List of top Questions asked in JEE Main- 2025

Let the area of a triangle $ \triangle PQR $ with vertices $ P(5, 4) $, $ Q(-2, 4) $, and $ R(a, b) $ be 35 square units. If its orthocenter and centroid are $ O(2, \frac{14}{5}) $ and $ C(c, d) $ respectively, then $ c + 2d $ is equal to:

Let R = {(1, 2), (2, 3), (3, 3)}} be a relation defined on the set $ \{1, 2, 3, 4\} $. Then the minimum number of elements needed to be added in $ R $ so that $ R $ becomes an equivalence relation, is:

Let $ A = \{1, 2, 3, \dots, 10\} $ and $ B = \left\{ \frac{m}{n} : m, n \in A, m <n \text{ and } \gcd(m, n) = 1 \right\} $. Then $ n(B) $ is equal to :

The calculated spin-only magnetic moments of $ K_3[Fe(OH)_6] $ and $ K_4[Fe(OH)_6] $ respectively are:

Let $ \hat{a} $ be a unit vector perpendicular to the vectors \[ \mathbf{b} = \hat{i} - 2\hat{j} + 3\hat{k} \quad \text{and} \quad \mathbf{c} = 2\hat{i} + 3\hat{j} - \hat{k}, \] $\text{and makes an angle of}$ $ \cos\left( -\frac{1}{3} \right) $ $\text{with the vector}$ $ \hat{i} + \alpha \hat{j} + \hat{k} $. $\text{If}$ $ \hat{a} $ $\text{makes an angle of}$ $ \frac{\pi}{3} $ $\text{with the vector}$ $ \hat{i} + \alpha \hat{j} + \hat{k} $, then the value of $ \alpha $ $\text{is:}$

Statement-1: $ \text{ClF}_3 $ has 3 possible structures.
Statement-2: $ \text{III} $ is the most stable structure due to least lone pair-bond pair (lp-bp) repulsion.

Which of the following options is correct?

Let the function $f(x) = (x^2 - 1)|x^2 - ax + 2| + \cos|x| $ be not differentiable at the two points $ x = \alpha = 2 $ and $ x = \beta $. Then the distance of the point $(\alpha, \beta)$ from the line $12x + 5y + 10 = 0$ is equal to:

Given below are two statements:
Statement I: Experimentally determined oxygen-oxygen bond lengths in the $ O_2 $ are found to be the same and the bond length is greater than that of a $ O=O $ (double bond) but less than that of a single $ O-O $ bond.
Statement II: The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond $ O=O $ but more than that of a single bond $ O-O $.
In light of the above statements, choose the correct answer from the options given below:

Let $ A = [a_{ij}] $ be a $3 \times 3 $ matrix such that: $$ A = \begin{bmatrix} 0 & 0 & 4 \\ 1 & 0 & 0 \\ 0 & 1 & 3 \\ \end{bmatrix}, A^{-1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 3 & 0 \\ 2 & 1 & 0 \end{bmatrix}. $$ Then $ a_{23} $ equals:

Given below are two statements:
Statement I:
will undergo alkaline hydrolysis at a faster rate than

Statement II:
In intramolecular substitution takes place first by involving lone pair of electrons on nitrogen.

A parallel plate capacitor was made with two rectangular plates, each with a length of $ l = 3 \, {cm} $ and breadth of $ b = 1 \, {cm} $. The distance between the plates is $ d = 3 \, \mu{m} $. Out of the following, which are the ways to increase the capacitance by a factor of 10?

A. l = 30 cm, b = 1 cm, d = 1 μm
B. l = 3 cm, b = 1 cm, d = 30 μm
C. l = 6 cm, b = 5 cm, d = 3 μm
D. l = 1 cm, b = 1 cm, d = 10 μm
E. l = 5 cm, b = 2 cm, d = 1 μm

Consider the above reaction, what mass of CaCl₂ will be formed if 250 ml of 0.76 M HCl reacts with 1000 g of CaCO₃?

A satellite is launched into a circular orbit of radius $ R $ around the earth. A second satellite is launched into an orbit of radius $ 1.03R $. The time period of revolution of the second satellite is larger than the first one approximately by:

A point particle of charge $ Q $ is located at $ P $ along the axis of an electric dipole 1 at a distance $ r $ as shown in the figure. The point $ P $ is also on the equatorial plane of a second electric dipole 2 at a distance $ r $. The dipoles are made of opposite charge $ q $ separated by a distance $ 2a $. For the charge particle at $ P $ not to experience any net force, which of the following correctly describes the situation?

Let $ \langle a_n \rangle $ be a sequence such that $ a_0 = 0 $, $ a_1 = \frac{1}{2} $, and $ 2a_{n+2} = 5a_{n+1} - 3a_n $.n= 0,1,2,3.... Then $ \sum_{k=1}^{100} a_k $ is equal to:

A compound 'X' absorbs 2 moles of hydrogen and 'X' upon oxidation with KMnO4 - H⁺ gives the following products:

The total number of $\sigma$ bonds present in the compound 'X' is ----.

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this? Given: Rydberg constant $ R_H = 10^5 \, \text{cm}^{-1} $, $ h = 6.6 \times 10^{-34} \, \text{J s} $, and $ c = 3 \times 10^8 \, \text{m/s} $

Arrange the following in increasing order of solubility product:
\[ {Ca(OH)}_2, {AgBr}, {PbS}, {HgS} \]

Let $ A $ be a matrix of order $ 3 \times 3 $ and $ |A| = 5 $. If $ |2 \, \text{adj}(3A \, \text{adj}(2A))| = 2^{\alpha} \cdot 3^{\beta} \cdot 5^{\gamma}, \quad \alpha, \beta, \gamma \in \mathbb{N} $ then $ \alpha + \beta + \gamma $ is equal to

For a short dipole placed at origin O, the dipole moment P is along the X-axis, as shown in the figure. If the electric potential and electric field at A are V and E respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the Y-axis is given by:

When sec-butylcyclohexane reacts with bromine in the presence of sunlight, the major product is:

The electric field of an electromagnetic wave in free space is \[ \vec{E} = \] \[57 \cos \left[7.5 \times 10^6 t - 5 \times 10^{-3} (3x + 4y)\right] \left( 4\hat{i} - 3\hat{j} \right) \, \text{N/C}. \] The associated magnetic field in Tesla is:

Let the matrix $ A = \begin{pmatrix} 1 & 0 & 0 \\1 & 0 & 1 \\0 & 1 & 0 \end{pmatrix} $ satisfy $ A^n = A^{n-2} + A^2 - I $ for $ n \geq 3 $. Then the sum of all the elements of $ A^{50} $ is:

Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl is Given : Molar mass of Mg is 24 g mol$^{-1}$.

The mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dilute HCl is: (Given molar mass of Mg = 24 g/mol)