The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$ is:

The number of points in $(-\infty, \infty)$ for which $x^2 - x \sin x - \cos x = 0$ is

The biquadratic equation,two of whose roots are $1+i$ and $1-\sqrt{2}$,is

Why does molten sodium chloride conduct electricity?

The primary and secondary coils of a transformer have $50$ and $1500$ turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi = \phi_0 + 4t$,where $\phi$ is in webers,$t$ is time in seconds,and $\phi_0$ is a constant,the output voltage across the secondary coil is ...... $volts$.

The rate of steady volume flow of water through a capillary tube of length $l$ and radius $r$, under a pressure difference of $p$ is $V$. This tube is connected with another tube of the same length but half the radius, in series. Then, the rate of steady volume flow through them is (The pressure difference across the combination is $p$.)