Two stars appear red and blue. Which of the following is true for both?

The wavelength of maximum emitted energy $(\lambda_m)$ of a body at $700 \ K$ is $4.08 \ \mu m$. If the temperature of the body is raised to $1400 \ K$,then the value of $\lambda_m$ will be (in $\mu m$)

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \, nm$. The radiation intensity for the star is: (Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$,Wien's constant $b = 2898 \, \mu m \cdot K$)

Experimental investigations show that the intensity of solar radiation is maximum for a wavelength $480 \, nm$ in the visible region. Estimate the surface temperature of the sun. Given Wien's constant $b = 2.88 \times 10^{-3} \, mK$.

The wavelength of maximum emission of radiation from a body at $2000 \ K$ is $4 \ \mu m$. What is the wavelength of maximum emission of radiation from the body at $2400 \ K$ in $\mu m$?

The intensity of radiation emitted by the sun has its maximum value at a wavelength of $510\;nm$ and that emitted by the north star has the maximum value at $350\;nm$. If these stars behave like black bodies,then the ratio of the surface temperature of the sun and north star is