With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $$\mathop A\limits^o $$ is observed at 5896 $$\mathop A\limits^o $$ ?

The length of a metal wire is l₁, when the tension in it is T₁ and is l₂ when the tension is T₂. The natural length of the wire is :

In an electromagnetic wave the electric field vector and magnetic field vector are given as $$\overrightarrow E = {E_0}\widehat i$$ and $$\overrightarrow B = {B_0}\widehat k$$ respectively. The direction of propagation of electromagnetic wave is along :

For a series LCR circuit with R = 100 $$\Omega$$, L = 0.5 mH and C = 0.1 pF connected across 220V$$-$$50 Hz AC supply, the phase angle between current and supplied voltage and the nature of the circuit is :