List of top Questions asked in JEE Main- 2023

A plane $E$ is perpendicular to the two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, and passes through the point $P (1,-1,1)$ If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3 \sqrt{2}$, then $( PQ )^2$ is equal to

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

What is the correct order of acidity of the protons marked A-D in the given compounds?

Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :

Solid fuel used in rocket is a mixture of Fe₂O₃ and Al (in ratio 1 : 2) the heat evolved (KJ) per gram of the mixture is ______ (Nearest integer)
Given $\Delta H_f^{\circ}(Al_2O_3) = -1700 \, \text{KJ mol}^{-1}$
$\Delta H_f^{\circ}(Fe_2O_3) = -840 \, \text{KJ mol}^{-1}$ }

The set of all values of $a$ for which $\displaystyle\lim _{x \rightarrow a}([x-5]-[2 x+2])=0$,where $[\propto]$ denotes the greatest integer less than or equal to $\propto$ is equal to

The number of functions $f:\{1,2,3,4\} \rightarrow\{ a \in: Z|a| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f( n +1)=1, \forall n \in\{1,2,3\}$ is

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): The first ionization enthalpy of $3d$ series elements is more than that of group 2 metals
Reason (R): In $3d$ series of elements successive filling of d-orbitals takes place
In the light of the above statements, choose the correct answer from the options given below :

Match List I with List II

LIST I		LIST II
A	Gauss's Law in Electrostatics	I	$\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}$
B	Faraday's Law	II	$\oint \vec{B} \cdot d \vec{A}=0$
C	Gauss's Law in Magnetism	III	$\oint \vec{B} \cdot d \vec{l}=\mu_0 i_c+\mu_0 \in_0 \frac{d \phi_E}{d t}$
D	Ampere-Maxwell Law	IV	$\oint \vec{E} \cdot d \vec{s}=\frac{q}{\epsilon_0}$

Choose the correct answer from the options given below:

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

If the mean deviation about median for the number $3,5,7,2 k , 12,16,21,24$ arranged in the ascending order, is 6 then the median is

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an AP If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is______

A particle moves in a circular path with uniform speed v. When it turns by 90°, find ratio of $\frac{v}{<\overrightarrow{v}>}$?

Let $ R = \{a, b, c, d, e\} $ and $ S = \{1, 2, 3, 4\} $. Total number of onto functions $ f: R \to S $ such that $ f(a) \neq 1 $, is equal to:

$0.3\, g$ of ethane undergoes combustion at $27^{\circ} C$ in a bomb calorimeter The temperature of calorimeter system (including the water) is found to rise by $05^{\circ} C$ The heat evolved during combustion of ethane at constant pressure is ___$kJ \, mol ^{-1}$ (Nearest integer) [Given : The heat capacity of the calorimeter system is $20 \, kJ\, K ^{-1}, R =83 \, JK ^{-1}\, mol ^{-1}$ Assume ideal gas behaviour Atomic mass of $C$ and $H$ are 12 and $1\, g\, mol ^{-1}$ respectively]

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature $T3 > T2 > T1$ as :

$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Let $f: R -\{2,6\} \rightarrow R$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$ Then range of $f$ is

The sum $\displaystyle\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7.5×10⁻⁴Ncm⁻¹. The radius of drop in cm will be : ( Take : g=10 m/s²)

The rms value of conduction current in a parallel plate capacitor is $69\, \mu A$ The capacity of this capacitor, if it is connected to $230 \, V$ ac supply with an angular frequency of $600\, rad / s$, will be :

The number of bijective functions $f :\{1,3,5$, $7, \ldots \ldots 99\} \rightarrow\{2,4,6,8, \ldots \ldots , 100\}$, such that $f (3) \geq f (9) \geq f (15) \geq f (21) \geq \ldots f (99), $ is _____

Number of molecules and moles in 2.8375 litre of O₂ at STP.