Which zone of the blast furnace has the highest temperature?

Two bar magnets $A$ and $B$ are placed one over the other and are allowed to vibrate in a vibration magnetometer. They make $20$ oscillations per minute when the similar poles of $A$ and $B$ are on the same side,while they make $15$ oscillations per minute when their opposite poles lie on the same side. If $M_A$ and $M_B$ are the magnetic moments of $A$ and $B$ and if $M_A > M_B$,the ratio of $M_A$ and $M_B$ is

The least value of the natural number $n$ satisfying $C(n, 5) + C(n, 6) > C(n+1, 5)$ is

The number of oxygen atoms bonded to one phosphorous atom in $P_4O_6$ is

The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc passing through its center is:

The area (in square units) of the region enclosed by the two circles $x^2+y^2=1$ and $(x-1)^2+y^2=1$ is