I don't know where your coming from with the Hindu relation tbh. Armenia, approx 2000 was originally part of Persia. The area where Armenia and Iran is today was originally and still inhabitated by the Aryan people. Today the Aryans, while mostly predominant in Iran, are still evident in relatively large proportion in Armenia, as well India and smaller surrounding countries that only recently in the last 150 years separated from Iran and Armenia.
The Indians, or Hindus, were for a long time part of the Persian/ aka Aryan Empire, but not in the same area as modern day Armenia. The Aryans expanded as far as India and China, and while people were encouraged to travel a lot during that era within the empire, I don't think that the Kardashians' ancestors were Indian.
Their name ''Kardashian'' is a old Persian and Armernian name. People with that or very similar surnames are commom among Armenia and Northern Iran, including my own and I myself are from northern Iran. The "ian" part means children of, and "kardash" I believe means "craftsmen". Hence, I'm pretty sure they are of Aryan ancestry as oppossed to Hindu.
Also keep in mind that Armenians and Aryans do classify as Caucasian also (in relation to the comment about chloe looking more Irish/causcasian). Hope that helps clear things up for you!