Light from a point source in air falls on a convex curved surface of radius $$20 \mathrm{~cm}$$ and refractive index 1.5. If the source is located at $$100 \mathrm{~cm}$$ from the convex surface, the image will be formed at ________ $$\mathrm{cm}$$ from the object.

A nucleus has mass number $$A_1$$ and volume $$V_1$$. Another nucleus has mass number $$A_2$$ and Volume $$V_2$$. If relation between mass number is $$A_2=4 A_1$$, then $$\frac{V_2}{V_1}=$$ __________.

The distance between charges $$+q$$ and $$-q$$ is $$2 l$$ and between $$+2 q$$ and $$-2 q$$ is $$4 l$$. The electrostatic potential at point $$P$$ at a distance $$r$$ from center $$O$$ is $$-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}$$, where the value of $$\alpha$$ is __________. (Use $$\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~Nm}^2 \mathrm{C}^{-2}$$)

The magnetic flux $$\phi$$ (in weber) linked with a closed circuit of resistance $$8 \Omega$$ varies with time (in seconds) as $$\phi=5 t^2-36 t+1$$. The induced current in the circuit at $$t=2 \mathrm{~s}$$ is __________ A.