The period of revolution of planet $$\mathrm{A}$$ around the sun is 8 times that of planet $$\mathrm{B}$$. How many times the distance of A from the sun is greater than that of B from the sun?

Two identical capacitors have the same capacitance '$$\mathrm{C}$$'. One of them is charged to potential '$$\mathrm{V_1}$$' and the other to $$\mathrm{V_2}$$. The negative ends of the capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring balance reads $$49 \mathrm{~N}$$, when the lift is stationary. If the lift moves downward with an acceleration of $$5 \mathrm{~m} / \mathrm{s}^2$$, the reading of the spring balance will be $$(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2)$$

In a potentiometer experiement, when three cells $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are connected in series, the balancing length is found to be $$420 \mathrm{~cm}$$. If cells $$\mathrm{A}$$ and $$\mathrm{B}$$ are connected in series the balancing length is $$220 \mathrm{~cm}$$ and for cells $$\mathrm{B}$$ and $$\mathrm{C}$$ connected in series in balancing length is $$320 \mathrm{~cm}$$. The emf of cells $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are respectively in the ratio of