List of top Questions asked in JEE Main- 2025

Let $\left\lfloor t \right\rfloor$ be the greatest integer less than or equal to $t$. Then the least value of $p \in \mathbb{N}$ for which

\[ \lim_{x \to 0^+} \left( x \left\lfloor \frac{1}{x} \right\rfloor + \left\lfloor \frac{2}{x} \right\rfloor + \dots + \left\lfloor \frac{p}{x} \right\rfloor \right) - x^2 \left( \left\lfloor \frac{1}{x^2} \right\rfloor + \left\lfloor \frac{2}{x^2} \right\rfloor + \dots + \left\lfloor \frac{9^2}{x^2} \right\rfloor \right) \geq 1 \]

is equal to __________.

Let $L_1: \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-1}{2}$ and $L_2: \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z}{1}$ be two lines. Let $L_3$ be a line passing through the point $(\alpha, \beta, \gamma)$ and be perpendicular to both $L_1$ and $L_2$. If $L_3$ intersects $L_1$, then $\left| 5\alpha - 11\beta - 8\gamma \right|$ equals:

The minimum value of $ n $ for which the number of integer terms in the binomial expansion $\left(7^{\frac{1}{3}} + 11^{\frac{1}{12}}\right)^n$ is 183, is

$\text{The number of solutions of the equation}$$\left(\frac{9}{x}-\frac{9}{\sqrt{x}}+2\right)\left(\frac{2}{x}-\frac{7}{\sqrt{x}}+3\right)=0\mathrm \; {is:}$

Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is:

Let A = $\begin{bmatrix} \log_5 128 & \log_4 5 \log_5 8 & \log_4 25 \end{bmatrix}$ \). If $A_{ij}$ is the cofactor of $ a_{ij} $, $ C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk} $, and $ C = [C_{ij}] $, then $ 8|C| $ is equal to:

Let the area of the region $ \{(x, y) : 2y \leq x^2 + 3, \, y + |x| \leq 3, \, y \geq |x - 1|\} $ be $ A $. Then $ 6A $ is equal to:

The integral is given by:

\[ 80 \int_{0}^{\frac{\pi}{4}} \frac{\sin\theta + \cos\theta}{9 + 16 \sin 2\theta} d\theta \]

is equals to?

Define a relation $ R $ on the interval $ [0, \frac{\pi}{2}] $ by $ xRy $ if and only if $ \sec^2 x - \tan^2 y = 1 $. Then $ R $ is:

The hydrocarbon (X) with molar mass 80 g mol$^{-1}$ and 90%carbon has ________________ degree of unsaturation.

The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is:________________

In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide (AgBr). The percentage of Bromine in the organic compound is ________________ × 10^-1% (Nearest integer).
(Given: Molar mass of Ag is 108 and Br is 80 g mol^-1)

Match List - I with List - II.

For the reaction, $$ H_2(g) + I_2(g) \rightleftharpoons 2HI(g) $$ Attainment of equilibrium is predicted correctly by:

The conditions and consequences that favour the $ t_{2g}^3 e_g^1 $ configuration in a metal complex are:

The successive 5 ionisation energies of an element are 800, 2427, 3658, 25024 and 32824 kJ/mol, respectively. By using the above values, predict the group in which the above element is present:

Given below are two statements:

Find the compound $ A $ from the following reaction sequences: \[ A \xrightarrow{\text{aqua regia}} B \xrightarrow{(1) \, \text{KNO}_3, \, \text{NH}_4\text{OH}} \text{yellow ppt}. \]

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: