List of top Questions asked in JEE Main- 2025

Let $ f : \mathbb{R} \setminus \{0\} \to (-\infty, 1) $ be a polynomial of degree 2, satisfying $ f(x)f\left( \frac{1}{x} \right) = f(x) + f\left( \frac{1}{x} \right) $. If $ f(K) = -2K $, then the sum of squares of all possible values of $ K $ is:

The integral \[ \int_0^\pi \frac{8x}{4\cos^2 x + \sin^2 x} \, dx \text{ is equal to:} \]

Let P be the foot of the perpendicular from the point $ (1, 2, 2) $ on the line \[ \frac{x-1}{1} = \frac{y + 1}{-1} = \frac{z - 2}{2} \] Let the line $ \mathbf{r} = (-\hat{i} + \hat{j} - 2\hat{k}) + \lambda (\hat{i} - \hat{j} + \hat{k})$, $ \lambda \in \mathbb{R} $, intersect the line $L$ at $Q$. Then $ 2(PQ)^2 $ is equal to:

The observed and normal molar masses of compound MX₂ are 65.6 and 164 respectively. The percent degree of ionisation of MX₂ is ________________% (Nearest integer).

Consider the following oxides:
V_2O_5, Cr_2O_3, Mn_2O_7, V_2O_3, VO_2
A number of oxides which are acidic is $ x $.
Consider the following complex compound:
[Co(NH_2CH_2CH_2NH_2)_3](SO_4)_3
The primary valency of the complex is $ y $.
What is the value of $ x + y $ is?

For positive integers $ n $, if $ 4 a_n = \frac{n^2 + 5n + 6}{4} $ and \[ S_n = \sum_{k=1}^{n} \left( \frac{1}{a_k} \right), \text{ then the value of } 507 S_{2025} \text{ is:} \]

Let $ |z_1 - 8 - 2i| \leq 1 $ and $ |z_2 - 2 + 6i| \leq 2 $, where $ z_1, z_2 \in \mathbb{C} $. Then the minimum value of $ |z_1 - z_2| $ is:

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 which expression is correct?

1 + 3 + $5^2$ + 7 + $9^2$ + $\ldots$ upto 40 terms is equal to

Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is:

If \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^2 \cos^2 x}{1 + e^x} dx = \pi(a\pi^2 + \beta), \quad a, \beta \in \mathbb{Z}, \] then $ (a + \beta)^2 $ equals:

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:

Let the triangle PQR be the image of the triangle with vertices $ (1, 3), (3, 1) $ and $ (2, 4) $ in the line $ x + 2y = 2 $. If the centroid of $ \Delta PQR $ is the point $ (\alpha, \beta) $, then $ 15(\alpha - \beta) $ is equal to :

An electron projected perpendicular to a uniform magnetic field $ B $ moves in a circle. If Bohr’s quantization is applicable, then the radius of the electronic orbit in the first excited state is:

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at the 40 cm mark. A mass of 400 g is suspended at the 10 cm mark. To maintain the balance of the rod, the mass to be suspended at the 90 cm mark is:

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have:

Choose the figure that will correctly replace the question mark $(?)$ in the given series.

In a YDSE setup, the slits are separated by 1.5 mm and the distance between the slits and the screen is 2 m. On using light of wavelength 400 nm, it is observed that 20 maxima of double slit experiment lie inside the central maxima of single slit diffraction. The width of each slit is μm.

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance $ R_p = 1 \, \Omega $ as shown in the figure. An external resistance of $ R_e = 2 \, \Omega $ is connected via the sliding contact.
The current $ i $ is :

Let the equation of the circle, which touches x-axis at the point $ (a, 0) $ and cuts off an intercept of length $ b $ on y-axis be $ x^2 + y^2 - cx + dy + e = 0 $. If the circle lies below x-axis, then the ordered pair $ (2a, b^2) $ is equal to:

Let $ f : \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all $ x, y \in \mathbb{R}. $

If $ f'(0) = \frac{1}{2} $, then the value of $ 24f''\left( \frac{5\pi}{3} \right) $ is:

The temperature of a body in air falls from $ 40^\circ \text{C} $ to $ 24^\circ \text{C} $ in 4 minutes. The temperature of the air is $ 16^\circ \text{C} $. The temperature of the body in the next 4 minutes will be:

Consider a complex reaction taking place in three steps with rate constants $k_1$, $k_2$, and $k_3$ respectively. The overall rate constant $k$ is given by the expression $ k = \sqrt{\frac{k_1 k_3}{k_2}} $. If the activation energies of the three steps are 60, 30, and 10 kJ mol$^{-1}$ respectively, then the overall energy of activation in kJ mol$^{-1}$ is ________________(Nearest integer).

Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is:

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 cm$^3$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm = $10^5$ Pa)