JEE Advanced Mock Test - 4 (Paper II) - JEE MCQ

A long current carrying straight wire having current I₁ = 10⁴ ampere is placed at the centre of an another current carrying loop having current I₂ = 10⁴ ampere. Straight wire is perpendicular to the plane of the loop as shown in the figure. The torque (in N m) acting on the loop about its center is 10x. Find the value of x. (Radius R = 1 m)

During an adiabatic process, the pressure of a gas is found to be proportional to cube of its absolute temperature, C_v / C_p is

A part of circuit in a steady state along with the currents flowing in the branches, the values of resistances, etc. is shown in the figure. Calculate the energy (in mJ) stored in the capacitor C (4μF).

(Round off up to 2 decimal places)

The figure below shows a conducting rod of negligible resistance that can slide on smooth U-shaped rail made of wire of resistance 2 Ω/m. The position of the conducting rod at t = 0 is shown. A time-dependent magnetic field B = 4t T is switched on at t = 0.

The rod moves towards right at 10 cm/s. The current (in A) in the loop at t = 3 s due to induced emf is

(Round off up to 2 decimal places)

A sample of air is initially at 533 K and 700 N/m², and occupies a volume of 0.028 m³. The air is expanded at constant pressure to three times. A polytropic process with n = 1.5 is then carried out followed by an isothermal process which completes the cycle.

The efficiency of the cycle (in %) is:

A sonometer wire resonates with a given turning fork forming standing waves with five antinodes between two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by M, the wire resonates with the same tuning fork forming three antinodes for the same positions of bridges. The value of M (in kg) is

If two structures of the same cross-sectional area but different numerical apertures NA₁ and NA₂ (NA₂ < NA₁) are joined longitudinally, the numerical aperture of the combined structure is ____.

1. 
2. NA₁ + NA₂
3. NA₁
4. NA₂
(Enter your answer as per respective numbering 1, 2, 3, 4 given above.)

For two structures namely S1 with n₁ = √⁴⁵/₄ and n₂ = 3/₂ and S₂ with n₁ = 8/₅ and n₂ = 7/₅, and taking the refractive index of water to be 4/₃ and that of air to be 1, consider the following statements:

1. NA of S₁ immersed in water is the same as that of S₂ immersed in a liquid of refractive index 16/_3√15.
2. NA of S₁ immersed in liquid of refractive index 6/_√15 is the same as that of S₂ immersed in water.
3. NA of S₁ placed in air is the same as that of S₂ immersed in liquid of refractive index 4/_√15.
4. NA of S₁ placed in air is the same as that of S₂ placed in water.

How many of the above given statements are correct?

If the piston is pushed at a speed of 5 mms^–1, the air comes out of the nozzle with a speed of ____ m/s.

If the density of air is p_a and that of the liquid is p_l, then for a given piston speed, the rate (volume per unit time) at which the liquid is sprayed will be proportional to _____.

(Enter your answer as per respective numbering 1, 2, 3, 4 given above.)

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

When a potential difference of 10³V is applied between A and B , a charge of 0.75 mC is stored in the system of capacitors. The value of C is (μF)

The decreasing order of hyperconjugative effect is

Enthalpy of dissociation of acetic acid obtained from Experiment 2 is _____. (kJ mol^-1)

The pH of the solution after Experiment 2 is k × 10^-1. What will be the value of k?

Compound X is

(Mark the compound as per their respective numbering given in the question.)

The major compound Y is

(Mark the compound as per their respective numbering given in the question.)

The value of r is .  Find the value of n.

If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is  . Find the value of m.

The value of   is nπ.  Find the value of n.

The value of  is

A sphere of radius R carries a positive charge whose volume density depends only on separation r from the sphere's centre. It is according to the formula where p₀ is a constant.
Which of the following is/are true?

The mass of a nucleus is less than the sum of the masses of (A – Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m₁ and m₂ only if (m₁ + m₂) < M. Also, two light nuclei of masses m₃ and m₄ can undergo complete fusing and form a heavy nucleus of mass M' only if (m₃ + m₄) > M'. The masses of some neutral atoms are given in the table below:

The kinetic energy (in keV) of the alpha particle, when the nucleus   at rest undergoes alpha decay, is:

Find which of the following compounds can have mass ratio of C : H : O as 6 : 1 : 24.

Which of the following represents Schotten-Baumann reaction?

The sum of the series 

If the number of terms in the expansion of (x - 2y + 3z)n is 45, then what is the value of n?