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 ............... $V$.

$A$ non-conducting body floats in a liquid at $20^{\circ} C$ with $\frac{2}{3}$ of its volume immersed in the liquid. When the liquid temperature is increased to $100^{\circ} C$, $\frac{3}{4}$ of the body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of the container of the liquid):

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows:

If the maximum and minimum voltage of an amplitude modulated wave are $V_{max}$ and $V_{min}$ respectively,then the modulation factor is:

The point $(3,-4)$ lies on both the circles $x^2+y^2-2x+8y+13=0$ and $x^2+y^2-4x+6y+11=0$. Then,the angle between the circles is

The solution of $\frac{dy}{dx} = \frac{y^2}{xy - x^2}$ is