List of top Questions asked in JEE Main- 2025

Let $( f(x) =$ $\int_0^{x^2 \frac{t^2 - 8t + 15}{e^t} dt}$, $x \in \mathbb{R}$. Then the numbers of local maximum and local minimum points of $ f $, respectively, are:

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + ... \infty = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + ... \infty = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + ... \infty = \beta, $ then $ \frac{\alpha}{\beta} $ is equal to:

A particle moves on a circular path of radius 1 m. Find its displacement when it moves from $ A \rightarrow B \rightarrow A $. Also, its distance are it moves from $ A \rightarrow B \rightarrow A $.

If $A_2B \;\text{is} \;30\%$ ionised in an aqueous solution, then the value of van’t Hoff factor $ i $ is:

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $ L_1 : 2x + y + 6 = 0 $ and $ L_2 : 4x + 2y - p = 0 $, $ p>0 $, at the points A and B, respectively. If $ AB = \frac{9}{\sqrt{2}} $ and the foot of the perpendicular from the point A on the line $ L_2 $ is M, then $ \frac{AM}{BM} $ is equal to

A particle is subjected to simple harmonic motions as: $ x_1 = \sqrt{7} \sin 5t \, \text{cm} $ $ x_2 = 2 \sqrt{7} \sin \left( 5t + \frac{\pi}{3} \right) \, \text{cm} $ where $ x $ is displacement and $ t $ is time in seconds. The maximum acceleration of the particle is $ x \times 10^{-2} \, \text{m/s}^2 $. The value of $ x $ is:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Knowing initial position $ x_0 $, and initial momentum $ p_0 $ is enough to determine the position and momentum at any time $ t $ for a simple harmonic motion with a given angular frequency $ \omega $.
Reason (R): The amplitude and phase can be expressed in terms of $ x_0 $ and $ p_0 $.
In the light of the above statements, choose the correct answer from the options given below:

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

The equation of a wave travelling on a string is $ y = \sin[20\pi x + 10\pi t] $, where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

Find output voltage in the given circuit.

A uniform magnetic field of $ 0.4 $ T acts perpendicular to a circular copper disc $ 20 $ cm in radius. The disc is having a uniform angular velocity of $ 10\pi $ rad/s about an axis through its center and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? ($\pi = 3.14$)

A ball having kinetic energy $ KE $, is projected at an angle of $ 60^\circ $ from the horizontal. What will be the kinetic energy of the ball at the highest point of its flight?

In the experiment for measurement of viscosity $ \eta $ of a given liquid with a ball having radius $ R $, consider following statements: A. Graph between terminal velocity $ V $ and $ R $ will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of $ \eta $ will change.

Given a charge $ q $, current $ I $ and permeability of vacuum $ \mu_0 $. Which of the following quantity has the dimension of momentum?

In the context of the photoelectric effect, what is the threshold frequency $ f_0 $ for a metal if the work function is $ \phi = 2 \, \text{eV} $?

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle $ \approx 0^\circ $) with $ 30^\circ $ inclined with vertical. The length of water risen in the capillary is ____ cm. (Take $ g = 9.8 $ m/s$^2 $)

A force $ \mathbf{F} = 2\hat{i} + 3\hat{j} + 5\hat{k} $ acts on a particle moving in the direction of $ \mathbf{r} = 2\hat{i} + 3\hat{j} + \beta \hat{k} $. Find the value of $ \beta $ when the work done is zero.

The kinetic energy of translation of the molecules in 50 g of CO$_2$ gas at 17°C is:

A positive ion A and a negative ion B has charges $6.67 \times 10^{-19}$ C and $9.6 \times 10^{-10}$ C, and masses $19.2 \times 10^{-27}$ kg and $9 \times 10^{-27}$ kg respectively. At an instant, the ions are separated by a certain distance $r$. At that instant, the ratio of the magnitudes of electrostatic force to gravitational force is $P \times 10^{-13}$, where the value of $P$ is:

A coil of area A and N turns is rotating with angular velocity $ \omega$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $ \vec{B}$ Magnetic flux $\varphi \text{ and induced emf } \varepsilon \text{ across it, at an instant when } \vec{B} \text{ is parallel to the plane of the coil, are:}$

The line $ L_1 $ is parallel to the vector $ \mathbf{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} $ and passes through the point $ (7, 6, 2) $, and the line $ L_2 $ is parallel to the vector $ \mathbf{b} = 2\hat{i} + \hat{j} + 3\hat{k} $ and passes through the point $ (5, 3, 4) $. The shortest distance between the lines $ L_1 $ and $ L_2 $ is:

If the probability that the random variable X takes the value x is given by $ P(X = x) = k(x + 1)3^{-x} $, $ x = 0, 1, 2, 3, ... $, where k is a constant, then $ P(X \ge 3) $ is equal to

In an arithmetic progression, if $ S_{40} = 1030 $ and $ S_{12} = 57 $, then $ S_{30} - S_{10} $ is equal to:

What is the solution to the differential equation $ \frac{dy}{dx} = \frac{y}{x} $ with the initial condition $ y(1) = 2 $?

The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet color in non-luminous flame under hot condition in borax bead test is: