The length of the transverse common tangent of the circles $x^2+y^2-2x+4y+4=0$ and $x^2+y^2+4x-2y+1=0$ is

$A$ right circular cylinder has a mass $m$,radius $r$,and a height $h$. The cylinder is completely submerged in a fluid of density $\rho$,as shown in the diagram. What is the magnitude of the net force on the cylinder?

Which one of the following elements on doping with germanium,makes it a $p$-type semiconductor?

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now,the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result,the particles move towards each other on the surface. The magnitude of acceleration,when the separation between them becomes $2x$,is

Yeast is used in the production of

In a co-axial,straight cable,the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero: