The speed of light is 300,000 km/s.
Light year is the distance travelled by light in one year.
Sun is the nearest star from Earth.
Alpha Centauri is 4.3 light years away from Earth.

$\displaystyle\frac{\Delta \lambda}{\lambda}=\frac{v}{c}$
Now, $\Delta\lambda=\displaystyle\frac{0.5}{100} \lambda$
$\Rightarrow \displaystyle\frac{\Delta\lambda}{\lambda}=\frac{0.5}{100}$
$\therefore v=\displaystyle\frac{0.5}{100}\times c=\frac{0.5}{100}\times 3\times 10^8$
$=1.5\times 10^6m/s$
increase in $\lambda$ indicates that the star is receding.

$1$ parsec = $3.26$ light years

Degeneracy pressure is the pressure which prevent the neutron star from becoming the Black hole.

$a 1-$ Solar mass star:

Fusion reactions take place and all hydrogen gets fuses to helium, thereby depleting hydrogen completely

Fusion reaction happen on star   such as sun where hydrogen combine to form $He$ a fusion reaction releasing energy and gravitational contraction occur due to very high gravitational pull.

Nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase.

When they reach this phase, hydrogen in them almost becomes depleted off and they become brighter and hotter and becomes low-mass white dwarfs

Flare stars have deep convection zone which help in rapid transition of energy produced in the star and also has convecting cores thus both deep convection zone and convecting cores make flare stars so active.

A red giant has lesser temperature and glows brighter and hence c is the correct option

A helium flash is a very brief thermal runaway nuclear fusion of large quantities of helium into carbon through the triple-alpha process in the core of low mass stars (between 0.8 solar masses ( M ) and 2.0 M ) during their red giant phase . This results in heating up the core and expansion of the core takes place as a result

At sufficiently high temperatures and densities, a 3-body reaction called the triple alpha process can occur: Two helium nuclei ("alpha particles") fuse to form unstable beryllium.

If another helium nucleus can fuse with the beryllium nucleus before it decays, stable carbon is formed along with a gamma ray.

Supernova being the last stages of a star, will happen only if the mass of the star exceeds the solar mass and hence a 10 solar mass star will have a high probability of becoming a supernova

Due to triple helium process, helium fusion takes place and carbon is formed due to convection from the core

A ring-shaped gaseous structure formed by an expanding shell of gas round an ageing star is known as nebula

A star's temperature is only 5,800 K, while a white dwarf has a temperature of 100,000 K. A white dwarf's faint luminosity comes from the emission of stored thermal energy; no fusion takes place in a white dwarf wherein mass is converted to energy. Hence it is dimmer than star

Once a black hole has formed, it can continue to grow by absorbing mass from its surroundings. The gravitational force becomes so intense that even light cannot escape from it

Massive stars live shorter lives than the common small stars because even though they have a larger amount of hydrogen for nuclear reactions, their rate of consuming their fuel is very much greater.

Helium and hydrogen being lighter gases are seen in other options other than option a. Thus , such options are incorrect options

 In approximately 5 billion years, the sun will begin the helium-burning process, turning into a red giant star. In a red giant, helium nuclei fuse to make carbon, followed by heavier elements such as nitrogen and oxygen.

The temperature of the stars are related to their colors by weins displacement law. Larger the temperature, smaller is their wavelength. Thus, of the colors given , red has maximum wavelength and hence smaller temperature, while bluish white has lesser wavelength and highest temperature. Thus, the star that emits bluish-white color has maximum temperature

White dwarf stars are characterized by a low luminosity, a mass on the order of that of the Sun, and a radius comparable to that of Earth.

The protonproton chain reaction is one of two known sets of nuclear fusion reactions by which stars convert hydrogen to helium. Using this method, the stars convert particles to energy

The HertzsprungRussell diagram, abbreviated HR diagram, HR diagram or HRD, is a scatter plot of stars showing the relationship between the stars' absolute magnitudes or luminosities versus their stellar classifications or effective temperatures. More simply, it plots each star on a graph measuring the star's brightness against its temperature (color).

Stars with very large masses can become black holes. A black hole releases a huge amount of gravitational energy, as material swirls toward its event horizon. This energy produces a jet of particles that streams over a distance of 300,000 light-years.