The observed magnetic moment of the complex $$\left.\left[\operatorname{Mn}(\underline{N} C S)_{6}\right)\right]^{x^{-}}$$ is $$6.06 ~\mathrm{BM}$$. The numerical value of $$x$$ is __________.

The solubility product of $$\mathrm{BaSO}_{4}$$ is $$1 \times 10^{-10}$$ at $$298 \mathrm{~K}$$. The solubility of $$\mathrm{BaSO}_{4}$$ in $$0.1 ~\mathrm{M} ~\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})$$ solution is ___________ $$\times 10^{-9} \mathrm{~g} \mathrm{~L}^{-1}$$ (nearest integer).

Given: Molar mass of $$\mathrm{BaSO}_{4}$$ is $$233 \mathrm{~g} \mathrm{~mol}^{-1}$$

If the boiling points of two solvents X and Y (having same molecular weights) are in the ratio $$2: 1$$ and their enthalpy of vaporizations are in the ratio $$1: 2$$, then the boiling point elevation constant of $$\mathrm{X}$$ is $$\underline{\mathrm{m}}$$ times the boiling point elevation constant of Y. The value of m is ____________ (nearest integer)

For complete combustion of ethene.

$$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$$

the amount of heat produced as measured in bomb calorimeter is $$1406 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ at $$300 \mathrm{~K}$$. The minimum value of $$\mathrm{T} \Delta \mathrm{S}$$ needed to reach equilibrium is ($$-$$) _________ $$\mathrm{kJ}$$. (Nearest integer)

Given : $$\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$