The Mongols conquered huge portions of Asia (and even some of Europe). Yes, they did move into some northern areas of India.

One thing about the Mongol Empire that set it apart from other empires was that they allowed religious freedom. They didn't have an established government religion, so their people were free to choose. I have no doubt that if there were Christians in the Mongol court (which there were), that there were Hindus as well.

As far as the "Aryans" thing goes, that one is a little more touchy. It walks awfully close to the things that Hitler said to support his causes.

yes it is true because all people are not lie they all look like a friend

The Aryan people, a branch of Indo-Europeans who spoke something very much like Sanskrit, came into the sub-continent throughout the 1st and 2nd millenia, BCE. They encountered an indigenous culture known to us as the Indus Valley, or Harrapan civilization. Many elements that would become Hinduism were already present, to which the Aryans added their own pantheon. This pantheon is recognizably IndoEuropean, and has similarities to the Iranian deities at the time, as well as more distant connections to the western deities. ('Iranian" = "Aryan")
Buddhism is a much later development which arose in the context of Northern Indian Hinduism. Jainism also developed at around the same time. The exact dates are disputed, but 6th century BCE is the ballpark figure.

Yes, true; but study the history,…deeper…!

As of my knowledge, people of mongoloid origin are found in NE India. These people enetered through Myanamar. They are called as tribes and presently known as Pnars, Khasis and Garos. They imbibed christian religion when the Britishers came to north east India. Intrestingly they are known as Indo mongoloids. However I am not a student of history, and if I am wrong , I may be pardoned.

It is true that Mongolian migrated to India , but they are not Aryans. What religion they followed can not be answered exactly. Research is going on.

The Aryan Invasion Theory, as it is known by historians and anthropologists, was the theory that a group of people who spoke a language prototypical of Sanskrit and Avesta (and greek, and latin, and english, and most of the other languages currently in use) migrated from the Steppes north of the Black Sea into India. These people would have practiced a religion very similar to the one found in the ancient Vedas - the scriptural foundation of modern Hinduism.

This theory has recently fallen out of favor among historians and they believe now that the people of the Vedas have been in India for much longer than they had originally thought. Nevertheless, the connection between the Vedas, Sanskrit, and the Proto-Indo-European (aka Aryans) people is very curious. Rather than a migration, scholars are thinking something more along the lines of cultural assimilation occured. Much like American culture is being spread around the world today.

You are mixing up things and it's lot difficult to answer.
Invaders did came to India from Mongolia, but they were not Aryans.

Aryans by all accounts and theories have been in India much much before.

Buddhism started somewhere around 600 B.C. Hinduism is much older than that.

Sorry I have no answer, just corrections. Whatever invaders came from Mongolia, they were assimilated.