JEE Advance 2021 Question Paper with Solutions - 2 - JEE MCQ

A physical quantity  is defined as , where  is electric field,  magnetic field and μ₀ is the permeability of free space. The dimensions of  are the same as the dimensions of which of the following quantities?

A heavy nucleus N, at rest, undergoes fission N → P + Q, where P and Q are two lighter nuclei. Let δ = M_N - M_P - M_Q, where M_P, M_Q and M_N are the masses of P, Q and N, respectively. E_P and E_Q are the kinetic energies of P and Q, respectively. The speeds of P and Q are V_P and V_Q, respectively. If c is the speed of light, which of the following statements is/are correct?

Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common centre, as shown in the figure. The smaller loop carries current I₁ in the anti-clockwise direction and the larger loop carries current I₂ in the clockwise direction, with I₂ > 2I₁.  denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statements is/are correct?

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test tube with some air (ideal gas) trapped as shown in the figure. The test tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc.
Initially the bottle is sealed at atmospheric pressure p₀ = 10⁵ Pa so that the volume of the trapped air is v₀ = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p₀ + Δp without changing its orientation.
At this pressure, the volume of the trapped air is v₀ - Δv.
Let Δv = X cc and Δp = Y x 10³ Pa.

Q. The value of X is _______.

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test tube with some air (ideal gas) trapped as shown in the figure. The test tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc.
Initially the bottle is sealed at atmospheric pressure p₀ = 10⁵ Pa so that the volume of the trapped air is v₀ = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p₀ + Δp without changing its orientation.
At this pressure, the volume of the trapped air is v₀ - Δv.
Let Δv = X cc and Δp = Y x 10³ Pa.

Q. The value of Y is _______.

A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m²/s. The kinetic energy of the pendulum just after the lift-off is K joules.

Q. The value of J is ______.

A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m²/s. The kinetic energy of the pendulum just after the lift-off is K joules.

Q. The value of K is ______.

In the circuit, a metal filament lamp is connected in series with a capacitor of capacitance CμF across a 200 V, 50 Hz supply. The power consumed by the lamp is 500 W while the voltage drop across it is 100 V. Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase angle (in degrees) between the current and supply voltage is ϕ. Assume π√3 ≈ 5.

Q. The value of C is _____.

In the circuit, a metal filament lamp is connected in series with a capacitor of capacitance CμF across a 200 V, 50 Hz supply. The power consumed by the lamp is 500 W while the voltage drop across it is 100 V. Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase angle (in degrees) between the current and supply voltage is ϕ. Assume π√3 ≈ 5.

Q. The value of ϕ is _____.

A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux.
The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius a, with its centre at the origin. A magnetic dipole of moment m is brought along the axis of this loop from infinity to a point at distance r (>> a) from the centre of the loop with its north pole always facing the loop, as shown in the figure below.
The magnitude of magnetic field of a dipole m, at a point on its axis at distance r, is , where μ₀ is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, m₁ and m₂, separated by a distance r on the common axis, with their north poles facing each other, is , where k is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.

Q. When the dipole m is placed at a distance r from the centre of the loop (as shown in the figure), the current induced in the loop will be proportional to

A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux.
The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius a, with its centre at the origin. A magnetic dipole of moment m is brought along the axis of this loop from infinity to a point at distance r (>> a) from the centre of the loop with its north pole always facing the loop, as shown in the figure below.
The magnitude of magnetic field of a dipole m, at a point on its axis at distance r, is , where μ₀ is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, m₁ and m₂, separated by a distance r on the common axis, with their north poles facing each other, is , where k is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.

Q. The work done in bringing the dipole from infinity to a distance r from the centre of the loop by the given process is proportional to

A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, C_V = 2R. Here, R is the gas constant. Initially, each side has a volume V₀ and temperature T₀. The left side has an electric heater, which is turned on at very low power to transfer heat Q to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to V₀/2. Consequently, the gas temperatures on the left and the right sides become T_L and T_R, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.

Q. The value of T_R/T₀ is

A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, C_V = 2R. Here, R is the gas constant. Initially, each side has a volume V₀ and temperature T₀. The left side has an electric heater, which is turned on at very low power to transfer heat Q to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to V₀/2. Consequently, the gas temperatures on the left and the right sides become T_L and T_R, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.

Q. The value of Q/RT₀ is

In order to measure the internal resistance r₁ of a cell of emf E, a meter bridge of wire resistance R₀ = 50Ω , a resistance R₀/2, another cell of emf E/2 (internal resistance r) and a galvanometer G are used in a circuit, as shown in the figure. If the null point is found at  ℓ = 72 cm, then the value of r₁ = ___Ω.

The distance between two stars of masses 3M_S and 6M_S is 9R. Here, R is the mean distance between the centres of the Earth and the Sun, and M_S is the mass of the Sun. The two stars orbit around their common centre of mass in circular orbits with period nT, where T is the period of Earth's revolution around the Sun.

Q. The value of n is ______.

In a photoemission experiment, the maximum kinetic energies of photoelectrons from metals P, Q and R are EP, E_Q and ER, respectively, and they are related by E_P = 2E_Q = 2E_R. In this experiment, the same source of monochromatic light is used for metals P and Q while a different source of monochromatic light is used for the metal R. The work functions for metals P, Q and R are 4.0 eV, 4.5 eV and 5.5 eV, respectively. The energy of the incident photon used for metal R, in eV, is ______.

The reaction sequence(s) that would lead to o-xylene as the major product is/are

Correct option(s) for the following sequence of reactions is/are:

For the following reaction 2X + Y  P, the rate of reaction is d[P]/dt = k[X]. Two moles of X are mixed with one mole of Y to make 1.0 L of solution. At 50 s, 0.5 mole of Y is left in the reaction mixture. The correct statement(s) about the reaction is/are:
(Use ln 2 = 0.693)

Some standard electrode potentials at 298 K are given below:
Pb²⁺/Pb - 0.13 V
Ni²⁺/Ni - 0.24 V
Cd²⁺/Cd - 0.40 V
Fe²⁺/Fe - 0.44 V
To a solution containing 0.001 M of X2+ and 0.1 M of Y²⁺, the metal rods X and Y are inserted (at 298 K) and connected by a conducting wire. This resulted in dissolution of X. The correct combination(s) of X and Y, respectively, is/are:
(Given: Gas constant, R = 8.314 J K^-1 mol^-1, Faraday constant, F = 96,500 C mol^-1)

The pair(s) of complexes wherein both exhibit tetrahedral geometry is/are
(Note: py = pyridine; Given: Atomic numbers of Fe, Co, Ni and Cu are 26, 27, 28 and 29, respectively)

The correct statement(s) related to oxoacids of phosphorus is/are:

At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 x 10² S cm² mol^-1. At 298 K, for an aqueous solution of the acid, the degree of dissociation is  and the molar conductivity is y x 10² S cm² mol^-1. At 298 K, upon 20 times dilution with water, the molar conductivity of the solution becomes 3y x 10² S cm² mol^-1.

Q. The value of α is _______.

At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 x 10² S cm² mol^-1. At 298 K, for an aqueous solution of the acid, the degree of dissociation is  and the molar conductivity is y x 10² S cm² mol^-1. At 298 K, upon 20 times dilution with water, the molar conductivity of the solution becomes 3y x 10² S cm² mol^-1.

Q. The value of y is _______.

Reaction of x g of Sn with HCl quantitatively produced a salt. Entire amount of the salt reacted with y g of nitrobenzene in the presence of required amount of HCl to produce 1.29 g of an organic salt (quantitatively).
(Use Molar masses (in g mol^-1) of H, C, N, O, Cl and Sn as 1, 12, 14, 16, 35 and 119, respectively)

Q. The value of x is _______.

Reaction of x g of Sn with HCl quantitatively produced a salt. Entire amount of the salt reacted with y g of nitrobenzene in the presence of required amount of HCl to produce 1.29 g of an organic salt (quantitatively).
(Use Molar masses (in g mol^-1) of H, C, N, O, Cl and Sn as 1, 12, 14, 16, 35 and 119, respectively)

Q. The value of y is _______.

A sample (5.6 g) containing iron is completely dissolved in cold dilute HCl to prepare a 250 mL of solution. Titration of 25.0 mL of this solution requires 12.5 mL of 0.03 M KMnO4 solution to reach the end point. Number of moles of Fe²⁺ present in 250 mL solution is x × 10⁻² (consider complete dissolution of FeCl₂). The amount of iron present in the sample is y% by weight.
(Assume: KMnO₄ reacts only with Fe²⁺ in the solution, Use: Molar mass of iron as 56 g mol⁻¹)

Q. The value of x is _______.