List of top Questions asked in JEE Main- 2021

A force of \(\vec F = (5y + 20)\,\hat{j}\ \mathrm{N}\) acts on a particle. The work done by this force when the particle is moved from \(y = 0\ \mathrm{m}\) to \(y = 10\ \mathrm{m}\) is ___________ J.

In a semiconductor, the number density of intrinsic charge carries at \(27^\circ\mathrm{C}\) is \(1.5\times10^{16}/\mathrm{m^3}\). If the semiconductor is doped with impurity atom, the hole density increases to \(4.5\times10^{22}/\mathrm{m^3}\). The electron density in the doped semiconductor is ___________ \(\times 10^{9}/\mathrm{m^3}\).

A system consists of two types of gas molecules A and B having same number density \(2\times10^{25}/\mathrm{m^3}\). The diameter of A and B are \(10\ \mathrm{\AA}\) and \(5\ \mathrm{\AA}\) respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ____________ \(\times 10^{-2}\)

From the given data, the amount of energy required to break the nucleus of aluminium \(^{27}_{13}\mathrm{Al}\) is __________ \(x \times 10^{-3}\ \mathrm{J}\).

Mass of neutron \(= 1.00866\ \mathrm{u}\)

Mass of proton \(= 1.00726\ \mathrm{u}\)

Mass of Aluminium nucleus \(= 27.18846\ \mathrm{u}\)

(Assume \(1\ \mathrm{u}\) corresponds to \(x\ \mathrm{J}\) of energy)

(Round off to the nearest integer)

Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the average power dissipated in one cycle will be same in both the circuits.

A light beam of wavelength \(500\ \mathrm{nm}\) is incident on a metal having work function of \(1.25\ \mathrm{eV}\), placed in a magnetic field of intensity \(B\). The electrons emitted perpendicular to the magnetic field \(B\), with maximum kinetic energy are bent into circular are of radius \(30\ \mathrm{cm}\). The value of \(B\) is ___________ \(\times 10^{-7}\ \mathrm{T}\).

Given \(hc = 20\times10^{-26}\ \mathrm{J\text{-}m}\), mass of electron \(= 9\times10^{-31}\ \mathrm{kg}\)

When radiation of wavelength \(\lambda\) is incident on a metallic surface, the stopping potential of ejected photoelectrons is \(4.8\ \mathrm{V}\). If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes \(1.6\ \mathrm{V}\). The threshold wavelength of the metal is :

In the given potentiometer circuit arrangement, the balancing length AC is measured to be \(250\ \mathrm{cm}\). When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes \(400\ \mathrm{cm}\). The ratio of the emf of two cells, \(\dfrac{\varepsilon_1}{\varepsilon_2}\) is :

A ray of light entering from air into a denser medium of refractive index \(\dfrac{4}{3}\), as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle \(\theta\) should be equal to :

The force is given in terms of time \(t\) and displacement \(x\) by the equation

\(F = A\cos Bx + C\sin Dt\)

The dimensional formula of \(\dfrac{AD}{B}\) is :

Two ideal electric dipoles A and B, having their dipole moment \(p_1\) and \(p_2\) respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of \(37^\circ\) with the axis. The ratio of the dipole moment of A and B, \(\dfrac{p_1}{p_2}\) is : (take \(\sin 37^\circ = \dfrac{3}{5}\))

Two spherical soap bubbles of radii \(r_1\) and \(r_2\) in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :

The instantaneous velocity of a particle moving in a straight line is given as
\(V = \alpha t + \beta t^2\)
, where \(\alpha\) and \(\beta\) are constants. The distance travelled by the particle between 1s and 2s is :

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

If \(q_f\) is the free charge on the capacitor plates and \(q_b\) is the bound charge on the dielectric slab of dielectric constant \(k\) placed between the capacitor plates, then bound charge \(q_b\) an be expressed as :

A balloon was moving upwards with a uniform velocity of \(10\ \mathrm{m/s}\). An object of finite mass is dropped from the balloon when it was at a height of \(75\ \mathrm{m}\) from the ground level. The height of the balloon from the ground when object strikes the ground was around :

(takes the value of g as \(10\ \mathrm{m/s^2}\))

A prism of refractive index \(\mu\) and angle of prism \(A\) is placed in the position of minimum angle of deviation. If minimum angle of deviation is also \(A\), then \(A\) in terms of refractive index is :

Let a curve \(y=f(x)\) pass through the point \((2,(\log_e2)^2)\) and have slope \(\frac{2y}{x\log_ex}\) for all positive real value of \(x\). Then the value of \(f(e)\) is equal to ______________.

If a rectangle is inscribed in an equilateral triangle of side length \(2\sqrt2\) as shown in the figure, then the square of the largest area of such a rectangle is _____________.

If the lines \(\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3}\) and \(\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1}\) are co-planar, then the value of \(k\) is _____________.

A force \(\vec F=(40\hat i+10\hat j)\,N\) acts on a body of mass 5 kg. If the body starts from rest, its position vector \(\vec r\) at time \(t=10\) s, will be :

If the co-efficient of \(x^7\) and \(x^8\) in the expansion of \(\left(2+\frac x3\right)^n\) are equal, then the value of \(n\) is equal to _____________.

A fair coin is tossed \(n\)-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of \(n\) is ______________.

If \(a+b+c=1,\ ab+bc+ca=2\) and \(abc=3\), then the value of \(a^4+b^4+c^4\) is equal to ______________.

If \((\vec a+3\vec b)\) is perpendicular to \((7\vec a-5\vec b)\) and \((\vec a-4\vec b)\) is perpendicular to \((7\vec a-2\vec b)\), then the angle between \(\vec a\) and \(\vec b\) (in degrees) is ____________.