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).

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$,then $A^3 - 4A^2 - 6A$ is equal to:

Which of the following does not contain any co-ordinate bond?

$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)

When a current of $2\, A$ flows in a battery from negative to positive terminal, the potential difference across it is $12\, V$. If a current of $3\, A$ flows in the opposite direction, the potential difference across the terminals of the battery is $15\, V$. The $emf$ of the battery is ............... $V$.

If there is an error of $\pm 0.04 \text{ cm}$ in the measurement of the diameter of a sphere,then the approximate percentage error in its volume,when the radius is $10 \text{ cm}$,is