If x = 1 is a critical point of the function
f(x) = (3x² + ax – 2 – a)e^x , then :

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

Nitrogen gas is at 300^oC temperature. The temperature (in K) at which the rms speed of a H₂ molecule would be equal to the rms speed of a nitrogen molecule, is _______.
(Molar mass of N₂ gas 28 g).

In an experiment to verify Stokes law, a small spherical ball of radius r and density $$\rho $$ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to :
(ignore viscosity of air)