$$1 \times 10^{-5} ~\mathrm{M} ~\mathrm{AgNO}_{3}$$ is added to $$1 \mathrm{~L}$$ of saturated solution of $$\mathrm{AgBr}$$. The conductivity of this solution at $$298 \mathrm{~K}$$ is _____________ $$\times 10^{-8} \mathrm{~S} \mathrm{~m}^{-1}$$.

[Given : $$\mathrm{K}_{\mathrm{SP}}(\mathrm{AgBr})=4.9 \times 10^{-13}$$ at $$298 \mathrm{~K}$$

$$ \begin{aligned} & \lambda_{\mathrm{Ag}^{+}}^{0}=6 \times 10^{-3} \mathrm{~S} \mathrm{~m}^{2} \mathrm{~mol}^{-1} \\ & \lambda_{\mathrm{Br}^{-}}^{0}=8 \times 10^{-3} \mathrm{~S} \mathrm{~m}^{2} \mathrm{~mol}^{-1} \\ & \left.\lambda_{\mathrm{NO}_{3}^{-}}^{0}=7 \times 10^{-3} \mathrm{~S} \mathrm{~m}^{2} \mathrm{~mol}^{-1}\right] \end{aligned} $$

Testosterone, which is a steroidal hormone, has the following structure.

The total number of asymmetric carbon atom/s in testosterone is ____________.

$$20 \%$$ of acetic acid is dissociated when its $$5 \mathrm{~g}$$ is added to $$500 \mathrm{~mL}$$ of water. The depression in freezing point of such water is _________ $$\times 10^{-3}{ }^{\circ} \mathrm{C}$$.

Atomic mass of $$\mathrm{C}, \mathrm{H}$$ and $$\mathrm{O}$$ are 12,1 and 16 a.m.u. respectively.

[Given : Molal depression constant and density of water are $$1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$ and $$1 \mathrm{~g} \mathrm{~cm}^{-3}$$ respectively.]

$$0.3 \mathrm{~g}$$ of ethane undergoes combustion at $$27^{\circ} \mathrm{C}$$ in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by $$0.5^{\circ} \mathrm{C}$$. The heat evolved during combustion of ethane at constant pressure is ____________ $$\mathrm{kJ} ~\mathrm{mol}{ }^{-1}$$. (Nearest integer)

[Given : The heat capacity of the calorimeter system is $$20 \mathrm{~kJ} \mathrm{~K}^{-1}, \mathrm{R}=8.3 ~\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$.

Assume ideal gas behaviour.

Atomic mass of $$\mathrm{C}$$ and $$\mathrm{H}$$ are 12 and $$1 \mathrm{~g} \mathrm{~mol}^{-1}$$ respectively]