The class 7 students were asked to provide the names of the people residing in four "countries", with Kashmir figuring among the list.
The Bihar Education Project Council (BEPC), which was conducting the examinations, later acknowledged the error and expressed an apology.
After a solved example -- "The people of China are called Chinese" -- the students of Vaishali district were asked to write what the residents of Nepal, England, Kashmir and India were called.
The question appeared in the English paper for the half- yearly examinations held earlier this week.
"It was a printing error for which we express our deep regret. The question will not be taken into account at the time of evaluation," Rajeev Ranjan Prasad, state programme officer with the BEPC, told PTI.
He said the examinations were being conducted as part of the Sarva Shiksha Abhiyan, a central government programme on elementary education.
The question was modelled on an exercise in an English textbook, in which students were asked to write how the people in a particular "country/state" were referred to.
"There would have been no problem if the oblique mark was there between country and state. The question papers, though prepared centrally, were printed locally in the districts and there were no complaints from anywhere else", Prasad said.
The BEPC will look into the matter and discuss possible measures to prevent such mistakes in the future, he added.