JEE Main 2021 February 25, Shift 2 Question Paper with Solutions

If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $\frac{1}{4\pi\varepsilon_0}\frac{\lvert e\rvert^2}{hc}$ has dimensions of :

A stone is dropped from the top of a building. When it crosses a point $5$ m below the top, another stone starts to fall from a point $25$ m below the top. Both stones reach the bottom of building simultaneously. The height of the building is :

A sphere of radius a and mass m rolls along a horizontal plane with constant speed $v_0$. It encounters an inclined plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

Thermodynamic process is shown below on a $P-V$ diagram for one mole of an ideal gas. If $V_2=2V_1$, then the ratio of temperature $\frac{T_2}{T_1}$ is :

Given below are two statements:
Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.
Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
In the light of the above statements, choose the correct answer from the options given below:

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :

The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36$ m and covers $30°$ in $0.1$ s. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$. The restoration force per unit mass when $P$ touches $M$ will be :

$Y=A\sin(\omega t+\phi_0)$ is the time-displacement equation of a SHM. At $t=0$ the displacement of the particle is $Y=\frac{A}{2}$ and it is moving along negative x-direction. Then the initial phase angle $\phi_0$ will be:

A charge q is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\vec{E}$ through the shaded area is:

In a ferromagnetic material, below the curie temperature, a domain is defined as:

An electron with kinetic energy $K_1$ enters between parallel plates of a capacitor at an angle $\alpha$ with the plates. It leaves the plates at angle $\beta$ with kinetic energy $K_2$. Then the ratio of kinetic energies $K_1:K_2$ will be :

Match List I with List II.

An L.C.R. circuit contains resistance of $110\ \Omega$ and a supply of $220$ V at $300\ \text{rad s}^{-1}$ angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by $45°$. If on the other hand, the only the inductor is removed the current leads by $45°$ with the applied voltage. The R.M.S. current flowing in the circuit will be:

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter $0.1\ \mu\text{m}$. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that

An electron of mass $m_e$ and a proton of mass $m_p=1836\ m_e$ are moving with the same speed. The ratio of their de Broglie wavelength $\frac{\lambda_{electron}}{\lambda_{proton}}$ will be :

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength $491$ nm is $0.710$ V. When the incident wavelength is changed to a new value, the stopping potential is $1.43$ V. The new wavelength is :

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from $n=2$ to $n=1$ state is:

The truth table for the following logic circuit is :

For extrinsic semiconductors; when doping level is increased;

If a message signal of frequency $f_m$ is amplitude modulated with a carrier signal of frequency $f_c$ and radiated through an antenna, the wavelength of the corresponding signal in air is

If $\vec{P}\times\vec{Q}=\vec{Q}\times\vec{P}$, the angle between $\vec{P}$ and $\vec{Q}$ is $\theta(0^\circ<\theta<360^\circ)$. The value of $\theta$ will be ___$^\circ$.

Two particles having masses $4$ g and $16$ g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is $n:2$. The value of n will be ___.

The initial velocity $v_i$ required to project a body vertically upward from the surface of the earth to reach a height of $10R$, where R is the radius of the earth, may be described in terms of escape velocity $v_e$ such that $v_i=\sqrt{\dfrac{x}{y}}\times v_e$. The value of x will be

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by $52$ K, its efficiency is doubled. The temperature in Kelvin of the source will be ___ .

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\%$, will be ___ $\%$.

The peak electric field produced by the radiation coming from the $8$ W bulb at a distance of $10$ m is $\dfrac{x}{10}\sqrt{\dfrac{\mu_0 c}{\pi}}\ \text{V m}^{-1}$. The efficiency of the bulb is $10\%$ and it is a point source. The value of x is,

Two small spheres each of mass $10$ mg are suspended from a point by threads $0.5$ m long. They are equally charged and repel each other to a distance of $0.20$ m. The charge on each of the sphere is $\dfrac{a}{21}\times10^{-8}$ C. The value of a will be ___.[Given $g=10\ \text{m s}^{-2}$]

Two identical conducting spheres with negligible volume have $2.1$ nC and $-0.1$ nC charges, respectively. They are brought into contact and then separated by a distance of $0.5$ m. The electrostatic force acting between the spheres is ___$\times10^{-9}$ N.
[Given : $4\pi\varepsilon_0=\dfrac{1}{9\times10^{9}}$ SI unit]

A current of $6$ A enters one corner P of an equilateral triangle PQR having $3$ wires of resistance $2\ \Omega$ each and leaves by the corner R. The currents $i_1$ in ampere is

The wavelength of an X-ray beam is $10$ Å. The mass of a fictitious particle having the same energy as that of the X-ray photons is $\dfrac{x}{3}\,h$ kg. The value of x is ___ . ($h=$ Planck's constant)

Which among the following species has unequal bond lengths?

The solubility of $\text{Ca(OH)}_2$ in water is :
[Given : The solubility product of $\text{Ca(OH)}_2$ in water $= 5.5 \times 10^{-6}$]

Water does not produce CO on reacting with :

Which of the following compound is added to the sodium extract before addition of silver nitrate for testing of halogens?

The correct order of acid character of the following compounds is :

Correct statement about the given chemical reaction is

The major product of the following reaction is :

The correct sequence of reagents used in the preparation of 4 -bromo-2-nitroethylbenzene from benzene is :

Given below are two statements :
Statement I: The pH of rain water is normally $\sim$5.6.
Statement II : If the pH of rain water drops below 5.6 , it is called acid rain.
In the light of the above statements, choose the correct answer from the options given below:

Which one of the following statements is FALSE for hydrophilic sols?

The method used for the purification of Indium is :

The correct order of bond dissociation enthalpy of halogens is :

Given below are two statements :
Statement I : $\alpha$ and $\beta$ forms of sulphur can change reversibly between themselves with slow heating or slow cooling.
Statement II : At room temperature the stable crystalline form of sulphur is monoclinic sulphur.
In the light of the above statements, choose the correct answer from the options given below: