Column-1 | Column-2 | ||
(i) | Propionibacterium Shermanii | (P) | Fermenting fruit prices to produce ethanol |
(ii) | Saccharomyces Cerevisiae | (Q) | Citric Acid |
(iii) | Aspergillus niger | (R) | Swiss Cheese |
(iv) | Trichoderma polysporum | (S) | Immuno-suppressive |
If the value of \( \cos \alpha \) is \( \frac{\sqrt{3}}{2} \), then \( A + A = I \), where \[ A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix}. \]
There are several valuable microorganisms that are beneficial to humans in various manners such as: