The number of common tangents to the two circles $x^2+y^2-8x+2y=0$ and $x^2+y^2-2x-16y+25=0$ is:

In the circuit shown,the current in the $1\,\Omega$ resistor is

$A$ sinusoidal voltage of peak value $200 \ V$ is connected to a diode and a resistor $R$ in the circuit shown,such that half-wave rectification occurs. If the forward resistance of the diode is negligible compared to $R$,the rms voltage (in volt) across $R$ is approximately:

$A$ straight wire of length $20 \ cm$ carrying a current of $\frac{3}{\pi^2} \ A$ is bent in the form of a circle. The magnetic field at the centre of the circle is

$A$ sample of $0.1 \ g$ of water at $100^{\circ} C$ and normal pressure $(1.013 \times 10^5 \ N m^{-2})$ requires $54 \ cal$ of heat energy to convert to steam at $100^{\circ} C$. If the volume of the steam produced is $167.1 \ cc$,the change in internal energy of the sample is ....... $J$.

Let $l_1$ and $l_2$ be two lines intersecting at $P$. If $A_1, B_1, C_1$ are points on $l_1$,and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and if none of these coincides with $P$,then the number of triangles formed by these eight points is: