List of top Questions asked in JEE Main

A sportsman runs around a circular track of radius $ r $ such that he traverses the path ABAB. The distance travelled and displacement, respectively, are:

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:

In the digital circuit shown in the figure, for the given inputs the P and Q values are:

Energy released when two deuterons $ \text{(H}_2\text{)} $ fuse to form a helium nucleus $ \text{(He}_4\text{)} $ is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason
(R): In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.
In the light of the above statements, choose the most appropriate answer from the options given below:

Let $ y = y(x) $ be the solution of the differential equation $$ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \sec^2 x $$ such that $ y(0) = \frac{5}{4} $. Then $ 12 \left( y \left( \frac{\pi}{4} \right) - e^2 \right) $ is equal to:

Let the area of the triangle formed by a straight line $ L: x + by + c = 0 $ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line $ L $ makes an angle of $ 45^\circ $ with the positive x-axis, then the value of $ b^2 + c^2 $ is:

Let the point $ P $ of the focal chord $ PQ $ of the parabola $ y^2 = 16x $ be $ (1, -4) $. If the focus of the parabola divides the chord $ PQ $ in the ratio $ m : n $, gcd($m, n$) = 1, then $ m^2 + n^2 $ is equal to:

If $ \sum_{r=0}^{10} \left( 10^{r+1} - 1 \right)$ $\,$$\binom{10}{r} = \alpha^{11} - 1 $, then $ \alpha $ is equal to :

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is:

$$ \int \frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}} \, dx - 3 \log \left( \sqrt{3} \right) $$ is equal to:

Given three identical bags each containing 10 balls, whose colours are as follows:

Bag I	3 Red	2 Blue	5 Green
Bag II	4 Red	3 Blue	3 Green
Bag III	5 Red	1 Blue	4 Green

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from Bag I is $ p $ and if the ball is Green, the probability that it is from Bag III is $ q $, then the value of $ \frac{1}{p} + \frac{1}{q} $ is:

If $ \theta \in \left[ \frac{7\pi}{6}, \frac{4\pi}{3} \right] $, then the number of solutions of $$ \sqrt{3} \csc^2\theta - 2(\sqrt{3} - 1) \csc\theta - 4 = 0, $$ is equal to:

If the system of equation $$ 2x + \lambda y + 3z = 5 \\3x + 2y - z = 7 \\4x + 5y + \mu z = 9 $$ has infinitely many solutions, then $ \lambda^2 + \mu^2 $ is equal to:

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is ______ m.

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60^\circ$. The refractive index of the prism material is $ \sqrt{2} $. The angle of incidence (in degrees) is ______ .

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ______ x $10^{10}$ J.
(Mass of earth = $6 \times 10^{24}$ kg, Radius of earth = $6.4 \times 10^6$ m, Gravitational constant = $6.67 \times 10^{-11}$ Nm$^2$ kg$^{-2}$)

A bi-convex lens has radius of curvature of both the surfaces same as $ \frac{1}{6} \, \text{cm} $. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $ (R_1 \neq R_2) $, without any change in lens power then possible combination of $ R_1 $ and $ R_2 $ is:

If $ \mu_0 $ and $ \epsilon_0 $ are the permeability and permittivity of free space, respectively, then the dimension of $ \left( \frac{1}{\mu_0 \epsilon_0} \right) $ is :

Consider a circular loop that is uniformly charged and has a radius $ \sqrt{2} $. Find the position along the positive $ z $-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in the $ xy $-plane at the origin:

The internal energy of air in $ 4 \, \text{m} \times 4 \, \text{m} \times 3 \, \text{m} $ sized room at 1 atmospheric pressure will be $ __ \times 10^6 \, \text{J} $. (Consider air as a diatomic molecule)

Assuming the validity of Bohr's atomic model for hydrogen-like ions, the radius of $ \text{Li}^{2+} $ ion in its ground state is given by $ \frac{1}{X} a_0 $, where $ a_0 $ is the first Bohr's radius.

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is $ V $. The potential difference between the points A and B (shown in the figure) is:

Identify the characteristics of an adiabatic process in a monatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $ T_1 $ to $ T_2 $ is proportional to $ (T_2 - T_1) $. Choose the correct answer from the options given below:

Two water drops each of radius $ r $ coalesce to form a bigger drop. If $ T $ is the surface tension, the surface energy released in this process is: