The fundamental frequency of an air column in a pipe open at both ends is ' $\mathrm{f}_1$ '. Now $80 \%$ of its length is immersed in water, the fundamental frequency of the air column becomes $f_2$. The ratio of $f_1: f_2$ is

Earth has mass ' $M_1$ ' radius ' $R_1$ ' and for moon mass ' $M_2$ ' and radius ' $R_2$ '. Distance between their centres is ' $r$ '. A body of mass ' $M$ ' is placed on the line joining them at a distance $\frac{\mathrm{r}}{3}$ from the centre of the earth. To project a mass ' $M$ ' to escape to infinity, the minimum speed required is

In an interference experiment, the $\mathrm{n}^{\text {th }}$ bright fringe for light of wavelength $\lambda_1(\mathrm{n}=0,1,2,3 \ldots)$ coincides with the $\mathrm{m}^{\text {th }}$ dark fringe for light of wavelength $\lambda_2(\mathrm{~m}=1,2,3 \ldots)$. The ratio $\frac{\lambda_1}{\lambda_2}$ is

Three inductances are connected as shown in figure. The equivalent inductance is