A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.

A series combination of resistor of resistance $$100 ~\Omega$$, inductor of inductance $$1 ~\mathrm{H}$$ and capacitor of capacitance $$6.25 ~\mu \mathrm{F}$$ is connected to an ac source. The quality factor of the circuit will be __________

A body of mass $$5 \mathrm{~kg}$$ is moving with a momentum of $$10 \mathrm{~kg} \mathrm{~ms}^{-1}$$. Now a force of $$2 \mathrm{~N}$$ acts on the body in the direction of its motion for $$5 \mathrm{~s}$$. The increase in the Kinetic energy of the body is ___________ $$\mathrm{J}$$.

The ratio of wavelength of spectral lines $$\mathrm{H}_{\alpha}$$ and $$\mathrm{H}_{\beta}$$ in the Balmer series is $$\frac{x}{20}$$. The value of $$x$$ is _________.