List of top Questions asked in JEE Main- 2021

A steel rod with \(y = 2.0\times10^{11}\ \mathrm{Nm^{-2}}\) and \(\alpha = 10^{-5}\ {}^\circ\mathrm{C^{-1}}\) of length 4 m and area of cross-section \(10\ \mathrm{cm^2}\) is heated from \(0^\circ\mathrm{C}\) to \(400^\circ\mathrm{C}\) without being allowed to extend. The tension produced in the rod is \(x\times10^5\) N where the value of \(x\) is ____________.

A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is ____________ \(\mathrm{ms^{-1}}\). (Take \(g = 10\ \mathrm{ms^{-2}}\))

The average translational kinetic energy of \(\mathrm{N_2}\) gas molecules at ............. \({}^\circ\mathrm{C}\) becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt. (Given \(k_B = 1.38\times10^{-23}\) J/K) (Fill the nearest integer).

A uniform heating wire of resistance \(36\ \Omega\) is connected across a potential difference of 240 V. The wire is then cut into half and potential difference of 240 V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be \(1 : x\), where \(x\) is ____________.

Experimentally reducing a functional group cannot be done by which one of the following reagents?

Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is \(2 \times 10^{3}\) km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is
\(\dfrac{\pi}{x}\ \mathrm{rad\,h^{-1}}\)
where \(x\) is ____________.

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by \(E = 20\cos(2\times10^{10}\,t - 200\,x)\) V/m. The dielectric constant of the medium is equal to : (Take \(\mu_r = 1\))

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is \(x : 4\) where \(x\) is ____________.

The temperature of 3.00 mol of an ideal diatomic gas is increased by \(40.0^\circ\)C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is \(\frac{x}{10}\). Then the value of x (round off to the nearest integer) is ___________. (Given R = 8.31 J mol^-1 K^-1)

When a body slides down from rest along a smooth inclined plane making an angle of \(30^\circ\) with the horizontal, it takes time \(T\). When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time \(\alpha T\), where \(\alpha\) is a constant greater than 1. The co-efficient of friction between the body and the rough plane is
\(\dfrac{1}{\sqrt{x}}\left(\dfrac{\alpha^2-1}{\alpha^2}\right)\)
where \(x\) = ____________.

A capacitor is connected to a 20 V battery through a resistance of \(10\,\Omega\). It is found that the potential difference across the capacitor rises to 2 V in \(1\,\mu\)s. The capacitance of the capacitor is __________ \(\mu\)F. Given : \(\ln\left(\frac{10}{9}\right) = 0.105\)

For the given circuit the current i through the battery when the key in closed and the steady state has been reached is __________.

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water (\(\mu = 4/3\)) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

In the given figure, each diode has a forward bias resistance of \(30\,\Omega\) and infinite resistance in reverse bias. The current \(I_1\) will be :

A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2 N along a frictionless surface with following surface profile.

The correct applied force vs distance graph will be :

Following plots show magnetization (M) vs magnetizing field (H) and magnetic susceptibility (\(\chi\)) vs temperature (T) graph :

Which of the following combination will be represented by a diamagnetic material?

A student determined Young's Modulus of elasticity using the formula \(Y = \frac{MgL^3}{4bd^3\delta}\). The value of g is taken to be 9.8 m/s², without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass (M)	1 g	2 kg
Length of bar (L)	1 mm	1 m
Breadth of bar (b)	0.1 mm	4 cm
Thickness of bar (d)	0.01 mm	0.4 cm
Depression (\(\delta\))	0.01 mm	5 mm

Then the fractional error in the measurement of Y is :

Two resistors \(R_1 = (4 \pm 0.8)\,\Omega\) and \(R_2 = (4 \pm 0.4)\,\Omega\) are connected in parallel. The equivalent resistance of their parallel combination will be :

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of \(0.8\sqrt{gh}\). The value of workdone by the air-friction is :

The ranges and heights for two projectiles projected with the same initial velocity at angles \(42^\circ\) and \(48^\circ\) with the horizontal are \(R_1, R_2\) and \(H_1, H_2\) respectively. Choose the correct option :

Let \(\vec{a}=2\hat{i}-\hat{j}+2\hat{k}\) and \(\vec{b}=\hat{i}+2\hat{j}-\hat{k}\). Let a vector \(\vec{v}\) be in the plane containing \(\vec{a}\) and \(\vec{b}\). If \(\vec{v}\) is perpendicular to the vector \(3\hat{i}+2\hat{j}-\hat{k}\) and its projection on \(\vec{a}\) is 19 units, then \(\left|2\vec{v}\right|^2\) is equal to ______________.

If the sum of the coefficients in the expansion of \((x+y)^n\) is 4096, then the greatest coefficient in the expansion is _____________.

A cube is placed inside an electric field, \(\vec{E}=150y^2\hat{j}\). The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :