$A$ particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then,its time period of vibration will be

If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1$ where $x \geq \frac{1}{2}$,then $\sqrt{4x^2-1}$ is equal to

Which artery is absent in a frog?

Which of the following metals will not reduce $H_2O$?

Two liquids $A$ and $B$ have vapour pressures in the ratio $P_A^0 : P_B^0 = 1 : 3$ at a certain temperature. If the ratio of mole fractions of $A$ to $B$ in the vapour phase is $4 : 3$,then the mole fraction of $B$ in the solution at the same temperature is

$A$ stone is dropped in a quiet lake and it is observed that waves move in circles. If the radius of a circular wave increases at the rate of $2 \text{ cm/sec}$,then the rate of increase in its area at the instant when its radius is $10 \text{ cm}$,is (in $\text{cm}^2/\text{sec}$): (in $pi$)