The bulb which glows with maximum intensity in the given circuit is

Column $- I$ gives certain physical terms associated with the flow of current through a metallic conductor. Column $- II$ gives some mathematical relations involving electrical quantities. Match Column $- I$ and Column $- II$ with appropriate relations.

Column $- I$	Column $- II$
$(A)$ Drift Velocity	$(P)$ $\frac{m}{n e^{2} \rho}$
$(B)$ Electrical Resistivity	$(Q)$ $n e v_{d}$
$(C)$ Relaxation Period	$(R)$ $\frac{e E}{m} \tau$
$(D)$ Current Density	$(S)$ $\frac{E}{J}$

In the following circuit,a bulb is rated as $1.5\, V$,$0.45\, W$. If the bulb glows with full intensity,then what will be the equivalent resistance between $X$ and $Y$? ............. $\Omega$

The terminal voltage $V$ across a battery of $emf$ $E$ and internal resistance $r$ can be:

The temperature at which thermo-emf is zero is

Due to cold weather,a $1\, m$ water pipe of cross-sectional area $1\, cm^2$ is filled with ice at $-10^{\circ}C$. Resistive heating is used to melt the ice. $A$ current of $0.5\, A$ is passed through a $4\, k\Omega$ resistance. Assuming that all the heat produced is used for melting,what is the minimum time required? (In $s$)
(Given: latent heat of fusion for water/ice $= 3.33 \times 10^5\, J/kg$,specific heat of ice $= 2 \times 10^3\, J/(kg\cdot K)$ and density of ice $= 10^3\, kg/m^3$)