JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 1

All possible values of $\theta\in[0,2\pi]$ for which $\sin2\theta+\tan2\theta>0$ lie in :

Trigonometric Ratio & Identities

$\left(0,\frac{\pi}{2}\right)\cup\left(\pi,\frac{3\pi}{2}\right)$$\left(0,\frac{\pi}{4}\right)\cup\left(\frac{\pi}{2},\frac{3\pi}{4}\right)\cup\left(\frac{3\pi}{2},\frac{11\pi}{6}\right)$$\left(0,\frac{\pi}{2}\right)\cup\left(\frac{\pi}{2},\frac{3\pi}{4}\right)\cup\left(\pi,\frac{7\pi}{6}\right)$$\left(0,\frac{\pi}{4}\right)\cup\left(\frac{\pi}{2},\frac{3\pi}{4}\right)\cup\left(\pi,\frac{5\pi}{4}\right)\cup\left(\frac{3\pi}{2},\frac{7\pi}{4}\right)$

JEE Main 2021 (Online) 24th February Morning ShiftQuestion 2

If $e^{\left(\cos^{2}x+\cos^{4}x+\cos^{6}x+\ldots\infty\right)\log_e2}$ satisfies the equation $t^{2}-9t+8=0$, then the value of $\frac{2\sin x}{\sin x+\sqrt{3}\cos x}\left(0<x<\frac{\pi}{2}\right)$ is :

Trigonometric Ratio & Identities

$\frac{1}{2}$$\sqrt{3}$$\frac{3}{2}$$2\sqrt{3}$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 3

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point $A$, with uniform speed. At that point, angle of depression of the boat with the man's eye is $30^{\circ}$ (Ignore man's height). After sailing for $20$ seconds, towards the base of the tower (which is at the level of water), the boat has reached a point $B$, where the angle of depression is $45^{\circ}$. Then the time taken (in seconds) by the boat from $B$ to reach the base of tower is :

Trigonometric Ratio & Identities

$10$$10(\sqrt{3}+1)$$10\sqrt{3}$$10(\sqrt{3}-1)$

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 4

The number of solutions of $\sin^{7}x+\cos^{7}x=1$, $x\in[0,4\pi]$ is equal to :

Trigonometric Ratio & Identities

$5$$7$$9$$11$

JEE Main 2021 (Online) 25th February Evening ShiftQuestion 5

If $0<x,y<\pi$ and $\cos x+\cos y-\cos(x+y)=\frac{3}{2}$, then $\sin x+\cos y$ is equal to :

Trigonometric Ratio & Identities

$\frac{1}{2}$$\frac{\sqrt{3}}{2}$$\frac{1-\sqrt{3}}{2}$$\frac{1+\sqrt{3}}{2}$