Two plates $$\mathrm{A}$$ and $$\mathrm{B}$$ have thermal conductivities $$84 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$$ and $$126 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $$\mathrm{A}$$ and $$\mathrm{B}$$ are kept at $$100^{\circ} \mathrm{C}$$ and $$0{ }^{\circ} \mathrm{C}$$ respectively, then the temperature of the surface of contact in steady state is _____________ $${ }^{\circ} \mathrm{C}$$.

In an experiment with sonometer when a mass of $$180 \mathrm{~g}$$ is attached to the string, it vibrates with fundamental frequency of $$30 \mathrm{~Hz}$$. When a mass $$\mathrm{m}$$ is attached, the string vibrates with fundamental frequency of $$50 \mathrm{~Hz}$$. The value of $$\mathrm{m}$$ is ___________ g.

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $$24 \mathrm{~cm}^{2}$$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $$12 ~\Omega$$. If an externally applied uniform magnetic field in the core along its axis changes from $$1.5 \mathrm{~T}$$ in one direction to $$1.5 ~\mathrm{T}$$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ___________ $$\mathrm{mC}$$.

In the circuit shown, the energy stored in the capacitor is $$n ~\mu \mathrm{J}$$. The value of $$n$$ is __________