JEE Advance 2021 Question Paper with Solutions - 1 - JEE MCQ

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decay of Q in the first one hour is

A projectile is thrown from a point O on the ground at an angle 45° from the vertical and with a speed 5√2m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after the splitting, falls to the ground at a distance x metres from the point O. The acceleration due to gravity g = 10 m/s².

The value of t is ____.

A projectile is thrown from a point O on the ground at an angle 45° from the vertical and with a speed 5√2 m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after the splitting, falls to the ground at a distance x metres from the point O. The acceleration due to gravity g = 10 m/s².
Q. The value of x is ____.

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q₁ μC. Then S is switched to position Q. After a long time, the charge on the capacitor is q₂ μC.

Q. The magnitude of q₁ is ____.

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q₁ μC. Then S is switched to position Q. After a long time, the charge on the capacitor is q₂ μC.

Q. The magnitude of q₂ is ____.

Two point charges -Q and +Q/√3 are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its centre at (b, 0). All lengths are measured in metres.

Q. The value of R is _______ metres.

Two point charges -Q and +Q/√3 are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its centre at (b, 0). All lengths are measured in metres.

Q. The value of b is _______ metres.

A horizontal force F is applied at the centre of mass of a cylindrical object of mass m and radius R, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is. The centre of mass of the object has an acceleration a. The acceleration due to gravity is g. Given that the object rolls without slipping, which of the following statement(s) is(are) correct?

A wide slab consisting of two media of refractive indices n1 and n2 is placed in the air as shown in the figure. A ray of light is incident from medium n1 to n2 at an angle, where sin is slightly larger than 1/n1. Take the refractive index of air as 1. Which of the following statement(s) is(are) correct?

A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = -l, y = -h), where l = 10 m and h = 1 m . The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s² along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by  and , respectively.  and  are unit vectors along the positive x, y and z directions, respectively. If , then which of the following statements is/are correct?

Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?

15:A long straight wire carries a current, l = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure).
A resistor R = 1.4 and a capacitor C₀ = 5.0 F are connected in series between the rails. At time t = 0, C₀ is uncharged. Which of the following statement(s) is(are) correct? [μ₀ = 4 × 10^–7 SI units. Take ln 2 = 0.7]

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle θ = 45°. P₁ and P₂ are pressures at points 1 and 2, respectively located at the base of the tube. Let β = (P₁ - P₂)/(ρgd), where ρ is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statements is/are correct?

An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii r_α and r_s respectively. The ratio r_s/r_α is ________.

A thin rod of mass M and length a is free to rotate in a horizontal plane about a fixed vertical axis passing through point O. A thin circular disc of mass M and of radius a/4 is pivoted on this rod with its centre at a distance a/4 from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity and the disc rotating about its vertical axis with angular velocity 4Ω. The total angular momentum of the syStatement about the point O is 

Q. The value of n is _________.

A small object is placed at the centre of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object becomes 100 K at t = t₁ and 50 K at t = t₂. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio (t₂/t₁) is ____,

The major product formed in the following reaction is

Among the following, the conformation that corresponds to the most stable conformation of meso-butane-2,3-diol is

For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately

The calculated spin only magnetic moments of [Cr(NH₃)₆]³⁺ and [CuF₆]^3- in BM respectively are:
(Atomic numbers of Cr and Cu are 24 and 29, respectively)

For the following reaction scheme, percentage yields are given along the arrow:

x g and y g are masses of R and U, respectively.
(Use molar mass (in g mol^-1) of H, C and O as 1, 12 and 16, respectively)
Q. The value of x is ___.

For the following reaction scheme, percentage yields are given along the arrow:

x g and y g are masses of R and U, respectively.
(Use molar mass (in g mol^-1) of H, C and O as 1, 12 and 16, respectively)
Q. The value of y is ___.

For the reaction: X(s)  Y(s) + Z(g), the plot of In  versus  is given below (in solid line), where p_z is the pressure (in bar) of the gas Z at temperature T and p^o = 1 bar.

(Given: , where the equilibrium constant, K =  and the gas constant, R = 8.314 J K^-1 mol^-1)
The value of standard enthalpy,  (in kJ mol^-1), for the given reaction is ______.

or the reaction: X(s)  Y(s) + Z(g), the plot of In  versus  is given below (in solid line), where p_z is the pressure (in bar) of the gas Z at temperature T and p^o = 1 bar.

(Given: , where the equilibrium constant, K =  and the gas constant, R = 8.314 J K^-1 mol^-1)
The value of  (in  J K^-1 mol^-1) for the given reaction at 1000 K is _______.

The boiling point of water in a 0.1 molal silver nitrate solution (solution A) is x°C. To this solution A, an equal volume of 0.1 molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions A and B is y × 10^-2 °C.
(Assume: Densities of the solutions A and B are the same as that of water and the soluble salts dissociate completely.
Use: Molal elevation constant (Ebullioscopic Constant), K_b = 0.5 K kg mol^-1; Boiling point of pure water is 100°C.)
Q. The value of x is ___.

The boiling point of water in a 0.1 molal silver nitrate solution (solution A) is x°C. To this solution A, an equal volume of 0.1 molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions A and B is y × 10^-2 °C.
(Assume: Densities of the solutions A and B are the same as that of water and the soluble salts dissociate completely.
Use: Molal elevation constant (Ebullioscopic Constant), K_b = 0.5 K kg mol^-1; Boiling point of pure water is 100°C.)
Q. The value of |y| is ___.

Given:

The compound(s) which on reaction with HNO₃ will give the product having degree of rotation [α]_D = -52.7° is/are