$A$ 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 $pi$)

The locus of the centre of a circle which passes through the origin and cuts off a chord of length $4$ units from the line $x=3$ is

In context with beryllium,which one of the following statements is incorrect?

Glauber's salt is

An organ pipe $P_1$,closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$,open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes,the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic).

The set of solutions of the equation $(\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2$ is