I use the term "Northern India" to encompass the northern half of modern India and all of Pakistan and Bangladesh. The history of this region is one of demographic stability punctuated by occasional large-scale invasions from Afghanistan. At the beginning of the study period, the region was ruled by the indigenous Gupta dynasty:
50: A mysterious group from Xinjiang (Western China today) called the Yu-Chi established the Kushan Empire. The Yu-Chi also conquered and ruled Northern India. Thus, if your ancestors were in North-western India/Pakistan in 500 CE, their ancestors could have lived anywhere in the Kushan Empire or in Xinjiang in 1 CE. The Yu-Chi formed the aristocracy until...
5th century: Around 400, Central Asian/ Mongolian nomads variously called White Huns, Hepthalites, and Huna, invaded from Central Asia and established themselves permanently as an aristocratic class in Afghanistan and Northern India. They remained culturally distinct long after they lost power, but eventually intermarried. Thus, if your ancestors were in Northern India in 500 CE, it's plausible that they had ancestors both there and in Central Asia and Afghanistan in 1 CE.
Throughout the study period, there has been maritime trade between Western India, Iran, Arabia, and the Horn of Africa. The Romans even had trade settlements in Western India. Thus, although it's hard to prove, if your ancestors were in a western coastal region of India in 1000 CE, it's not crazy to think that their ancestors could have come from anywhere on the western rim of the Indian ocean in 1 CE.
1192: Muslim armies under Central Asian Turkic commanders conquer most of Northern Indian region. It's not clear who served in these armies, presumably mostly Turks and Iranians. If your ancestors were in North India in 1490 CE, their ancestors could have come from North India, Iran, or Central Asia in 1000 CE. If they were Muslims, then it's highly likely.
1397 Like Iran and Afghanistan, the Northern Indian region was hit by the Timurid Turkic invaders under Timur (Tamerlane) who supplied yet another upper class of Central Asian and Mongolian origin.
1510 - The Portuguese founded the colony of Goa on the west coast south of Bombay, between Maharashtra and Karnataka. This colony persisted until the 20th century. If your ancestors were in this area in 1800 CE, there's a decent chance that in 1490 you had ancestors in Portugal, especially if your features are anomolously Western European looking. If you are of Indian extraction and have a Portuguese surname, like Indian defense minister George Fernandes, you don't have to wonder.
1504 - The Mughals (= Moguls = "Mongols" although they were Turkic) invade from Central Asia. Like the Timurids, they were Turkic. Of all the Central Asian conquerors, they were the most successful, conquering Northern India. They established the Mughal Empire, (AKA Mogul) which retained cohesion until the mid 18th Century and added most of Southern India to its heartland in Afghanistan and Indus-Ganges. The upshot is that if your ancestors were in Northern India in 1800 CE, it's possible that their ancestors were anywhere in the Mughal Empire or in Central Asia or Mongolia in 1490.
1610 - 1948. The British gradually enlarged their influence in India, first through trade agreements with the proxy British East India Company, then directly through the crown after 1858. Throughout this interval, British people (English, Scottish, Irish, Welsh) lived and worked in India. Although there was not widespread intermarriage, there were doubtless plenty of sneaky exchanges of genes. If your ancestors lived anywhere in the British Raj in 1900, then you could have had ancestors in the British Isles in 1800 or 1490. Consider this especially if your features are uncharacteristically Western-European looking.
The biggest mass migration of all occurred in the 20th century with the tragic partitioning of the British Protectorate of India into modern India and Pakistan. Your families will know if your ancestors were involved in this horrible event. Just remember, if your ancestry is Pakistani or Bangladeshi, your earlier ancestors could have come from anywhere in India. Likewise if Indian.