An inductor of $2\,H$ and a resistance of $10\,\Omega$ are connected in series with a battery of $5\,V$. The initial rate of change of current is.....$A/s$.

If the vector $a = 2\hat{i} + 3\hat{j} + 6\hat{k}$ and $b$ are collinear and $|b| = 21$,then $b$ is equal to:

The given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths $A, B, C$. Let $Q, W$,and $\Delta U$ represent the heat supplied to the gas,work done by the gas,and the change in internal energy of the gas,respectively. Which of the following conditions is true?

$A$ wire of length $l$ is bent into a circular loop of radius $R$ and carries a current $I$. The magnetic field at the centre of the loop is $B$. The same wire is now bent into a double loop of equal radii. If both loops carry the same current $I$ and it is in the same direction,the magnetic field at the centre of the double loop will be

The solution of the differential equation $\frac{dy}{dx} = \frac{x-2y+1}{2x-4y}$ is

The rate of formation of new organic matter by a rabbit in a grassland is called: