List of top Questions asked in JEE Main- 2025

If $ A = \begin{pmatrix} 2 & 2 + p & 2 + p + q \\ 4 & 6 + 2p & 8 + 3p + 2q \\ 6 & 12 + 3p & 20 + 6p + 3q \end{pmatrix} $, then the value of $ \det(\text{adj}(\text{adj}(3A))) = 2^m \cdot 3^n $, then $ m + n $ is equal to:

Let $ A = \{-3, -2, -1, 0, 1, 2, 3\} $ and $ R $ be a relation on $ A $ defined by $ xRy $ if and only if $ 2x - y \in \{0, 1\} $. Let $ l $ be the number of elements in $ R $. Let $ m $ and $ n $ be the minimum number of elements required to be added in $ R $ to make it reflexive and symmetric relations, respectively. Then $ l + m + n $ is equal to:

Let the focal chord PQ of the parabola $ y^2 = 4x $ make an angle of $ 60^\circ $ with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, $ S $ being the focus of the parabola, touches the y-axis at the point $ (0, \alpha) $, then $ 5\alpha^2 $ is equal to:

Let $ a_n $ be the $ n $-th term of an A.P. If $ S_n = a_1 + a_2 + a_3 + \cdots + a_n = 700 $, $ a_6 = 7 $, and $ S_7 = 7 $, then $ a_n $ is equal to:

In a group of 3 girls and 4 boys, there are two boys $ B_1 $ and $ B_2 $. The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $ B_1 $ and $ B_2 $ are not adjacent to each other, is:

Consider a circular disc of radius 20 cm with center located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of the center of mass of the residual or remaining disc from the origin will be:

The position of a particle moving on x-axis is given by $ x(t) = A \sin t + B \cos^2 t + Ct^2 + D $, where $ t $ is time. The dimension of $ \frac{ABC}{D} $ 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 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):

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:

A capacitor, $ C_1 = 6 \, \mu F $, is charged to a potential difference of $ V_1 = 5 \, \text{V} $ using a 5V battery. The battery is removed and another capacitor, $ C_2 = 12 \, \mu F $, is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges $ q_1 $ and $ q_2 $ on the capacitors $ C_1 $ and $ C_2 $ when equilibrium condition is reached?

A particle is projected with velocity $ u $ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $ \frac{nu^2}{25g} $, where value of $ n $ is : (Given 'g' is the acceleration due to gravity).

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440^th position in this arrangement is:

A solution is made by mixing one mole of volatile liquid A with 3 moles of volatile liquid B. The vapor pressure of pure A is 200 mm Hg and that of the solution is 500 mm Hg. The vapor pressure of pure B and the least volatile component of the solution, respectively, are:

The IUPAC name of the following compound is:

A body of mass $ m $ connected to a massless and unstretchable string goes in a vertical circle of radius $ R $ under gravity $ g $. The other end of the string is fixed at the center of the circle. If velocity at the top of the circular path is $ v = \sqrt{ngR} $, where $ n \geq 1 $, then the ratio of kinetic energy of the body at bottom to that at top of the circle is:

Given below are two statements:
Statement I: D-glucose pentaacetate reacts with 2,4-dinitrophenylhydrazine.
Statement II: Starch, on heating with concentrated sulfuric acid at 100°C and 2-3 atmosphere pressure, produces glucose.
In the light of the above statements, choose the correct answer from the options given below:

Which of the following circuits has the same output as that of the given circuit?

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

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

Given below are two statements:
Statement (I): The radius of isoelectronic species increases in the order: \[ \text{Mg}^{2+} < \text{Na}^{+} < \text{F}^{-} < \text{O}^{2-} \] Statement (II): The magnitude of electron gain enthalpy of halogens decreases in the order: \[ \text{Cl} > \text{F} > \text{Br} > \text{I} \] In light of the above statements, choose the most appropriate answer from the options given below:

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:

The value of $ (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) $ is:

The total number of compounds from below when treated with hot KMnO4 giving benzoic acid is:

The product B formed in the following reaction sequence is: \[ {C}_6{H}_5{CN} \xrightarrow{{HCl}} (A) \xrightarrow{{AgCN}} (B) \]