Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is

A uniform circular disc of mass $$12 \mathrm{~kg}$$ is held by two identical springs. When the disc is slightly pressed down and released, it executes S.H.M. of period 2 second. The force constant of each spring is (nearly) (Take $$\pi^2=10$$ )

A charge $$17.7 \times 10^{-4} \mathrm{C}$$ is distributed uniformly over a large sheet of area $$200 \mathrm{~m}^2$$. The electric field intensity at a distance $$20 \mathrm{~cm}$$ from it in air will be $$\left[\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\right]$$

Sound waves of frequency $$600 \mathrm{~Hz}$$ fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound $$=300 \mathrm{~ms}^{-1}$$ )