- Amylase: This is a polysaccharide found in plants, with \( \alpha \)-1,4 and \( \alpha \)-1,6 linkages between glucose units, so the correct linkage type is \( \alpha \)-C1-C4 plant (IV).
- Cellulose: Cellulose is a polysaccharide made of \( \beta \)-1,4 linkages, commonly found in plants, so the correct linkage is \( \beta \)-C1-C4 plant (I).
- Glycogen: Glycogen is a polysaccharide found in animals, consisting of \( \alpha \)-1,4 and \( \alpha \)-1,6 linkages between glucose units, so the correct linkage is \( \alpha \)-C1-C4 \( \alpha \)-C1-C6 plant (III).
- Amylopectin: Similar to glycogen, it is found in plants and is made of \( \alpha \)-1,4 and \( \alpha \)-1,6 linkages, so the correct linkage is \( \alpha \)-C1-C4 plant (II). Thus, the correct answer is (2).
Match List - I with List - II.
Consider the following statements:
(A) Availability is generally conserved.
(B) Availability can neither be negative nor positive.
(C) Availability is the maximum theoretical work obtainable.
(D) Availability can be destroyed in irreversibility's.
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: