A tuning fork gives 3 beats with $$50 \mathrm{~cm}$$ length of sonometer wire. If the length of the wire is shortened by $$1 \mathrm{~cm}$$, the number of beats is still the same. The frequency of the fork is

The depth at which acceleration due to gravity becomes $$\frac{\mathrm{g}}{2 \mathrm{n}}$$ is $$(\mathrm{R}=$$ radius of earth, $$\mathrm{g}=$$ acceleration due to gravity on earth's surface, $$\mathrm{n}$$ is integer)

Two resistance $$\mathrm{X}$$ and $$\mathrm{Y}$$ are connected in the two gaps of a meterbridge and the null points is obtained at $$20 \mathrm{~cm}$$ from zero end. When the resistance of $$20 \Omega$$ is connected in series with the smaller of the two resistance $$\mathrm{X}$$ and $$\mathrm{Y}$$, the null point shifts to $$40 \mathrm{~cm}$$ from left end. The value of smaller resistance in ohm is

Three point charges $$\mathrm{+Q,+2q}$$ and $$+\mathrm{q}$$ are placed at the vertices of a right angled isosceles triangle. The net electrostatic potential energy of the configuration is zero, if $$Q$$ is equal to