For the reaction

2Fe³⁺(aq) + 2I^$$-$$(aq) $$ \to $$ 2Fe²⁺(aq) + I₂(s)

the magnitude of the standard molar Gibbs free energy change, $$\Delta$$_rG$$_m^o$$ = $$-$$ ___________ kJ (Round off to the Nearest Integer).

$$\left[ {\matrix{ {E_{F{e^{2 + }}/Fe(s)}^o = - 0.440V;} & {E_{F{e^{3 + }}/Fe(s)}^o = - 0.036V} \cr {E_{{I_2}/2{I^ - }}^o = 0.539V;} & {F = 96500C} \cr } } \right]$$

Complete combustion of 3g of ethane gives x $$\times$$ 10²² molecules of water. The value of x is __________. (Round off to the Nearest Integer). [Use : N_A = 6.023 $$\times$$ 10²³; Atomic masses in u : C : 12.0; O : 16.0; H : 1.0]

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :

The solutions of the equation $$\left| {\matrix{ {1 + {{\sin }^2}x} & {{{\sin }^2}x} & {{{\sin }^2}x} \cr {{{\cos }^2}x} & {1 + {{\cos }^2}x} & {{{\cos }^2}x} \cr {4\sin 2x} & {4\sin 2x} & {1 + 4\sin 2x} \cr } } \right| = 0,(0 < x < \pi )$$, are