Two blocks $A$ and $B$ of masses $1\,kg$ and $2\,kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.s$ of both the blocks is

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $-\frac{2q}{3}$ placed at points $A, B$ and $C$ respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and $\angle CAB = 60^\circ$.

Four successive members of the first series of the transition metals are listed below. For which one of them the standard electrode potential $(E^o_{M^{2+}/M})$ value has a positive sign?

If $\left[\begin{array}{rrr}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix,then $x$ is equal to

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$,the piston moves through a length of $5 ~cm$. The total length of the cylindrical vessel in $cm$ is:

$A$ speaker emits a sound wave of frequency $f_0$. When it moves towards a stationary observer with speed $u$,the observer measures a frequency $f_1$. If the speaker is stationary,and the observer moves towards it with speed $u$,the measured frequency is $f_2$. Then: