The effective resistance between $P$ and $Q$ for the following network is: (in $\Omega$)

The equivalent resistance of a series combination of two resistors is $s$. When they are connected in parallel,the equivalent resistance is $p$. If $s = np$,then the minimum value for $n$ is (Round off to the nearest integer).

Three unequal resistors in parallel are equivalent to a resistance of $1 \ \Omega$. If two of them are in the ratio $1:2$ and if no resistance value is fractional,then the largest of the three resistances in ohms is

$A$ copper wire of radius $r$ and length $\ell$ is coated with a nickel layer until its radius becomes $2r$. If the resistivities of copper and nickel are $\rho_c$ and $\rho_n$ respectively,find the equivalent resistance of the wire.

Find the effective resistance between $A$ and $B$ in the given circuit.

$A$ heating coil can heat the water of a vessel from $20\,^oC$ to $60\,^oC$ in $30$ minutes. Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be ............ $min$ (neglecting thermal capacity of the coils).