A beam of light having wavelength $$5400 \mathrm{~A}$$ from a distant source falls on a single slit $$0.96 \mathrm{~mm}$$ wide and the resultant diffraction pattern is observed on a screen $$2 \mathrm{~m}$$ away. What is the distance between the first dark fringe on either side of central bright fringe?

In the part of an a.c. circuit as shown, the resistance $$R=0.2 \Omega$$. At a certain instant $$(\mathrm{V_A-V_B})= 0.5 \mathrm{~V}, \mathrm{I}=0.5 \mathrm{~A}$$ and $$\frac{\Delta \mathrm{I}}{\Delta \mathrm{t}}=8 \mathrm{~A} / \mathrm{s}$$. The inductance of the coil is

In the circuit shown in the figure, a.c. source gives voltage $$\mathrm{V}=20 \cos (2000 \mathrm{t})$$. Impedance and r.m.s. current respectively will be

When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed, then the corresponding mode of vibration is