For the reaction 2A + B $$ \to $$ C, the values of initial rate at diffrent reactant concentrations are given in the table below. The rate law for the reaction is :

[A] (mol L-1)	[B] (mol L-1)	Initial Rate (mol L-1s-1)
0.05	0.05	0.045
0.10	0.05	0.090
0.20	0.10	0.72

The vapour pressures of pure liquids A and B are 400 and 600 mmHg, respectively at 298 K on mixing the two liquids, the sum of their initial volume is equal ot the volume of the final mixture. The mole fraction of liquid B is 0.5 in the mixture, The vapour pressure of the final solution, the mole fractions of components A and B in vapour phase, respectively are :

For silver, C_p(J K^–1 mol^–1) = 23 +0.01 T. If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of $$\Delta H$$ will be close to :

If $$\alpha = {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$, $$\beta = {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$ where $$0 < \alpha ,\beta < {\pi \over 2}$$ , then $$\alpha $$ - $$\beta $$ is equal to :