- 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).
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____
If \[ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6 \], then f(1) is equal to: