Frequency of the series limit of Balmer series of hydrogen atom of Rydberg's constant ' $R$ ' and velocity of light ' $C$ ' is

The co-ordinates of a moving particle at any time ' $t$ ' are given by $x=\alpha t^3$ and $y=\beta t^3$ where $\alpha$ and $\beta$ are constants. The speed of the particle at time ' $t$ ' is given by

A bucket full of hot water is kept in a room. If it cools from $75^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$ in $t_1$ minutes, from $70^{\circ} \mathrm{C}$ to $65^{\circ} \mathrm{C}$ in $\mathrm{t}_2$ minutes and $65^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in $t_3$ minutes, then

A cylinder contains water upto a height ' $H$ '. It has three orifices $\mathrm{O}_1, \mathrm{O}_2, \mathrm{O}_3$ as shown in the figure. Let $V_1, V_2, V_3$ be the speed of efflux of water from the three orifices. Then