For the reaction A_(g) $$ \to $$ B_(g) the value of the equilibrium constant at 300 K and 1 atm is equal to 100.0. The value of $$\Delta $$_rG for the reaction at 300 K and 1 atm in J mol^-1 is – xR, where x is _______. (Rounded off to the nearest integer)
[R = 8.31 J mol^–1K^-1 and ln 10 = 2.3)

Gaseous cyclobutene isomerises to butadiene in a first order process which has a 'k' value of 3.3 $$ \times $$ 10^-4 s^-1 at 153°C. The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is ______.
(Rounded off to the nearest integer)

If $$\int {{{\cos x - \sin x} \over {\sqrt {8 - \sin 2x} }}} dx = a{\sin ^{ - 1}}\left( {{{\sin x + \cos x} \over b}} \right) + c$$, where c is a constant of integration, then the ordered pair (a, b) is equal to :

If f : R $$ \to $$ R is a function defined by f(x)= [x - 1] $$\cos \left( {{{2x - 1} \over 2}} \right)\pi $$, where [.] denotes the greatest integer function, then f is :