Let $$\,\,f\left( x \right) = {x^{ - \left( {1/3} \right)}}\,\,$$ and $${\rm A}$$ denote the area of the region bounded by $$f(x)$$ and the $$X-$$axis, when $$x$$ varies from $$-1$$ to $$1.$$ Which of the following statements is/are TRUE?
$${\rm I}.$$ $$f$$ is continuous in $$\left[ { - 1,1} \right]$$
$${\rm I}{\rm I}.$$ $$f$$ is not bounded in $$\left[ { - 1,1} \right]$$
$${\rm I}{\rm I}{\rm I}.$$ $${\rm A}$$ is nonzero and finite

Let $$𝑅$$ be the relation on the set of positive integers such that $$aRb$$ if and only if $$𝑎 $$ and $$𝑏$$ are distinct and have a common divisor other than $$1.$$ Which one of the following statements about $$𝑅$$ is true?

Consider the following two statements.

$$S1:$$ If a candidate is known to be corrupt, then he will not be elected
$$S2:$$ If a candidate is kind, he will be elected

Which one of the following statements follows from $$S1$$ and $$S2$$ as per sound inference rules of logic?

The larger of the two eigenvalues of the matrix $$\left[ {\matrix{ 4 & 5 \cr 2 & 1 \cr } } \right]$$ is ______.