For the reaction,
A(g) + B(g) $$ \to $$ C(g) + D(g), $$\Delta $$H^o and $$\Delta $$S^o are, respectively, − 29.8 kJ mol⁻¹ and −0.100 kJ K⁻¹ mol⁻¹ at 298 K. The equilibrium constant for the reaction at 298 K is :

Let x, y, z be positive real numbers such that x + y + z = 12 and x³y⁴z⁵ = (0.1) (600)³. Then x³ + y³ + z³is equal to :

If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :

If   $$\int {{{dx} \over {{{\cos }^3}x\sqrt {2\sin 2x} }}} = {\left( {\tan x} \right)^A} + C{\left( {\tan x} \right)^B} + k,$$

where k is a constant of integration, then A + B +C equals :