JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 25th February Evening ShiftQuestion 56

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}$

JEE Main 2021 (Online) 17th March Evening ShiftQuestion 57

The number of solutions of the equation $x+2\tan x=\frac{\pi}{2}$ in the interval $[0,2\pi]$ is :

Trigonometric Ratio & Identities

$2$$3$$4$$5$

JEE Main 2020 (Online) 4th September Evening ShiftQuestion 58

Let $\bigcup_{i=1}^{50}X_i=\bigcup_{i=1}^{n}Y_i=T$, where each $X_i$ contains $10$ elements and each $Y_i$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_i$'s and exactly $6$ of sets $Y_i$'s, then $n$ is equal to :

Sets, Relations and Function

$15$$30$$45$$50$

JEE Main 2020 (Online) 4th September Morning ShiftQuestion 59

Let $[t]$ denote the greatest integer $\le t$. Then the equation in $x$, $[x]^2+2[x+2]-7=0$ has :

Sets, Relations and Function

no integral solution.exactly two solutions.exactly four integral solutions.infinitely many solutions.

JEE Main 2020 (Online) 3rd September Morning ShiftQuestion 60

Consider the two sets : $A=\{m\in\mathbf{R}$ : both the roots of $x^2-(m+1)x+m+4=0$ are real$\}$ and $B=[-3,5)$. Which of the following is not true ?

Sets, Relations and Function

$A\cup B=\mathbf{R}$$A\cap B=\{-3\}$$A-B=(-\infty,-3)\cup(5,\infty)$$B-A=(-3,5)$

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