List of top Questions asked in JEE Main- 2021

Let $ z = \frac{1 - i\sqrt{3}}{2}, \, i = \sqrt{-1} $. Then the value of

\[ 21 + \left( z + \frac{1}{z} \right)^3 + \left( z^2 + \frac{1}{z^2} \right)^3 + \left( z^3 + \frac{1}{z^3} \right)^3 + \dots + \left( z^{21} + \frac{1}{z^{21}} \right)^3 \] is _________.

The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units, is a circle of diameter $d$. Then $d^2$ is equal to _________.

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius $2.0 \times 10^{-5}$ m and density $1.2 \times 10^3$ kgm$^{-3}$? Take viscosity of liquid $= 1.8 \times 10^{-5}$ Nsm$^{-2}$. (Neglect buoyancy due to air).

Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :

The resultant of these forces $\vec{OP}, \vec{OQ}, \vec{OR}, \vec{OS}$ and $\vec{OT}$ is approximately ________ N.
[Take $\sqrt{3} = 1.7, \sqrt{2} = 1.4$. Given $\hat{i}$ and $\hat{j}$ unit vectors along x, y axis]

Which of the following is not a dimensionless quantity ?

If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :

An ideal gas is expanding such that $PT^3 = \text{constant}$. The coefficient of volume expansion of the gas is :

A balloon carries a total load of 185 kg at normal pressure and temperature of 27°C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is -7°C. Assuming the volume constant ?

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.
The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure :

Calculate the amount of charge on capacitor of 4 $\mu$F. The internal resistance of battery is 1 $\Omega$:

A uniformly charged disc of radius R having surface charge density $\sigma$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :

Five identical cells each of internal resistance 1 $\Omega$ and emf 5 V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same ?

Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

A bar magnet is passing through a conducting loop of radius R with velocity v. The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve :

Electric field in a plane electromagnetic wave is given by E = 50 sin(500x - 10 $\times$ 10$^{10}$t) V/m. The velocity of electromagnetic wave in this medium is : (Given C = speed of light in vacuum)

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is $d_1$ from C and the distance of the image formed is $d_2$ from C, the radius of curvature of this mirror is :

Find the distance of the image from object O, formed by the combination of lenses in the figure :

In a photoelectric experiment, increasing the intensity of incident light :

There are 10$^{10}$ radioactive nuclei in a given radioactive element. Its half-life time is 1 minute. How many nuclei will remain after 30 seconds ? ($\sqrt{2}$ = 1.414)

For a transistor in CE mode to be used as an amplifier, it must be operated in :

A circuit is arranged as shown in figure. The output voltage $V_o$ is equal to ________ V.

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angles 45$^\circ$ and 60$^\circ$ with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is $\frac{1}{\sqrt{x}}$. The value of x is ________.

If the velocity of a body related to displacement x is given by $v = \sqrt{5000 + 24x}$ m/s, then the acceleration of the body is ________ m/s$^2$.

A body of mass (2M) splits into four masses m, M-m, m, M-m, which are rearranged to form a square as shown in the figure. The ratio of $\frac{M}{m}$ for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ________.