The correct answer is: A. Hoshiarpur district.
Una district was part of Hoshiarpur district during the British period. This is evident from the fact that the Una district was created in 1972, after the partition of Punjab. The Una district was carved out of the Hoshiarpur district.
The other options are incorrect because they are not districts that Una was part of during the British period.
A. Hoshiarpur district: Una district was part of Hoshiarpur district during the British period.
B. Ludhiana district: Una district was not part of Ludhiana district during the British period.
C. Jalandhar district: Una district was not part of Jalandhar district during the British period.
D. Patiala district: Una district was not part of Patiala district during the British period.