Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to

The function $f: R \rightarrow R$ is defined by $f(x) = \cos^2 x + \sin^4 x$ for $x \in R$. Then the range $f(R)$ is equal to

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P, Q,$ and $R$ having emf's $E, E,$ and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

In which of the following are Chlorophyll-$a$,Chlorophyll-$d$,and Phycoerythrin found?

There are two identical small holes of cross-sectional area $a$ on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. The tank is resting on a smooth horizontal surface. The horizontal force which will have to be applied on the tank to keep it in equilibrium is

The figure shows the volume $V$ versus temperature $T$ graphs for a certain mass of a perfect gas at two constant pressures of $P_1$ and $P_2$. What inference can you draw from the graphs?