Discovery flew the first dedicated Department of Defense mission, STS-51-C, in January 1985.
The mission launched from Kennedy Space Center on January 24, 1985, carrying a classified military payload. NASA publicly disclosed few details because the mission was devoted to the U.S. Department of Defense; the payload was deployed using an Inertial Upper Stage booster. Discovery landed at Kennedy three days later, on January 27.
STS-51-C was originally designated STS-10 and was expected to use Challenger. Discovery replaced Challenger after engineers encountered problems with Challenger’s thermal-protection tiles. The flight was Discovery’s third mission and the 15th mission in the overall shuttle program.
The other orbiters in the answer choices also flew military-related missions later, which can cause confusion. The question asks for the first mission dedicated to the Department of Defense, and that distinction belongs specifically to Discovery’s STS-51-C flight. Many details of the mission remain classified.