List of top Questions asked in JEE Main- 2021

A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is \(x\times10^{-1}\) atm. Value of x is ________.
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form \(y = -0.21\sin(x+30t)\) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is \(x\times10^{-2}\) N. Value of x is _________. (Round off to the nearest integer)
In an electrical circuit, a battery is connected to pass 20C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15V. The workdone by the battery is __________J.
The normal density of a material is \(\rho\) and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision.
Reason R : During elastic collision, the momentum and kinetic energy are both conserved.
In the light of the above statements, choose the most appropriate answer from the options given below :
A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8 m/s2 will be ______________ N. [g = 10 m/s2]
In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.
Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and B is :
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
If two similar springs each of spring constant \(K_1\) are joined in series, the new spring constant and time period would be changed by a factor :
Given below are two statements : one is labeled as Assertion A and the other is labelled as Reason R.
Assertion A : An electron microscope can achieve better resolving power than an optical microscope.
Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light.
In the light of the above statements, choose the correct answer from the options given below :
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is \(a = \frac{\sqrt{3}}{2}L\).
A planet revolving in elliptical orbit has :
A. a constant velocity of revolution.
B. has the least velocity when it is nearest to the sun.
C. its areal velocity is directly proportional to its velocity.
D. areal velocity is inversely proportional to its velocity.
E. to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below :
The temperature \(\theta\) at the junction of two insulating sheets, having thermal resistances \(R_1\) and \(R_2\) as well as top and bottom temperatures \(\theta_1\) and \(\theta_2\) (as shown in figure) is given by :
A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :
Consider the combination of 2 capacitors \(C_1\) and \(C_2\) with \(C_2\gt C_1\), when connected in parallel, the equivalent capacitance is \(\frac{15}{4}\) times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, \(\frac{C_2}{C_1}\).
In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :
LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is 1.9 eV. Calculate the wavelength of light emitted and its colour.
[\(h=6.63\times10^{-34}\) Js and \(c=3\times10^{8}\) ms\(^{-1}\)]
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
If \(y=y(x)\) is the solution of the equation
\(e^{\sin y}\cos y\,\frac{dy}{dx}+e^{\sin y}\cos x=\cos x\), \(y(0)=0\); then
\(1+y\left(\frac{\pi}{6}\right)+\frac{\sqrt3}{2}\,y\left(\frac{\pi}{3}\right)+\frac{1}{\sqrt2}\,y\left(\frac{\pi}{4}\right)\) is equal to ____________.
If \(\sqrt3\,(\cos^2x)=(\sqrt3-1)\cos x+1\), the number of solutions of the given equation when \(x\in\left[0,\frac{\pi}{2}\right]\) is __________.
The difference between degree and order of a differential equation that represents the family of curves given by \(y^2=a\left(x+\frac{\sqrt{a}}{2}\right)\), \(a\gt0\) is _________.
The number of integral values of 'k' for which the equation \(3\sin x+4\cos x=k+1\) has a solution, \(k\in\mathbb{R}\) is ___________.
The area bounded by the lines \(y=\big|\,|x-1|-2\,\big|\) is ___________.
Let \(m,n\in\mathbb{N}\) and \(\gcd(2,n)=1\). If \(30\binom{30}{0}+29\binom{30}{1}+\cdots+2\binom{30}{28}+1\binom{30}{29}=n\cdot2^m\), then \(n+m\) is equal to __________.
(Here \(\binom{n}{k}={}^nC_k\))