If the time period $T \propto P^a d^b E^c$,where $P$ is pressure,$d$ is density,and $E$ is energy,then the value of $c$ is:

If the time period $t$ of the oscillation of a drop of liquid of density $d$,radius $r$,vibrating under surface tension $s$ is given by the formula $t = \sqrt{r^{2b} s^c d^{a/2}}$. It is observed that the time period is directly proportional to $\sqrt{\frac{d}{s}}$. The value of $b$ should therefore be

If energy is given by $U = \frac{A\sqrt{x}}{x^2 + B}$,then the dimensions of $AB$ are:

$1 \, J$ of energy is to be converted into a new system of units in which length is measured in $10 \, m$,mass in $10 \, kg$,and time in $1 \, minute$. The numerical value of $1 \, J$ in the new system is:

In the equation $[X+\frac{a}{Y^2}][Y-b]= RT$,$X$ is pressure,$Y$ is volume,$R$ is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is

When a wave traverses a medium,the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$,where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?