The difference between the $n^{\text{th}}$ and $(n+1)^{\text{th}}$ Bohr's radius of a hydrogen atom is equal to the $(n-1)^{\text{th}}$ Bohr's radius. The value of $n$ is:

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 equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{\pi x}{3} \cos 40 \pi t$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The separation between two adjacent nodes is .... $cm$.

$A$ conducting rod with resistance $r$ per unit length is moving inside a vertical magnetic field $\vec B$ at constant speed $v$ on two horizontal parallel ideal conductor rails. The ends of the rails are connected to a resistor $R$. The separation between the rails is $d$. The rod maintains a tilted angle $\theta$ to the rails. Find the external force required to keep the rod moving.

Which of the following elements does not form a monoxide?

The maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is