Consumption of which one of the following foods can prevent the kind of blindness associated with vitamin-$A$ deficiency?

The derivative of ${\tan ^{ - 1}}\left( {\frac{{\sqrt {1 + {x^2}} - 1}}{x}} \right)$ with respect to ${\tan ^{ - 1}}\left( {\frac{{2x\sqrt {1 - {x^2}} }}{{1 - 2{x^2}}}} \right)$ at $x = 0$ is:

Acetaldehyde forms a white crystalline precipitate on mixing with a ...... solution of

$A$ river of salty water is flowing with a velocity $2 ~m/s$. If the density of the water is $1.2 ~g/cc$,then the kinetic energy of each cubic metre of water is

$A$ 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

For a particle executing $S.H.M.$,the displacement $x$ is given by $x = A \cos \omega t$. Identify the graphs which represent the variation of potential energy $(P.E.)$ as a function of time $t$ and displacement $x$.