The United States and other countries opposed the admission (and recognition) of the PRC in the UN, and the ROC, now based in Taiwan, kept its membership of the UN until October 25, 1971.
The United Nations General Assembly passed Resolution 2758 on Oct. 25, 1971, deciding that the People's Republic of China is the only lawful representative of China to the United Nations. As a result, the PRC was able to take over the ROC's membership in the United Nations, and its permanent seat in the United Nations Security Council. The ROC lost its membership of the United Nations and membership of the United Nations Security Council. The resolution was supported by most of the communist states including Soviet Union and the Non-Aligned countries such as India, along with some Western European countries including the United Kingdom and France.
With the Resolution 2758 the UN simply recognized the PRC as the legitimate Chinese Government, that from 1949 until 1971, had been deprived of its right of representing China.
The PRC has instituted the "One-China policy", under which it actively opposes any moves seen to be endorsement of the ROC (or Taiwan) as an independent sovereign state or as a rival "China", although two Chinas effectively exist. While the PRC claims sovereignty over all of China and claims that Taiwan is part of China, it does not exercise sovereignty over Taiwan, and has never done so.,
Pertinent questions who opposed resolution 2758. Next how did the world change its stance on legitimate Chinese government to be PRC from ROC.
Also States have the ability to de-recognise and put in place recognition that is different from earlier stated positions even ones that are legitimate.
East Timor - any similarity with Tibet.
How many countries recognised ROC as the legitimate Chinese government before resolution 2758. And how many countries recognise ROC until till this day (is it zero). Recognition and legitimacy can change overnight due to certain events (please refer to examples)
The PRC back stabbed the Russians that enabled a channel that resulted in American support for its one china policy that resulted in actualisation of un resolution 2758 (that the Americans voted against - smart). World affairs can change long held positions.
Tibet is like the ROC it is open to question on its recognition and legitimacy in the future. Would that be needed. The question of recognition and legitimacy of Tibet makes the PRC ask other states (nearly every year) to express their position on Tibet because it is open to question. That's the discussion here.
With reference to India the position on Tibet has been silent in most recent years. There has been no express validation. The Sikkim recognition part of India by PRC is worth a discussion since it expressed certain positions by India that is relevant to this date.
In either case India won't be the lead in making recognition of Tibet different there are others who will want to and can do.
http://en.wikipedia.org/wiki/China_and_the_United_Nations
http://en.wikipedia.org/wiki/United_Nations_General_Assembly_Resolution_2758