In determining the temperature of a distant star,one makes use of

$Assertion :$ For higher temperature, the peak emission wavelength of a blackbody shifts to lower wavelengths.
$Reason :$ Peak emission wavelength of a blackbody is proportional to the fourth power of temperature.

The colour of a star is an indication of its

Use the formula $\lambda_{m} T = 0.29 \; cm \cdot K$ to obtain the characteristic temperature ranges for different parts of the electromagnetic spectrum. What do the numbers that you obtain tell you?

$A$ black body is at a temperature of $5760 \ K$. The energy of radiation emitted by the body at wavelength $250 \ nm$ is $U_1$,at wavelength $500 \ nm$ is $U_2$ and that at $1000 \ nm$ is $U_3$. Wien's constant,$b = 2.88 \times 10^6 \ nm \ K$. Which of the following is correct?

$A$ black body has a maximum wavelength $\lambda_{m}$ at a temperature of $2000 \ K$. Its corresponding wavelength at a temperature of $3000 \ K$ will be: