Charges of $2 \mu C$ and $-3 \mu C$ are placed at two points $A$ and $B$ separated by $1 \ m$. The distance of the point from $A$,where the net potential is zero,is (in $m$)

The time taken for a calorimeter containing $75 \ g$ of water at $62^{\circ} C$ to cool to $58^{\circ} C$ is $9 \ \text{minutes}$. When the calorimeter contains $105 \ g$ of water, it takes $12 \ \text{minutes}$ to cool from $62^{\circ} C$ to $58^{\circ} C$. The water equivalent of the calorimeter is: (in $g$)

$A$ car is moving along a straight line,say $OP$ in the given figure. It moves from $O$ to $P$ in $18 \; s$ and returns from $P$ to $Q$ in $6.0 \; s$. What are the average velocity and average speed of the car in going from $O$ to $P$?

$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to

$A$ thermodynamic system is taken through the cycle $PQRS P$ process as shown in the figure. The net work done by the system is ......... $J$.

The locus of the point $z = x + iy$ satisfying the equation $\left|\frac{z-1}{z+1}\right| = 1$ is given by: