$A$ string is stretched between fixed points separated by $75.0 \ cm$. It is observed to have resonant frequencies of $420 \ Hz$ and $315 \ Hz$. There are no other resonant frequencies between these two. Then,the lowest resonant frequency for this string is .... $Hz$.

The wavelength of ${K_\alpha }$ $X-$rays produced by an $X-$ray tube is $0.76 \ \mathring A$. The atomic number of the anode material of the tube is:

$Mg$ is obtained by

If the magnitudes of $a, b$ and $a+b$ are respectively $3, 4$ and $5$,then the magnitude of $(a-b)$ is

$A$ flask of volume $10^3 \text{ cc}$ is completely filled with mercury at $0 \ ^\circ\text{C}$. The coefficient of cubical expansion of mercury is $180 \times 10^{-6} / ^\circ\text{C}$ and that of glass is $40 \times 10^{-6} / ^\circ\text{C}$. If the flask is now placed in boiling water at $100 \ ^\circ\text{C}$,how much mercury (in $\text{cc}$) will overflow?

In an $FM$ system, a $7\, kHz$ signal modulates a $108\, MHz$ carrier such that the frequency deviation is $50\, kHz$. The carrier swing is: (in $ kHz$)