Questions: In what year did the United States conduct its first census of conquered territories?

The answer is 1850.

The United States conducted its first census of conquered territories in 1850. This was after the Mexican-American War, which ended in 1848 with the Treaty of Guadalupe Hidalgo. The treaty resulted in the U.S. acquiring territories such as California, New Mexico, and others. The 1850 census was the first to include these newly acquired territories.

The year 1849 is incorrect because the census was conducted in 1850. The U.S. was still organizing the newly acquired territories in 1849.

The year 1836 is incorrect because it predates the Mexican-American War and the acquisition of the territories in question.

The year 1876 is incorrect because it is much later than the first census of the conquered territories, which took place in 1850.