Oxidation numbers of $P$ in $PO_{4}^{3-}$,of $S$ in $SO_{4}^{2-}$ and that of $Cr$ in $Cr_{2}O_{7}^{2-}$ are respectively

If the vertex of the conic $y^{2}-4y=4x-4a$ always lies between the straight lines $x+y=3$ and $2x+2y-1=0$,then

The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

The sensitivity of a galvanometer that measures current is decreased by $\frac{1}{40}$ times by using a shunt resistance of $10 \Omega$. Then,the value of the resistance of the galvanometer is (in $Omega$)

$S_1, S_2, \ldots, S_{10}$ are the speakers in a conference. If $S_1$ addresses only after $S_2$,then the number of ways the speakers address is

$A$ thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $v$,the kinetic energy of the system is (neglect friction).