JEE Maths PYQ Practice, chapter-wise

JEE Main 2025 (Online) 2nd April Morning ShiftQuestion 46

Let $A$ be the set of all functions $f:\mathbf{Z}\to\mathbf{Z}$ and $R$ be a relation on $A$ such that $R=\{(f,g):f(0)=g(1)\text{ and }f(1)=g(0)\}$. Then $R$ is :

Sets, Relations and Function

Reflexive but neither symmetric nor transitiveSymmetric but neither reflexive nor transitiveTransitive but neither reflexive nor symmetricSymmetric and transitive but not reflexive

JEE Main 2021 (Online) 26th August Morning ShiftQuestion 47

Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments, then $K$ can not belong to the set :

Sets, Relations and Function

$\{84,86,88,90\}$$\{80,83,86,89\}$$\{79,81,83,85\}$$\{84,87,90,93\}$

JEE Main 2024 (Online) 8th April Evening ShiftQuestion 48

Let $A=\{2,3,6,8,9,11\}$ and $B=\{1,4,5,10,15\}$. Let $R$ be a relation on $A\times B$ defined by $(a,b)R(c,d)$ if and only if $3ad-7bc$ is an even integer. Then the relation $R$ is

Sets, Relations and Function

an equivalence relation.reflexive but not symmetric.transitive but not symmetric.reflexive and symmetric but not transitive.

JEE Main 2024 (Online) 27th January Morning ShiftQuestion 49

Let $S=\{1,2,3,\ldots,10\}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $R=\{(A,B):A\cap B\neq\phi;\ A,B\in M\}$ is :

Sets, Relations and Function

symmetric and transitive onlysymmetric and reflexive onlysymmetric onlyreflexive only

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 50

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)$

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