List of top Questions asked in JEE Main- 2023

In the circuit shown, the energy stored in the capacitor is $ n \, \mu \text{J} $. The value of $ n $ is:

The equations of the sides $AB , BC$ and $CA$ of a triangle $ABC$ are : $2 x+y=0, x+p y=21 a,(a \neq 0)$ and $x-y=3$ respectively Let $P (2, a )$ be the centroid of $\triangle ABC$ Then $( BC )^2$ is equal to

Arrange the following orbitals in decreasing order of energy
A. $n=3, l =0, m =0$
B. $n =4, l =0, m =0$
C. $n =3, l =1, m =0$
D. $n =3, l =2, m =1$
The correct option for the order is :

Evaluate the following statements for their correctness
A. The elevation in boiling point temperature of water will be same for $01 \,M \,NaCl$ and $01\, M$ urea
B. Azeotropic mixtures boil without change in their composition
C. Osmosis always takes place from hypertonic to hypotonic solution
D. The density of $32 \% H _2 SO _4$ solution having molarity $409\, M$ is approximately $126\, g mL ^{-1}$
E. A negatively charged sol is obtained when KI solution is added to silver nitrate solution
Choose the correct answer from the options given below :

Let $f$ be $a$ differentiable function defined on $\left[0, \frac{\pi}{2}\right]$ such that $f(x)>0;$ and $f(x)+\int\limits_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]$ Then $\left(6 \log _e f\left(\frac{\pi}{6}\right)\right)^2$ is equal to _______

When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of $A$?

If $\frac{1^3+2^3+3^3+\ldots \text { up to } n \text { terms }}{1 \cdot 3+2 \cdot 5+3 \cdot 7+\ldots \text { up to } n \text { terms }}=\frac{9}{5}$, then the value of $n$ is

Given below are two statements :
Statement I : Upon heating a borax bead dipped in cupric sulphate in a luminous flame, the colour of the bead becomes green.
Statement II : The green colour observerd is due to the formation of copper(I) metaborate.
In the light of the above statements, choose the most appropriate answer from the options given below :

If the area of the region bounded by the curves $y ^2-2 y=-x, x+y=0$ is $A$, then $8 A$ is equal to _________

Three urns $A, B$ and $C$ contain $4$ red, $6$ black; $5$ red, $5$ black; and $\lambda$ red, $4$ black balls respectively One of the urns is selected at random and a ball is drawn If the ball drawn is red and the probability that it is drawn from urn $C$ is $0.4$ then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola $y^2 = \lambda x$ with one vertex at the vertex of the parabola, is

The value of the integral:$\int\limits_{\frac{3 \sqrt{2}}{4}}^{\frac{3 \sqrt{3}}{4}} \frac{48}{\sqrt{9-4 x^2}} d x$ is equal to

Which of the following compounds are not used as disinfectants?
A. Chloroxylenol
B. Bithional
C. Veronal
D. Prontosil
E. Terpineol
Choose the correct answer from the options given below:

The number of square matrices of order 5 with entries from the set $\{0,1\}$, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1 , is

Let $p$ and $q$ be two statements Then $\sim(p \wedge(p \Rightarrow \sim q))$ is equivalent to

In Dumas method for the estimation of $N _2$, the sample is heated with copper oxide and the gas evolved is passed over :

The locus of the mid points of the chords of the circle $C_1:(x-4)^2+(y-5)^2=4$ which subtend an angle $\theta_i$ at the centre of the circle $C_1$, is a circle of radius $r_i$ If $\theta_1=\frac{\pi}{3}, \theta_3=\frac{2 \pi}{3}$ and $r_1^2=r_2^2+r_3^2$, then $\theta_2$ is equal to

Let $\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}$ and $\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}$ Let $\vec{\beta}_1$ be parallel to $\vec{\alpha}$ and $\vec{\beta}_2$ be perpendicular to $\vec{\alpha}$ If $\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2$, then the value of $5 \vec{\beta}_2 \cdot(\hat{i}+\hat{j}+\hat{k})$ is

Let the plane containing the line of intersection of the planes $P 1: x+(\lambda+4) y+z=1$ and $P 2: 2 x+$ $y+z=2$ pass through the points $(0,1,0)$ and $(1,0,1)$ Then the distance of the point $(2 \lambda, \lambda,-\lambda)$ from the plane $P 2$ is

Two light waves of wavelengths 800 and $600 nm$ are used in Young's double slit experiment to obtain interference fringes on a screen placed $7 m$ away from plane of slits If the two slits are separated by $0.35 mm$, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ___$mm$

If the system of equations $ x+2 y+3 z=3$ $ 4 x+3 y-4 z=4 $ $ 8 x+4 y-\lambda z=9+\mu$ has infinitely many solutions, then the ordered pair $(\lambda, \mu)$ is equal to :

For the given circuit, in the steady state, $\left| V _{ B ^{-}}- V _{ D }\right|=$___$V$

Two parallel plate capacitors $C_1$ and $C_2$ each having capacitance of $10 \mu F$ are individually charged by a $100 V D C$ source Capacitor $C_1$ is kept connected to the source and a dielectric slab is inserted between it plates Capacitor $C_2$ is disconnected from the source and then a dielectric slab is inserted in it Afterwards the capacitor $C_1$ is also disconnected from the source and the two capacitors are finally connected in parallel combination The common potential of the combination will be ___$V$
(Assuming Dielectric constant $=10$ )

If a wire of resistance R is connected across Vo, then power is Po. The wire is cut into two equal parts and connected with Vo individually, then the sum of power dissipated is P1, then $\frac{Po}{Pi}$ is $\frac{1}{x}$. Find the value of x.

A particle is performing $SHM$ having position $x$ = $A\; cos\; 30°$, and $A\; = 40 \;cm$. If its kinetic energy at this position is $200 \;J$, the value of force constant in $(kN/m)$ is?

If the binding energy of ground state electron in a hydrogen atom is $136 eV$, then, the energy required to remove the electron from the second excited state of $Li ^{2+}$ will be : $x \times 10^{-1} eV$. The value of $x$ is