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

There are two samples A and B of a certain gas, which are initially at the same temperature and pressure. Both are compressed from volume v to $\frac{\mathrm{v}}{2}$. Sample A is compressed isothermally while sample B is compressed adiabatically. The final pressure of $A$ is

A single slit diffraction pattern is formed with light of wavelength $6195 \mathop A\limits^o$. The second secondary maximum for this wavelength coincides with the third secondary maximum in the pattern for light of wavelength ' $\lambda_0$ '. The value of ' $\lambda_0$ ' is

Two rods, one of aluminium and the other of steel, having initial lengths ' $\mathrm{L}_1$ ' and ' $\mathrm{L}_2$ ' are connected together to form a single rod of length $\left(L_1+L_2\right)$. The coefficients of linear expansion of aluminium and steel are ' $\alpha_1$ ' and ' $\alpha_2$ ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by $\mathrm{t}^{\mathrm{L}} \mathrm{C}$, then the ratio $\frac{L_1}{L_1+L_2}$ will be