $\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0$, is equal tori

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Q JEE-Main 2023

From the top A of a vertical wall AB of height 30 m, the angles of depression of the top...

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Q JEE MAIN 2023

The number of elements in the set $S=\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$...

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Q JEE-Main 2023

From the top A of a vertical wall AB of height 30 m, the angles of depression of the top...

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Q JEE MAIN 2024

If $\sin x = - \frac{3}{5}$, where $\pi < x < \frac{{3\pi }}{2}$, then $...

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Q JEE-Main 2024

Let P be the point (10,-2,-1) and Q be the foot of the perpendicular drawn from the point R(1,7,6) on...

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Q JEE MAIN

Let $|\cos \theta \cos (60-\theta) \cos (60-\theta)| \leq \frac{1}{8}, \theta \in[0,2 \pi]$ Then, the sum of all $\theta \in[0,2 \pi]$,...

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Q JEE MAIN 2024

Suppose θ∈[0,π/4] is a solution of 4cos⁡θ-3sin⁡θ=1. Then cos⁡θ is equal to :

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Q JEE MAIN 2024

If $2 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=0$ has exactly 3 solutions in the interval $...

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Q JEE MAIN

If $\alpha,-\frac{\pi}{2}

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Q JEE MAIN 2024

Let the set of all $a \in R$ such that the equation $\cos 2 x+a \sin x=2 a-7$ has a...

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Q

The interior angles of a polygon with $n$ sides, are in an A.P. with common difference $6^{\circ}$. If the largest...

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Q JEE MAIN 2025

If $\sum_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a, b \in Z$, then $a^{2}+b^{2}$ is equal to :

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Q JEE MAIN 2025

If for $\theta \in \left[ { - \frac{\pi }{3},0} \right]$, the points $...

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Q JEE MAIN 2025

If $10{\sin ^4}\theta + 15{\cos ^4}\theta = 6$, then the value of $...

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Q JEE MAIN 2025

The number of solutions of the equation $...

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Q JEE MAIN 2025

If $\theta \in [ - 2\pi ,2\pi ]$, then the number of solutions of $...

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