Role of PM and his Council of Ministers

Who should be PM and who should all be in his Cabinet? Is the whole council supposed to include the intellectual or is it supposed to represent the people?
From what I can infer from whatever I was taught in Civics in my bachpan its meant to be the latter. So then why are Members of Rajya Sabha allowed in this council? As the Members of Rajya Sabha are supposedly best brains of the country (not just best brains but best citizens in general) then why should they be in Council? They dont have the peoples mandate. They have not been elected by the people.

Now this is in reference to the current council. First of all I'd like to clarify few things:

• I know Manmohan Singh is very popular so everybody would like to see him continue as PM.
• Also in this election there was a mandate for Manmohan Singh himself. Officially it cant be said as such because he didnt contest from anywhere but we all know that he was projected as PM so people voted for him (unlike 2004 when people voted for Sonia Gandhi).

The main purpose of the council is to run a country in such a way that is beneficial for the people. As the council is supposedly answerable to public so it is expected that they will do best for people (we all know the reality when all big politicians are corrupt so it isnt true for them. but lets just talk what was the intention of the constitution in ideal scenario!). This council will be helped by the best brain of the country which form the bureaucracy (here again we know how much best brain goes and how much 'best' it remains). But what is happening now is not how the Council should behave. There are demands to make Montek as our Finance Minister. Granted he is a good economist and can handle all his files well. But does he really know what India wants. Not just the Indian Industry but also the poor. Will he run this country like a company for maximum profit (GDP, sensex or whatever be the scale) or will he run such that all sections of the society benefit (although even if he just help industries it will 'someday' help the poor too. probably). Same with Manmohan Singh. Give him a free hand and he will start all the disinvestment and all the international business practices. It was because of both Left and Congress Party leadership that he brought out schemes like Guaranteed Employment and others. I concede that by now he will be wiser and will behave more like a politician with Congress party's future at stake.
But I still believe that Council should only for elected representatives. Who are supposed to take care of the public. If technical knowledge was deemed necessary for such posts then constitution would have provided for some entrance test and not elections. It is upto the people to choose wisely. If they cant do that then it is their loss.
As for all the brains of such topics (take any ministry), they should just be adviser's to the Government. Not the Government itself.

Well these are just my views though I fully support Congress Government :)