List of top Questions asked in JEE Main- 2021

A 0.07 H inductor and a 12 $\Omega$ resistor are connected in series to a 220 V, 50 Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $\pi$ as 22/7]

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a << A) : 

 

In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross-sections having radii $r_1$ and $r_2 (r_2<r_1)$. Choose the correct option as one moves from P to Q : 

 

Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be :

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be : (Given area of plate = A) 

 

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is $\frac{3E}{4}$ then its displacement 'y' is given by :
Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$\theta$' with the vertical ?

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A $\rightarrow$ B and C $\rightarrow$ D are $T_1$ and $T_2$ ($T_1>T_2$) respectively. Choose the correct option out of the following for work done if processes BC and DA are adiabatic. 

 

A body takes 4 min. to cool from 61$^\circ$C to 59$^\circ$C. If the temperature of the surroundings is 30$^\circ$C, the time taken by the body to cool from 51$^\circ$C to 49$^\circ$C is :
The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy $2 \times 10^{-9}$ J per molecule is :

Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that $|\vec{AB}| = |\vec{BC}| = |\vec{CD}|$, then $\vec{AB} + \vec{AC} + \vec{AD} = 4\vec{AO} + \vec{OB} + \vec{OC}$ 
Reason R : Polygon law of vector addition yields $\vec{AB} + \vec{BC} + \vec{CD} = \vec{AD} = 2\vec{AO}$ 

The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (which is $\perp$ to the plane of the disc and passing through its centre) to MI of smaller disc around one of its diameters lying on its plane ? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia) 

 

Choose the correct answer from the options given below : 

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is : 

 

A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.
Reason R : Least Count = $\frac{\text{Pitch}}{\text{Total divisions on circular scale}}$

Suppose two planets (spherical in shape) of radii R and 2 R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $\sqrt{\frac{aGM}{7R}}$ then the value of 'a' is _________. [Given : The two planets are fixed in their position] 

 

In a uniform magnetic field, the magnetic needle has a magnetic moment $9.85 \times 10^{-2}$ A/m$^2$ and moment of inertia $5 \times 10^{-6}$ kg m$^2$. If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is _________ mT. [Take $\pi^2$ as 9.85]
A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section $10^{-6}$ m$^2$ stretched by an amount 0.04 m. The velocity of the projected stone is _________ m/s. (Young's modulus of rubber = $0.5 \times 10^9$ N/m$^2$)
A transistor is connected in common emitter circuit configuration, the collector supply voltage is 10 V and the voltage drop across a resistor of 1000 $\Omega$ in the collector circuit is 0.6 V. If the current gain factor ($\beta$) is 24, then the base current is _________ $\mu$A. (Round off to the Nearest Integer)

A prism of refractive index $n_1$ and another prism of refractive index $n_2$ are stuck together (as shown in the figure). $n_1$ and $n_2$ depend on $\lambda$, the wavelength of light, according to the relation $n_1 = 1.2 + \frac{10.8 \times 10^{-14}}{\lambda^2}$ and $n_2 = 1.45 + \frac{1.8 \times 10^{-14}}{\lambda^2}$. The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _________ nm. 

 

A particle of mass $9.1 \times 10^{-31}$ kg travels in a medium with a speed of $10^6$ m/s and a photon of a radiation of linear momentum $10^{-27}$ kg m/s travels in vacuum. The wavelength of photon is _________ times the wavelength of the particle.
A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 $\mu$F is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _________ $\Omega$.
In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 Å. If the speed of the electron is $2.2 \times 10^6$ m/s, then the current associated with the electron will be _________ $\times 10^{-2}$ mA. [Take $\pi$ as 22/7]

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then $T_1$ is connected to $T_2$. As the current in R = 6 $\Omega$ attains a maximum value of steady state level, $T_1$ is disconnected from $T_2$ and immediately connected to $T_3$. Potential drop across r = 3 $\Omega$ resistor immediately after $T_1$ is connected to $T_3$ is _________ V. (Round off to the Nearest Integer)