Which is incorrect about cofactor?
A) Every coenzyme is a cofactor and every cofactor is a coenzyme.
B) Every coenzyme is a cofactor and every cofactor is not a coenzyme.
C) Most of the coenzymes are nucleotides and are composed of vitamins.
D) Coenzymes are the active constituents of the enzymes.

Hint: Cofactor is the non protein part of the enzyme. Cofactors are considered as the assistant molecules which help in biochemical reactions.

Complete Answer:
A) A cofactor is a non-protein compound or a metallic ion required by an enzyme to carry out enzymatic catalysis. . Organic cofactors are vitamins or are derived from vitamins. Cofactors are continuously recycled in a reaction.
Some examples of cofactors are calcium ion, magnesium ion, organic molecules etc.

B) Cofactors which are organic molecules are called the Coenzymes. They are derived from vitamins and other organic essential nutrients which bind at the active site and help the substrate to bind. Coenzymes can act as a cofactor and enhance the enzymatic activity. This statement A, C, D is correct.

C) Cofactors do not bind the enzymes but their presence brings about an enzymatic reaction. Hence they are not coenzymes. This statement is incorrect about cofactor.

Thus the correct answer is (B). All the coenzymes are cofactors but all cofactors cannot be coenzymes.

Note: Cofactors can be metallic ions or organic molecules. Cofactors do not bind at the active site whereas coenzymes bind at the active site to aid substrate binding.