I have the Impression India did a little bit of invading in 1971
After building tensions during the Bangladesh Liberation war, Pakistan launched a pre-emptive attack against India, which responded with air-strikes.
This marked the official start of the Indo-Pakistani War of 1971. Prime Minister Indira Gandhi ordered the immediate mobilisation of troops and launched the full-scale invasion. This involved Indian forces in a massive coordinated air, sea, and land assault. Indian Air Force started flying sorties against Pakistan from midnight. The main Indian objective on the western front was to prevent Pakistan from entering Indian soil. There was no Indian intention of conducting any major offensive into West Pakistan.
The invasion didn't last long but troops crossed international borders and engaged in armed conflict with the government of a foreign nation, forcing its surrender.
And as Richard Terret points out above,
[In 1948] the Indian Armed Forces invaded the State of Hyderabad and ended the rule of Nizam, annexing the state into the Indian Union.
See The Fall of Hyderabad and Operation Polo
Since the question asks about the last 10,000 years, we can consider examples prior to the establishment of India as a fully independent state.
In 1944 Indian troops participated in the invasion of Italy
it was hoped that the invasion would distract German attention and forces from France.
The next attempt or Second Battle of Cassino
was made by Lieutenant-General Sir Bernard
Freyberg’s newly formed New Zealand Corps,
consisting of Major-General Tuker’s 4th Indian
Division and the 2nd New Zealand Division.
From The Battles for Monte Casino
Maybe this is a case of irregular verb conjugation: I liberate; You invade; He, She or It fight a border war?
A number of commenters have attempted to dispute the inclusion of the events above on several grounds:
- It's not an invasion if your motives are good.
- It's not an invasion if the target is somehow not a country.
Motivation is irrelevant. In 1944 Britain and the USA invaded France†. At that time France was governed by a French government (the Vichy government) put in place by the Nazis. The British motivation was the liberation of France from Nazi occupation. They invaded France at the request of the Free-French government in exile. Their motives were good and their actions after 1945 proved this.
However it was still an invasion and described as such. Example
The word invasion can validly be used where the target is not a country. For example, when a burglar enters my house, it is described as a home invasion. When a journalist listens to the phone messages of a member of the public it is described as an invasion of privacy.
However the intent of the question obviously is aimed at violent military takeover of foreign territory. (foreign meaning outside the internationally recognised borders of the invading force)
In English, the words Country, Nation and State are often used interchangeably. There is a great deal of dispute about what constitutes a country and how many exist.
For example which of England, Britain, Great Britain and the United Kingdom are or are not countries? If I invade London, am I simultaneously invading one, two, three or four countries?
Another example: Is the Principality of Monaco a country? Would it be nonsense to ask whether Monaco has ever been or could be invaded? Would any violent military takeover of Monaco by a foreign country not count as an invasion under any circumstances?
The intent of the above question is best addressed by interpreting country to mean something like the kind of independent sovereign states recognised by the U.N. We should not get hung up over terms like "principality" or "princely state" - we should consider whether they meet common criteria such as internationally recognised borders, independent government and so on.
† A great many other nations participated in the invasion of France (or in it's liberation if you prefer), I haven't listed them all for brevity - not from a lack of recognition or respect for the scale and value of their contribution and losses.