On observing light from three different stars \(P,\) \(Q,\) and \(R,\) it was found that the intensity of the violet colour is maximum in the spectrum of \(P,\) the intensity of the green colour is maximum in the spectrum of \(R\) and the intensity of the red colour is maximum in the spectrum of \(Q.\) If \(T_P,\) \(T_Q,\) and \(T_R\) are the respective absolute temperatures of \(P,\) \(Q,\) and \(R,\) then it can be concluded from the above observations that:
1. \(T_P>T_Q>T_R\)
2. \(T_P>T_R>T_Q\)
3. \(T_P<T_R<T_Q\)
4. \(T_P<T_Q<T_R\)

A black body maintained at \(200~\text{K}\) emits maximum radiation at a wavelength of \(14~\mu \text{m}.\) If its temperature is increased to \(1000~\text{K},\) at what wavelength will the maximum radiation now be emitted?
1. \(14~\mu\text{m}\)
2. \(70~\mu\text{m}\)
3. \(2.8~\mu\text{m}\)
4. \(2.8~\text{nm}\)