List of top Questions asked in JEE Main- 2025

Match List - I with List - II:

Choose the correct answer from the options given below:

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per meter in the solenoid is ________________.

The increase in pressure required to decrease the volume of a water sample by 0.2percentage is $ P \times 10^5 \, \text{Nm}^{-2} $. Bulk modulus of water is $ 2.15 \times 10^9 \, \text{Nm}^{-2} $. The value of $ P $ is ________________.

A string of length $ L $ is fixed at one end and carries a mass of $ M $ at the other end. The mass makes $ \frac{3}{\pi} $ rotations per second about the vertical axis passing through the end of the string as shown. The tension in the string is ________________ ML.

The ratio of the power of a light source $ S_1 $ to that of the light source $ S_2 $ is 2. $ S_1 $ is emitting $ 2 \times 10^{15} $ photons per second at 600 nm. If the wavelength of the source $ S_2 $ is 300 nm, then the number of photons per second emitted by $ S_2 $ is ________________ $ \times 10^{14} $.

Acceleration due to gravity on the surface of earth is $ g $. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________________ g.

In photoelectric effect, the stopping potential $ V_0 $ vs frequency $ \nu $ curve is plotted. $ h $ is the Planck's constant and $ \phi_0 $ is the work function of metal.
(A) $ V_0 $ vs $ \nu $ is linear.
(B) The slope of $ V_0 $ vs $ \nu $ curve is $ \frac{\phi_0}{h} $.
(C) $ h $ constant is related to the slope of $ V_0 $ vs $ \nu $ line.
(D) The value of electric charge of electron is not required to determine $ h $ using the $ V_0 $ vs $ \nu $ curve.
(E) The work function can be estimated without knowing the value of $ h $.
Choose the correct answer from the options given below:

N equally spaced charges each of value $ q $ are placed on a circle of radius $ R $. The circle rotates about its axis with an angular velocity $ \omega $ as shown in the figure. A bigger Amperian loop $ B $ encloses the whole circle, whereas a smaller Amperian loop $ A $ encloses a small segment. The difference between enclosed currents, $ I_B - I_A $ for the given Amperian loops is:

The position vector of a moving body at any instant of time is given as r = ( 5t²$\hat{i}$ - 5t$\hat{j}$) m. The magnitude and direction of velocity at $ t = 2 \, \text{s} $ are:

A solid sphere and a hollow sphere of the same mass and of the same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $ t_1 $ and $ t_2 $, respectively, then:

The energy $ E $ and momentum $ p $ of a moving body of mass $ m $ are related by some equation. Given that $ c $ represents the speed of light, identify the correct equation:

A small uncharged conducting sphere is placed in contact with an identical sphere but having $ 4 \times 10^{-6} \, \text{C} $ charge and then removed to a distance such that the force of repulsion between them is $ 9 \times 10^{-3} \, \text{N} $. The distance between them is (Take $ \frac{1}{4\pi \epsilon_0} = 9 \times 10^9 $ in SI units):

A particle oscillates along the $ x $-axis according to the law, $ x(t) = x_0 \sin^2 \left( \frac{\pi t}{T} \right) $, where $ x_0 = 1 \, \text{m} $ and $ T $ is the time period of oscillation. The kinetic energy ($ K $) of the particle as a function of $ x $ is correctly represented by the graph:

The magnitude of heat exchanged by a system for the given cyclic process ABC (as shown in the figure) is (in SI units):

Let $ H_1: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ and $ H_2: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1 $ be two hyperbolas having lengths of latus rectums $ 15\sqrt{2} $ and $ 12\sqrt{5} $ respectively. Let their eccentricities be $ e_1 = \frac{5}{\sqrt{2}} $ and $ e_2 $ respectively. If the product of the lengths of their transverse axes is $ 100\sqrt{10} $, then $ 25e_2^2 $ is equal to:

If \[ \int \frac{2x^2 + 5x + 9}{\sqrt{x^2 + x + 1}} \, dx = \sqrt{x^2 + x + 1} + \alpha \sqrt{x^2 + x + 1} + \beta \log_e \left( \left| x + \frac{1}{2} + \sqrt{x^2 + x + 1} \right| \right) + C, \] where $ C $ is the constant of integration, then $ \alpha + 2\beta $ is equal to ________________

Let $ P $ be the image of the point $ Q(7, -2, 5) $ in the line $ L: \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z}{4} $, and let $ R(5, p, q) $ be a point on $ L $. Then the square of the area of $ \triangle PQR $ is:

Let $ y = y(x) $ be the solution of the differential equation \[ 2\cos x \frac{dy}{dx} = \sin 2x - 4y \sin x, \quad x \in \left( 0, \frac{\pi}{2} \right). \]
If $ y\left( \frac{\pi}{3} \right) = 0 $, then $ y\left( \frac{\pi}{4} \right) + y\left( \frac{\pi}{4} \right) $ is equal to ________.

Let the position vectors of three vertices of a triangle be $ \overrightarrow{p} = 4\hat{i} + \hat{j} - 3\hat{k} $, $ \overrightarrow{q} = -5\hat{i} + 2\hat{j} + 3\hat{k} $, and $ \overrightarrow{r} = -5\hat{i} + 3\hat{j} + 2\hat{k} $. Then $ \alpha + 2\beta + 5\gamma $ is equal to:

If $ 7 = 5 + \frac{1}{7}(5 + \alpha) + \frac{1}{7^2}(5 + 2\alpha) + \frac{1}{7^3}(5 + 3\alpha) + \cdots $, then the value of $ \alpha $ is:

Let $ A = [a_{ij}] $ be a square matrix of order 2 with entries either 0 or 1. Let $ E $ be the event that $ A $ is an invertible matrix. Then the probability $ P(E) $ is:

Let $ \mathbf{a} = 3\hat{i} - \hat{j} + 2\hat{k} $, $ \mathbf{b} = \mathbf{a} \times (\hat{i} - 2\hat{k}) $ and $ \mathbf{c} = \mathbf{b} \times \hat{k} $. Then the projection of $ \mathbf{c} - 2\hat{j} $ on $ \mathbf{a} $ is:

If the equation of the parabola with vertex $\left( \frac{3}{2}, 3 \right)$ and the directrix $x + 2y = 0$ is $$ ax^2 + by^2 - cxy - 30x - 60y + 225 = 0, \text{ then } \alpha + \beta + \gamma \text{ is equal to:} $$

Let $ f: (0, \infty) \to \mathbb{R} $ be a function which is differentiable at all points of its domain and satisfies the condition $ x^2 f'(x) = 2f(x) + 3 $, with $ f(1) = 4 $. Then $ 2f(2) $ is equal to:

If $ \alpha>\beta>\gamma>0 $, then the expression \[ \cot^{-1} \beta + \left( \frac{1 + \beta^2}{\alpha - \beta} \right) + \cot^{-1} \gamma + \left( \frac{1 + \gamma^2}{\beta - \gamma} \right) + \cot^{-1} \alpha + \left( \frac{1 + \alpha^2}{\gamma - \alpha} \right) \] is equal to:

List - I	List - II
(A) Adenine	(I)
(B) Cytosine	(II)
(C) Thymine	(III)
(D) Uracil	(IV)