Name the gas that can readily decolourise acidified $KMnO_4$ solution.

If $a \sin^2 \theta + b \cos^2 \theta = c$,then $\tan^2 \theta$ is equal to

$A$ square is inscribed in the circle $x^{2} + y^{2} - 2x + 4y - 93 = 0$ such that its sides are parallel to the coordinate axes. The coordinates of its vertices are:

The sum of the fourth powers of the roots of the equation $x^3+x+1=0$ is

The electronic configuration of the phosphide ion $(P^{3-})$ is similar to that of:

With a standard rectangular bar magnet of length $l$,breadth $b$ $(b \ll l)$,and magnetic moment $M$,the time period of the magnet in a vibration magnetometer is $4 \ s$. If the magnet is cut normal to its length into four equal pieces,the time period (in seconds) with one of the pieces is: