$A$ cylindrical metallic rod,in thermal contact with two heat reservoirs at its two ends,conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. The amount of heat conducted by the new rod,when placed in thermal contact with the same two reservoirs in time $t$,is:

Alternating current of peak value $\left(\frac{2}{\pi}\right) \text{ A}$ flows through the primary coil of a transformer. The coefficient of mutual inductance between the primary and secondary coil is $1 \text{ H}$. The peak $EMF$ induced in the secondary coil is (Frequency of $AC = 50 \text{ Hz}$): (in $\text{ V}$)

$A$ stationary horizontal disc is free to rotate about its axis. When a torque is applied on it,its kinetic energy as a function of $\theta$,where $\theta$ is the angle by which it has rotated,is given as $K \theta^2$. If its moment of inertia is $I$,then the angular acceleration of the disc is:

An object is projected with a velocity of $20 \ m/s$ making an angle of $45^{\circ}$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$,where $h$ is the height,$x$ is the horizontal distance,and $A$ and $B$ are constants. The ratio $A:B$ is $(g = 10 \ m/s^2)$.

Two rectangular blocks,having identical dimensions,can be arranged either in configuration $I$ or in configuration $II$ as shown in the figure. One of the blocks has thermal conductivity $k$ and the other $2k$. The temperature difference between the ends along the $x-$ axis is the same in both the configurations. It takes $9 \ s$ to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is .......... $\sec$.

Which one of the following equations is correct for the reaction $N_{2(g)} + 3H_{2(g)} \longrightarrow 2NH_{3(g)}$?