Break the question into two separate checks: is the wave stationary or progressive, and is it longitudinal or transverse.
The sitar wire is tied down at both ends, so any wave sent along it bounces back from each end. The forward wave and the returning wave add together, and this addition produces fixed nodes and antinodes that do not move along the wire. A pattern like this is called a stationary or standing wave, not a progressive one.
In a longitudinal wave, particles move back and forth along the same line as the wave. In a transverse wave, particles move perpendicular to the wave direction. Plucking a sitar string displaces it sideways, and it keeps vibrating up and down while the disturbance travels along the length of the wire, which is transverse motion.
Combining both checks, the vibration is stationary and transverse, so option D is correct.