224 mL of SO_2(g) at 298 K and 1 atm is passed through 100 mL of 0.1 M NaOH solution. The non-volatile solute produced is dissolved in 36g of water. The lowering of vapour pressure of solution (assuming the solution in dilute) (P$$_{({H_2}O)}^o$$ $$-$$ 24 mm of Hg) is x $$\times$$ 10^$$-$$2 mm of Hg, the value of x is ___________. (Integer answer)

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 :