The resistance in the following circuit is increased at a particular instant. At this instant,the value of resistance is $10 \, \Omega$. The current in the circuit will be now:

$A$ thin wire of length $l$ and mass $M$ is bent in the form of a semicircle. What is its moment of inertia about an axis passing through the ends of the wire?

For a ray of light,the critical angle is minimum when it travels from

If the number of diagonals of a regular polygon is $35$,then the number of sides of the polygon is

If $\sin^{-1}(\frac{x}{5}) + \csc^{-1}(\frac{5}{4}) = \frac{\pi}{2}$,then $x = $

Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $k_1$ and $k_2$ respectively. $A$ steady temperature difference of $12^{\circ} C$ is maintained across the composite slab. If $k_1 = \frac{k_2}{2}$,the temperature difference across slab $A$ is (in $^{\circ} C$)