In Young's double slit experiment, the distance between the two coherent sources is ' d ' and the distance between the source and screen is ' D '. When the wavelength $(\lambda)$ of light source used is $\frac{d^2}{3 D}$, then $n^{\text {th }}$ dark fringe is observed on the screen, exactly in front of one of the slits. The value of ' $n$ ' is

A particle starts oscillating simple harmonically from its equilibrium position with time period ' T '. What is the ratio of potential energy to kinetic energy of the particle at time $t=\frac{T}{12}$ ? $$\left(\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}\right)$$

A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of combination is

A particle performs linear S.H.M. When the displacement of the particle from mean position is 3 cm and 4 cm , corresponding velocities are $8 \mathrm{~cm} / \mathrm{s}$ and $6 \mathrm{~cm} / \mathrm{s}$ respectively. Its periodic time is