List of top Questions asked in JEE Main- 2021

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 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)

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 ____________.

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 ____________.

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?

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 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 : \(\ln\left(\frac{10}{9}\right) = 0.105\)

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 :

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

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 :

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?

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 :

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 :

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 :

A man starts walking from the point P(\(-3\), 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then \(50\left((PR)^2+(RQ)^2\right)\) 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 _____________.

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is ___________.

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 ______________.

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 :

Let [t] denote the greatest integer \(\le t\). The number of points where the function \(f(x)=[x]\left|x^2-1\right|+\sin\left(\frac{\pi}{[x]+3}\right)-[x+1],\ x\in(-2,2)\) is not continuous is _____________.

A square loop of side 20 cm and resistance \(1\,\Omega\) is moved towards right with a constant speed \(v_0\). The right arm of the loop is in a uniform magnetic field of 5 T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value \(4\,\Omega\). What should be the value of \(v_0\) so that a steady current of 2 mA flows in the loop?

Let f(x) be a polynomial of degree 3 such that \(f(k)=-\frac{2}{k}\) for k = 2, 3, 4, 5. Then the value of \(52-10f(10)\) is equal to :

Let X be a random variable with distribution.

x	\(-2\)	\(-1\)	3	4	6
P(X = x)	\(\frac15\)	a	\(\frac13\)	\(\frac15\)	b

If the mean of X is 2.3 and variance of X is \(\sigma^2\), then \(100\sigma^2\) is equal to :

If for the complex numbers z satisfying \(|z-2-2i|\le1\), the maximum value of \(|3iz+6|\) is attained at \(a+ib\), then \(a+b\) is equal to ______________.