JEE Main 2025 (Online) 4th April Morning Shift

An alternating current is represented by the equation,
$i=100 \sqrt{2} \sin (100 \pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are

Considering the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{\text {th }}$ orbit of the electron in $\mathrm{Li}^{2+}$ and $\mathrm{He}^{+}$is

Four capacitors each of capacitance $16 \mu F$ are connected as shown in the figure. The capacitance between points $A$ and $B$ is : _________ (in $\mu F$).

Current passing through a wire as function of time is given as $I(t)=0.02 t+0.01 \mathrm{~A}$. The charge that will flow through the wire from $t=1 \mathrm{~s}$ to $t=2 \mathrm{~s}$ is

A small mirror of mass $m$ is suspended by a massless thread of length $l$. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror
($\mathrm{c}=$ speed of light in ...

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$
Assertion A : In photoelectric effect, on increasing the intensity of incident light the stopping potential increases.
Reason R ...

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\frac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of $10 \mathrm{~cm} / \mathrm{s}$, induc...

The Boolean expression $\mathrm{Y}=A \bar{B} C+\bar{A} \bar{C}$ can be realised with which of the following gate configurations.
A. One 3-input AND gate, 3 NOT gates and one 2-input OR gate, One 2-input AND gate,
B. One 3 -input AND gate, 1...

Two infinite identical charged sheets and a charged spherical body of charge density ' $\rho$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D points is...

Two small spherical balls of mass 10 g each with charges $-2 \mu \mathrm{C}$ and $2 \mu \mathrm{C}$, are attached to two ends of very light rigid rod of length 20 cm . The arrangement is now placed near an infinite nonconducting charge shee...

When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved :

Distance between object and its image (magnified by $-\frac{1}{3}$ ) is 30 cm . The focal length of the mirror used is $\left(\frac{x}{4}\right) \mathrm{cm}$,
where magnitude of value of $x$ is _________.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A : The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2} \mathrm{m...

Consider the sound wave travelling in ideal gases of $\mathrm{He}, \mathrm{CH}_4$, and $\mathrm{CO}_2$. All the gases have the same ratio $\frac{P}{\rho}$, where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound...

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7} \mathrm{~m}$ and $600 \mathrm{~m} / \mathrm{s}$, respectively. Find the frequency of its collisions.

A body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3} T_2$, the angles $\theta_1$ and $\...

Two liquids $A$ and $B$ have $\theta_A$ and $\theta_B$ as contact angles in a capillary tube. If $K=\cos \theta_A / \cos \theta_B$, then identify the correct statement:

Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness $d_1$ and $d_2$ such that $d_2=2 d_1$ and $l>d_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearin...

Which of the following are correct expression for torque acting on a body?
A. $\vec{\tau}=\vec{r} \times \vec{L}$
B. $\vec{\tau}=\frac{d}{d t}(\vec{r} \times \vec{p})$
C. $\vec{\tau}=\vec{r} \times \frac{d \vec{p}}{d t}$
D. $\vec{\tau}=I \v...

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector as $\vec{r}=a(\hat{i} \cos \omega t+\hat{j} \sin \omega t)$. The direction of force is

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\frac{x}{5}}$ where $x=$ ________.

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then ...

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^P L^Q T^R A^S$, where value of ' $Q$ ' and ' $R$ ' are

In a Young's double slit experiment, the slits are separated by 0.2 mm . If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is :

In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by