Two pipes of lengths $\mathrm{L}_1$ and $\mathrm{L}_2$, open at both ends are joined in series. If ' $f_1$ ' and ' $f_2$ ' are the fundamental frequencies of two pipes, then the fundamental frequency of series combination will be (neglect end correction)

A long wire carrying a steady current is bent into a circle of single turn. The magnetic field at the centre of the coil is ' B '. If it is bent into a circular loop of radius ' $\mathrm{r}_1$ ' having ' n ' turns, the magnetic field at the centre of the coil for same current is

Two spheres each of mass $M$ and radius $R$ are connected with a massless rod of length 4 R . The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod will be

In Young's double slit experiment, for the $n$th dark fringe ( $\mathrm{n}=1,2,3 \ldots$ ) the phase difference of the interfering waves in radian will be