List of top Questions asked in JEE Main

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of bigger body is 400 K. If the energy radiate from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding to be negligible):

If $ B $ is magnetic field and $ \mu_0 $ is permeability of free space, then the dimensions of $ \frac{B}{\mu_0} $ is:

Match List-I with List-II:

Given below are two statements: Statement I: One mole of propyne reacts with excess of sodium to liberate half a mole of H₂ gas. Statement II: Four g of propyne reacts with NaNH₂ to liberate NH₃ gas which occupies 224 mL at STP. In the light of the above statements, choose the most appropriate answer from the options given below:

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:

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:

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $ P_1 $. The reading of the pressure gauge falls to $ P_2 $ when the valve is opened. The speed of water flowing in the pipe is proportional to:

A particle of mass $ m $ and charge $ q $ is fastened to one end $ A $ of a massless string having equilibrium length $ l $, whose other end is fixed at point $ O $. The whole system is placed on a frictionless horizontal plane and is initially at rest. If a uniform electric field is switched on along the direction as shown in the figure, then the speed of the particle when it crosses the x-axis is:

Find the equivalent resistance between two ends of the following circuit:

Two iron solid discs of negligible thickness have radii $ R_1 $ and $ R_2 $ and moment of inertia $ I_1 $ and $ I_2 $, respectively. For $ R_2 = 2R_1 $, the ratio of $ I_1 $ and $ I_2 $ would be $ \frac{1}{x} $, where $ x $ is:

Given below are two statements:

will undergo alkaline hydrolysis at a faster rate than

involving lone pair of electrons on nitrogen.

Let $ [x] $ denote the greatest integer function, and let $ m $ and $ n $ respectively be the numbers of the points, where the function $ f(x) = [x] + |x - 2| $, $ -2<x<3 $, is not continuous and not differentiable. Then $ m + n $ is equal to:

Let $ (2, 3) $ be the largest open interval in which the function $ f(x) = 2 \log_e (x - 2) - x^2 + ax + 1 $ is strictly increasing, and $ (b, c) $ be the largest open interval, in which the function $ g(x) = (x - 1)^3 (x + 2 - a)^2 $ is strictly decreasing. Then $ 100(a + b - c) $ 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:

The elemental composition of a compound is 54.2%C, 9.2%H, and 36.6%O. If the molar mass of the compound is 132 g/mol, the molecular formula of the compound is:

For hydrogen atom, the orbital/s with lowest energy is/are:

Let $ y = y(x) $ be the solution of the differential equation \[ \cos(x \log(\cos x))^2 \, dy + (\sin x - 3 \sin x \log(\cos x)) \, dx = 0, \quad x \in \left( 0, \frac{\pi}{2} \right) \] If $ y\left( \frac{\pi}{4} \right) = -1 $, then $ y\left( \frac{\pi}{6} \right) $ is equal to:

If $ \lim_{t \to \infty} \left( \int_0^{1} \left( 3x + 5 \right)^t dx \right) = \frac{\alpha}{5e} \left( \frac{8}{5} \right)^{\frac{3}{2}}, $ then $ \alpha $ is equal to ____ :

Which among the following halides will generate the most stable carbocation in a nucleophilic substitution reaction?

If \[ \text{C(diamond)} \rightarrow \text{C(graphite)} + X \, \text{kj mol}^{-1} \] \[ \text{C(diamond)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Y \, \text{kj mol}^{-1} \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Z \, \text{kj mol}^{-1} \] At constant temperature. Then:

In the sulphur estimation, 0.20 g of a pure organic compound gave 0.40 g of barium sulphate. The percentage of sulphur in the compound is

The perpendicular distance of the line $ \frac{x - 1}{2} = \frac{y + 2}{-1} = \frac{z + 3}{2} $ from the point $ P(2, -10, 1) $ is:

Let $$ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b \quad \text{and} \quad H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1. $$ Let the distance between the foci of $E$ and the foci of $H$ be $2\sqrt{3}$. If $a - A = 2$, and the ratio of the eccentricities of $E$ and $H$ is $\frac{1}{3}$, then the sum of the lengths of their latus rectums is equal to:

Let $ A = \{1,2,3\} $. The number of relations on $ A $, containing $ (1,2) $ and $ (2,3) $, which are reflexive and transitive but not symmetric, is ______.

A force $ \mathbf{F} = 2\hat{i} + b\hat{j} + \hat{k} $ is applied on a particle and it undergoes a displacement $ \mathbf{r} = \hat{i} - 2\hat{j} - \hat{k} $. What will be the value of $ b $, if the work done on the particle is zero?