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

The maximum value of $\frac{\log x}{x}, 0 < x < \infty$ is

$A$ particle moves in a circle of radius $25 \ cm$ at two revolutions per second. The acceleration of the particle in $m/s^2$ is

The equation $\frac{1}{r} = \frac{1}{8} + \frac{3}{8} \cos \theta$ represents

If due to some injury the chordae tendineae of the tricuspid valve of the human heart are partially non-functional,what will be the immediate effect?

$A$ bag contains $2n+1$ coins. It is known that $n$ of these coins have a head on both sides,whereas the remaining $n+1$ coins are fair. $A$ coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\frac{31}{42}$,then $n$ is equal to