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Polymer of $\alpha - D$ glucose is
(A) Glycogen
(B) Cellulose
(C) Inulin
(D) Callose

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Answer
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Hint: Polysaccharides are polymers or chains of monosaccharides and are macromolecules. They are threads (literally a cotton thread) containing different monosaccharides as building blocks and are branched or unbranched. In a polysaccharide the individual monosaccharides are linked by a glycosidic bond. The right end of a polysaccharide is reducing end while the left end is non-reducing end.

Complete answer:
There are two types of polysaccharides namely:
Homopolysaccharides: they are polysaccharides that consist of only one type of monosaccharide monomer. Starch and glycogen both are polymers of glucose and serve as a storage form in plants and animals respectively.
Heteropolysaccharides: these consist of more than one type of monosaccharide monomer, that is they are heteropolymers and are more complex polysaccharides.
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 Diagram showing the polymer in which glucose molecules are linked
 Now let us know the polymer given in options :-
Glycogen :- Glycogen is made up of about 30,000 glucose residues. It's a branched structure having $\alpha $1,4 and 1, 6 linkage. It gives red colour with iodine. Thus, this option is correct.
Cellulose :- Cellulose is the main structural unbranched homopolysaccharide of plants. One molecule of cellulose has about 6000 $\beta $-glucose residues and not $\alpha $ residues. Thus, this option is not correct.
Inulin :- Inulin is a polymer of fructose. It is a storage polysaccharide of roots and tubers of dahlia and related plants.
Callose :- it is a type of plant polysaccharide but it is made up of $\beta $ 1, 3 glucose linkage. Thus this option is not correct.

Our required answer is A) glycogen.

Note: One more polymer of glucose is starch. Starch has two components - amylose (an unbranched polymer) and amylopectin (a branched polymer).
Amylopectin : Consists of 2000 - 200,000 glucose molecules forming straight chain and branches (after 25 glucose units). Branching point has a $\alpha $ 1-6 glycosidic linkage.
Amylose : Consists of , $\alpha $ 1-4 glycosidic linkage between $\alpha - D$ glucose molecules. It is a straight chain of 200 - 1000 glucose units. It is helical, each turn consists of 6 glucose units.