Two insulated circular loop A and B of radius '$$a$$' carrying a current of '$$\mathrm{I}$$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $$2 \mathrm{~kg}$$ is :

An electric toaster has resistance of $$60 \Omega$$ at room temperature $$\left(27^{\circ} \mathrm{C}\right)$$. The toaster is connected to a $$220 \mathrm{~V}$$ supply. If the current flowing through it reaches $$2.75 \mathrm{~A}$$, the temperature attained by toaster is around : ( if $$\alpha=2 \times 10^{-4}$$/$$^\circ \mathrm{C}$$)

A spherical body of mass $$100 \mathrm{~g}$$ is dropped from a height of $$10 \mathrm{~m}$$ from the ground. After hitting the ground, the body rebounds to a height of $$5 \mathrm{~m}$$. The impulse of force imparted by the ground to the body is given by : (given, $$\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$$)