$P,Q,R,S,T,U,V,$ and $W$ are seated around a circular table. $S$ is seated opposite to $W$ $U$ is seated at the second place to the right of $R$ $T$ is seated at the third place to the left of $R$ $V$ is a neighbour of $S$ Which of the following must be true? $P$ is a neighbour of $R$ $Q$ is a neighbour of $R$ $P$ is not seated opposite to $Q$ $R$ is the left neighbour of $S$

The number of molecules of a nucleotide of molecular weight $300\:g$/mol present in $10$ picomoles is ____________ $\times10^{12}$ (round off to $2$ decimal places).

To facilitate mass transfer from a gas to a liquid phase, a gas bubble of radius $r$ is introduced into the liquid. The gas bubble then breaks into $8$ bubbles of equal radius. Upon this change, the ratio of the interfacial surface area to the gas phase volume for the system changes from $3/r$ to $3n/r$. The value of $n$ is _____________________.

A variable $Y$ is a function of $t$. Given that $Y\left ( t=0 \right )=1$ and $Y\left ( t=1 \right )=2,\dfrac{dY}{dt}$ in the interval $t=\left [ 0,1 \right ]$ can be approximated as _________________.

A block of ice at $0 \:^{\circ}C$ is supplied heat at a constant rate to convert ice to superheated steam. Which one of the following trajectories correctly represents the trend of the temperature of the system with time? Assume that the Specific heat of $H_{2}O$ is not a function of temperature.