If $\cos x + \cos^2 x = 1$,then the value of $\sin^2 x + \sin^4 x$ is

Power dissipated across the $8\,\Omega$ resistor in the circuit shown here is $2\,W$. The power dissipated in watt units across the $3\,\Omega$ resistor is

Which of the following is a scalar quantity?

The number of solutions of the system of equations $2x + y - z = 7$, $x - 3y + 2z = 1$, and $x + 4y - 3z = 5$ is

The specific conductance of a $0.1 \ N \ KCl$ solution at $23 \ ^oC$ is $0.012 \ \Omega^{-1} \ cm^{-1}$. The resistance of the cell containing the solution at the same temperature was found to be $55 \ \Omega$. The cell constant will be ............. $cm^{-1}$.

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and is then compressed to the original volume $V_1$ adiabatically. The initial pressure is $P_1$ and the final pressure is $P_3$. The total work done is $W$. Then: