$A$ conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires $AB$ and $CD$ are

Electric charges of $+10\,\mu C$,$+5\,\mu C$,$-3\,\mu C$,and $+8\,\mu C$ are placed at the corners of a square of side $\sqrt{2}\,m$. The potential at the centre of the square is:

The solution of $x \frac{dy}{dx} = y + x e^{y/x}$ with $y(1) = 0$ is

The truth table for the system of four $NAND$ gates as shown in the figure is:

An electronic transition in a hydrogen atom results in the formation of the $H_\alpha$ line of the hydrogen spectrum in the Lyman series. The energies associated with the electron in each of the orbits involved in the transition (in $kcal \ mol^{-1}$) are:

The origin is translated to $(1,2)$. The point $(7,5)$ in the old system undergoes the following transformations successively.
$I$. Moves to the new point under the given translation of origin.
$II$. Translated through $2$ units along the negative direction of the new $X$-axis.
$III$. Rotated through an angle $\frac{\pi}{4}$ about the origin of the new system in the clockwise direction. The final position of the point $(7,5)$ is