JEE Advanced Mi...

An ideal gas has adiabatic exponent γ. In some process, its molar heat capacity varies as C = α/T , where α is a constant. Work performed by one mole of gas during its heating from T_o to nT_o will be

Two non-conducting solid spheres of radi R and 2R having uniform volume charge densities ρ₁ and ρ₂ respectively, touch each other. The net electric field at a distance 2R from centre of the smaller sphere is zero. The ratio ρ₁/ρ₂ can be

A thin uniform rod of mass M and length L is hinged at its upper end and released from rest in a horizontal position. Find the tension at a point located at a distance L/3 from the hinge point, when the rod becomes vertical.

Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is

The radioactive decay ₈₃Bi²¹¹ ⟶ ₈₁Tl²⁰⁷, takes place in 100 L, 27°C. Starting with 2 moles of ₈₃Bi²¹¹(t_1/2 =130 sec) sec the pressure development in the vessel after 520 sec will be:

Which chloro derivative of benzene among the following would undergo hydrolysis most readily with aqueous sodium hydroxide to furnish the corresponding hydroxyl derivative?

Let F : R → R be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x ∈ (1/2, 3). Let f(x) = xF(x) for all x ∈ R.

Which of the following statements is incorrect?

Football teams T₁ and T₂ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T₁ winning, drawing and losing a game against T₂ are 1/2, 1/6, and 1/3 respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored, respectively, by teams T₁ and T₂, after two games.

The value of the function f(x) = 1 + x + ∫^x₁(log²t + 2 log t)dt, where f′(x) vanishes