JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 27th August Evening ShiftQuestion 21

Let $\mathbb{Z}$ be the set of all integers, $A=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}:(x-2)^{2}+y^{2}\le4\}$, $B=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}:x^{2}+y^{2}\le4\}$ and $C=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}:(x-2)^{2}+(y-2)^{2}\le4\}$. If the total number of relations from $A\cap B$ to $A\cap C$ is $2^{p}$, then the value of $p$ is :

Sets, Relations and Function

$9$$16$$25$$49$

JEE Main 2021 (Online) 31st August Morning ShiftQuestion 22

Which of the following is not correct for relation $R$ on the set of real numbers ?

Sets, Relations and Function

$(x,y)\in R\Leftrightarrow|x-y|\le1$ is reflexive and symmetric.$(x,y)\in R\Leftrightarrow|x|-|y|\le1$ is reflexive but not symmetric.$(x,y)\in R\Leftrightarrow0<|x|-|y|\le1$ is neither transitive nor symmetric.$(x,y)\in R\Leftrightarrow0<|x-y|\le1$ is symmetric and transitive.

JEE Main 2021 (Online) 16th March Evening ShiftQuestion 23

Let $A=\{2,3,4,5,\ldots,30\}$ and '$\simeq$' be an equivalence relation on $A\times A$, defined by $(a,b)\simeq(c,d)$, if and only if $ad=bc$. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to :

Sets, Relations and Function

$5$$6$$7$$8$

JEE Main 2023 (Online) 11th April Morning ShiftQuestion 24

An organization awarded $48$ medals in event 'A', $25$ in event 'B' and $18$ in event 'C'. If these medals went to total $60$ men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

Sets, Relations and Function

$15$$9$$10$$21$

JEE Main 2021 (Online) 26th February Morning ShiftQuestion 25

Let $R=\{(P,Q)\mid P$ and $Q$ are at the same distance from the origin$\}$ be a relation, then the equivalence class of $(1,-1)$ is the set :

Sets, Relations and Function

$S=\{(x,y)\mid x^{2}+y^{2}=4\}$$S=\{(x,y)\mid x^{2}+y^{2}=2\}$$S=\{(x,y)\mid x^{2}+y^{2}=1\}$$S=\{(x,y)\mid x^{2}+y^{2}=\sqrt{2}\}$

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