One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27$$^\circ$$ C to 37$$^\circ$$ C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol^$$-$$1 k^$$-$$1]

An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $$t = {T \over 4}s$$ starting from mean position. Assume that the initial phase of the oscillation is zero.

Match List I with List II.

	List - I		List - II
(a)	Capacitance, C	(i)	$${M^1}{L^1}{T^{ - 3}}{A^{ - 1}}$$
(b)	Permittivity of free space, $${\varepsilon _0}$$	(ii)	$${M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$$
(c)	Permeability of free space, $${\mu _0}$$	(iii)	$${M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$$
(d)	Electric field, E	(iv)	$${M^1}{L^1}{T^{ - 2}}{A^{ - 2}}$$

Choose the correct answer from the options given below

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that E_mech = 8 J, the incorrect statement for this system is :


[ where K.E. = kinetic energy ]