The key idea here is the definition of a composite muscle: one that arises from two separate myotomic masses and as a result carries a dual nerve supply, with each part keeping the nerve of its original mass.
Test the options against that rule. Flexor digitorum profundus splits its innervation between the median nerve through the anterior interosseous branch for the index and middle finger portion and the ulnar nerve for the ring and little finger portion, a textbook dual supply. Pectineus straddles the boundary between the anterior and medial thigh compartments, so it commonly receives both the femoral nerve and the obturator nerve. Biceps femoris is built from a long head and a short head that take their nerves from the two divisions of the sciatic nerve, tibial for the long head and common fibular for the short head. All three therefore qualify as composite.
Flexor carpi ulnaris breaks the pattern. It comes from the single common flexor origin and is innervated only by the ulnar nerve, with no second nerve and no second mass. It is a simple, not composite, muscle.
$\therefore$ the muscle that is not composite is flexor carpi ulnaris.
\[\boxed{\text{Flexor carpi ulnaris}}\]