The apparent wavelength of light from a star moving away from the earth is $0.02 \%$ more than the actual wavelength. The velocity of the star is $[c = 3 \times 10^8 \ m/s]$. (in $km/s$)

Due to the Doppler effect, the shift in wavelength observed is $0.1 \text{ Å}$ for a star producing a wavelength of $6000 \text{ Å}$. The velocity of recession of the star will be: (in $\text{ km/s}$)

In the hydrogen spectrum,the wavelength of the ${H_\alpha}$ line is $656 \ nm$,whereas in the spectrum of a distant galaxy,the ${H_\alpha}$ line wavelength is $706 \ nm$. The estimated speed of the galaxy with respect to the Earth is:

$A$ rocket is moving away from the Earth at a speed of $0.2c$,where $c$ is the speed of light. It emits a signal of frequency $4 \times 10^7 \text{ Hz}$. What will be the frequency observed by an observer on the Earth?

Assuming that the universe is expanding,if the spectrum of light coming from a star which is moving away from the Earth is tested,then in the wavelength of light:

The $6563 \ \mathring{A}$ line emitted by a hydrogen atom in a star is found to be red-shifted by $5 \ \mathring{A}$. The speed with which the star is receding from the Earth is: