Start the test Question no. 1 Suppose, ω and ω 2 are two distinct cube roots of unity different from 1. Then, what is (ω 1 - ω 2 ) 2 equal to? 3   1   -1   -3 Question no. 2 What is the argument of the complex number (−1 − i) , where i = √(−1)?   5π/4   -5π/4   3π/4 None of these Question no. 3 What is one of the square roots of 3 + 4i, where i = √(−1)? 2+i   2-i   -2 + i   -3 - i Question no. 4 Consider the following statements I. ( ω 10 +1) 7 + ω = 0 II. ( ω 105 +1) 10 = p 10 for some prime number p, where, ω ≠ 1 is a cubic root of unity. Which of the above statement(s) is/are correct? Only I   Only II   Both I and II   Neither I nor II Question no. 5 The origin and the roots of the equation z 2 + pz + q = 0 form an equilateral triangle, if p 2 = q ...

Biochemical oxygen demand Biochemical Oxygen Demand (BOD) is a way to measure how much oxygen is needed by microorganisms to break down organic material in water. Think of it as a test to see how "dirty" the water is with organic waste. The higher the BOD, the more polluted the water is, because it means there's a lot of organic matter that needs to be broken down. How does BOD affect aquatic life? High Biochemical Oxygen Demand (BOD) levels can significantly impact aquatic life. The following are: Oxygen Depletion: When BOD is high, it means there’s a lot of organic matter in the water that microorganisms need to break down. This process consumes a lot of oxygen, reducing the amount available for fish and other aquatic organisms. Stress on Aquatic Life: Low oxygen levels can stress aquatic organisms, making it difficult for them to survive. Fish, in particular, need a certain amount of dissolved oxygen to breathe. Death of Aquatic Organisms: If ...