In Young's double slit experiment, the $$10^{\text {th }}$$ maximum of wavelength '$$\lambda_1$$' is at a distance of '$$Y_1$$' from the central maximum. When the wavelength of the source is changed to '$$\lambda_2$$', $$5^{th}$$ maximum is at a distance '$$Y_2$$' from the central maximum. The ratio $$\frac{Y_1}{Y_2}$$ is

A mass $$0.4 \mathrm{~kg}$$ performs S.H.M. with a frequency $$\frac{16}{\pi} \mathrm{Hz}$$. At a certain displacement it has kinetic energy $$2 \mathrm{~J}$$ and potential energy $$1.2 \mathrm{~J}$$. The amplitude of oscillation is

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is '$$V_e$$', then the escape velocity from the planet is

A biconvex lens $$\left(R_1=R_2=30 \mathrm{~cm}\right)$$ has focal length equal to the focal length of concave mirror. The radius of curvature of concave mirror is [Refractive index of material of lens $$=1.6$$ ]