United Kingdom
This is Knot a Hussar

Unsigned Carte-de-Visite
Lancer Officer in frock coat

That's a tricky one - frock coats won't tell you much, and his trousers have two stripes. He could very well be a Hussar - except his pillbox hat displays the crossed lines pattern on the top that was typical of the Lancers.

Carte-de-Visite C. Smith "1st Bett. K.O.B. India"
Private from the 9th (Queen's Royal) Lancers

Other dress orders  though don't leave room for doubt, as lancers were fitted with a very specific tunic pattern - quite like their counterparts over Europe.

This specific gentleman has seen some action as shown by his campaign medals : he's sporting the Afghan War Medal (left) and the Kabul to Kandahar Star.

If you're interested in those events I'll refer you to Garen Ewing's excellent website.

To make it short, the Kabul to Kandahar Star commemorates the action from 9thto 31st august 1880. 243 such stars would have been awarded to 9th Lancers. The two bars on the 1878-1880 Afghanistan Medal can be either Charasia 6th october 1879 (87 issued to "A3 Squadron), Kabul 10th to 23rd december 187 (253 issued) or Kandahar 1st september 1881(244 issued).