$A$ torch bulb rated as $4.5\, W, 1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ............. $V$.

Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations $(i)$,$(ii)$ and $(iii)$ are in the ratio:

Which of the following reactions will not result in the formation of carbon-carbon bonds?

In an electroplating experiment,$m \ g$ of silver is deposited when $4 \ A$ of current flows for $2 \ min$. The amount (in $g$) of silver deposited by $6 \ A$ of current flowing for $40 \ s$ will be:

If $\int \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} = (\tan x)^A + C(\tan x)^B + k,$ where $k$ is a constant of integration,then $A + B + C$ equals

Two sources of equal emf $E$ are connected in series to an external resistance $R$. The internal resistances of the two sources are $R_1$ and $R_2$ $(R_2 > R_1)$. If the potential difference across the source having internal resistance $R_2$ is zero,then the value of $R$ is: