Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature R = 6 cm as shown. Consider oil to act a thin lens. An object S is placed 24 cm above water surface. The location of its image is at x cm above the bottom of the tank. Then x is __________.
One mole of a monatomic gas is taken through a cycle ABCDA as shown in the PV diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I.
| Column I | Column II | ||
|---|---|---|---|
| (A) | Process A$$ \to $$ B | (P) | Internal energy decreases. |
| (B) | Process B$$ \to $$C | (Q) | Internal energy increase. |
| (C) | Process C$$ \to $$D | (R) | Heat is lost. |
| (D) | Process D$$ \to $$A | (S) | Heat is gained. |
| (T) | Work is done on the gas. |
Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $$\lambda$$f. Match each system with statements given in Column II describing the nature and wavelength of the standing waves :
