If $a^{1/x} = b^{1/y} = c^{1/z}$ and $b^2 = ac$,then $x + z = $

$A$ wheel of mass $10 \ kg$ has a moment of inertia of $160 \ kg \cdot m^2$ about its own axis. The radius of gyration will be ....... $m$.

There are $9$ balls to be placed in $9$ boxes. If $5$ of the balls cannot fit into $3$ specific small boxes,find the number of ways of arranging one ball in each of the boxes.

The coordinate axes are rotated through an angle $135^{\circ}$. If the coordinates of a point $P$ in the new system are known to be $(4, -3)$,then the coordinates of $P$ in the original system are

$A$ potentiometer consists of a wire of length $4\, m$ and resistance $10\,\Omega$. It is connected to a cell of $emf$ $2\, V$. The potential difference per unit length of the wire will be ............ $V/m$.

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. $A$ block starting from rest at the top of the plane will again come to rest at the bottom,if the coefficient of friction between the block and the lower half of the plane is given by: