A homogeneous ideal gaseous reaction $$A{B_{2(g)}} \rightleftharpoons {A_{(g)}} + 2{B_{(g)}}$$ is carried out in a 25 litre flask at 27$$^\circ$$C. The initial amount of AB₂ was 1 mole and the equilibrium pressure was 1.9 atm. The value of K_p is x $$\times$$ 10^$$-$$2. The value of x is _________. (Integer answer)

[R = 0.08206 dm³atm K^$$-$$1mol^$$-$$1]

A certain gas obeys P(V_m $$-$$ b) = RT. The value of $${\left( {{{\partial Z} \over {\partial P}}} \right)_T}$$ is $${{xb} \over {RT}}$$. The value of x is _________. (Integer answer) (Z : compressibility factor)

The maximum value of the term independent of 't' in the expansion
of $${\left( {t{x^{{1 \over 5}}} + {{{{(1 - x)}^{{1 \over {10}}}}} \over t}} \right)^{10}}$$ where x$$\in$$(0, 1) is :

The value of $$\mathop {\lim }\limits_{h \to 0} 2\left\{ {{{\sqrt 3 \sin \left( {{\pi \over 6} + h} \right) - \cos \left( {{\pi \over 6} + h} \right)} \over {\sqrt 3 h\left( {\sqrt 3 \cosh - \sinh } \right)}}} \right\}$$ is :