People with shallow knowledge end up making such ludicrous assumptions. It was not that "India couldn't fight LTTE", the fact is that India never wanted to fight LTTE, they are Tamil people! India sent a "Peace keeping force" there, which was a stupid step by Rajiv Gandhi, but their aim was not to fight the LTTE, only due to some wrong turn of events they ended up engaging in skirmishes with the LTTE, that resulted in huge protest back in India, and the peace keeping forces were withdrawn. If India wanted war on LTTE, then there would have been only one outcome.
About Bangladesh war, even after India completely cutting off West Pakistan's supplies and reinforcements from reaching Bangladesh for nine long months, and with all the training and support provided by India, the Mukti Bahini was proved to be inadequate to fight back the Pakistani army and Bangladeshi rajakars, not all Bangladeshis were looking for freedom from West Pakistan! India was compelled to intervene because Mukti Bahini was cornered in certain pockets and was running out of options. Those people fought bravely, this I give it to them, but it would be extremely ungrateful for the Bangladeshis to ignore or deny the huge contribution of India in creation of their country before, during, and after the war, no other country in the history of the world did so much for another country. But then, it seems that ungratefulness is in the nature of the Bangladeshi people, maybe Pakistani leadership was not quite off the mark with their assessment of Bangladeshi people, as it appears now.