The specific conductance of a $0.1 \ N \ KCl$ solution at $23 \ ^oC$ is $0.012 \ \Omega^{-1} \ cm^{-1}$. The resistance of the cell containing the solution at the same temperature was found to be $55 \ \Omega$. The cell constant will be ............. $cm^{-1}$.

If $A$ is the areal velocity of a planet of mass $M$,its angular momentum is

If $a$ and $b$ are two non-zero perpendicular vectors, then a vector $y$ satisfying the equations $a \cdot y = c$ (where $c$ is a scalar) and $a \times y = b$ is

$A$ light string fixed at one end to a clamp on the ground passes over a fixed pulley and hangs on the other side. It makes an angle of $30^{\circ}$ with the ground. $A$ monkey of mass $5 \, kg$ climbs up the rope. The clamp can tolerate a vertical force of $40 \, N$ only. The maximum acceleration in the upward direction with which the monkey can climb safely is ............ $m/s^2$ (neglect friction and take $g = 10 \, m/s^2$).

The product $\begin{array}{*{20}{c}} {CH_2 - O - COCH_3} \\ {|} \\ {CH_2 - O - COCH_3} \end{array}$ is obtained by the reaction of which of the following?

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is: