JEE Advanced Mi...

Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle.

Assume that the sound of the whistle is composed of components varying in frequency from f₁ = 800 Hz to f₂ = 1120 Hz, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s.

The spread of frequency as observed by the passengers in train B is

A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s^-2).

The magnitude of the normal reaction that acts on the block at the point Q is

Work function of metal A is equal to the ionization energy of hydrogen atom in first excited state. Work function of metal B is equal to the ionization energy of He+ ion in second orbit. Photons of same energy E are incident on both A and B. Maximum kinetic energy of photoelectrons emitted from A is twice that of photoelectrons emitted from B.

Value of E ( in eV) is

A glass tube AD of uniform cross-section of length 100 cm100 cm sealed at both ends contains two columns of ideal gas AB and CD separated by a column of mercury of length 20 cm20 cm. When the tube is held horizontally, AB = 20 cm cm and CD = 60 cm. When the tube is held vertically with the end A up, the mercury column moves down 10 cm10 cm. What will be the length of gas column AB when the tube is held vertically with the end D up? (Give answer upto two digits after decimal point.)

A gas is enclosed in a cylinder with a piston. Weights are added to the piston, giving a total mass of 2.20 kg. As a result, the gas is compressed and the weights are lowered 0.25 m. At the same time, 1.50 J of heat is evolved from the system. What is the change in internal energy of the system? (Take g = 9.8 m/sec²)

.0 L each of CH₄ (g) at 1.00 atm, and O₂ (g) at 4.00 atm, at 300^oC are taken and allowed to react by initiating the reaction with the help of a spark.

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g), ΔH = -802 kJ 

Mass of CO₂ (g) produced in the reaction is

(Round off up to 2 decimal places)

The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match, the probability that in a 5-match series, India's second win occurs in the third test, is (Round off up to 2 decimal places)

The order of the differential equation whose general solution is given by y = (c₁ + c₂) cos(x + c₃) - c₄ex + c₅, where c₁, c₂, c₃, c₄ and c₅ are arbitrary constants is

If z is any complex number satisfying |z - 3 - 2i| ≤ 2, then the minimum value of |2z - 6 + 5i| is