We are told that evolution is a continuing phenomenon for all living things. Are humans also evolving? Justify your answer.

Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

Do you think it is ethical to manipulate organisms for human benefits? Justify your answer.

Though the confict between humans and wildlife started with ebolution of man, the intensity of conflict has increased due to activities of modern man. Justify your answer with suitable examples.

In a given habitat we have 20 plant species and 20 animal species. Should we call this as 'diversity' or biodiversity'? Justify your answer.

Consider the binary operations * : RxxRrarrR and o : RxxRrarrR defined as a*b = |a – b| and aob = a, forall a, b in R Show that ∗ is commutative but not associative, o is associative but not commutative. Further, show that ∀ a, b, c in R , a * (b o c) = (a * b) o (a * c) . [If it is so, we say that the operation ∗ distributes over the operation o]. Does o distribute over ∗? Justify your answer.

Let f:NrarrN be defined by, f(n) = {((n+1)/2,,if n is odd,,),(n/2,,if n is even,,):} for all n in N . State whether the function f is bijective. Justify your answer.

A capacitor of 10 microfarad is connected in series with a resistance of 2.2 xx 10^5 ohm. Determine the time constant for the circuit. Can we think of oscillations in this circuit, such that the frequency is equal to the inverse of the time constant? Justify your answer with proper explanation.

State whether the following statement is always true, always false or ambiguous. Justify your answer. All humans are mortal.

State whether the following statements are always true, always false or ambigous. Justify your answer : All human beings grow old.

State whether the following statements are always true, always false or ambigous. Justify your answer : All mathematics textbooks are interesting.