Catalyst A reduces the activation energy for a reaction by 10 kJ mol^$$-$$1 at 300 K. The ratio of rate constants, $${{{}^kT,\,Catalysed} \over {{}^kT,\,Uncatalysed}}$$ is e^x. The value of x is ___________. [nearest integer]

[Assume that the pre-exponential factor is same in both the cases. Given R = 8.31 J K^$$-$$1 mol^$$-$$1]

Reaction of [Co(H₂O)₆]²⁺ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of electrons present in t_2g-orbitals of the product is ___________.

The moles of methane required to produce 81 g of water after complete combustion is _____________ $$\times$$ 10^$$-$$2 mol. [nearest integer]

Let f : R $$\to$$ R be defined as f (x) = x $$-$$ 1 and g : R $$-$$ {1, $$-$$1} $$\to$$ R be defined as $$g(x) = {{{x^2}} \over {{x^2} - 1}}$$.

Then the function fog is :