A body of mass (2M) splits into four masses (m, M $$-$$ m, m, M $$-$$ m}, which are rearranged to form a square as shown in the figure. The ratio of $${M \over m}$$ for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ............ .

The alternating current is given by $$i = \left\{ {\sqrt {42} \sin \left( {{{2\pi } \over T}t} \right) + 10} \right\}A$$

The r.m.s. value of of this current is ................. A.

A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V₀. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1 : $$\sqrt y $$ where y is ................. .

First, a set of n equal resistors of 10 $$\Omega$$ each are connected in series to a battery of emf 20V and internal resistance 10$$\Omega$$. A current I is observed to flow. Then, the n resistors are connected in parallel to the same battery. It is observed that the current is increased 20 times, then the value of n is ............... .