As long as the Indian visa is not defaced or damaged (eg. stamped "CANCELLED" or the corners cut or a hole punched through it), it remains valid even if it is in an old passport, provided it is presented simultaneously with a valid passport of the same type issued by the same country.

If you prefer not to carry two passports, you can also choose to pay a nominal fee to the nearest Indian consulate and they will place a new visa sticker in the new passport with the same validity as the original visa.