Consider the following statements relating to the level of poker play of four players $$P, Q, R$$ and $$S.$$

$$\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,$$ P always beats Q
$$\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,\,$$ R always beats S
$$\,\,\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,\,\,$$ S loses to P only sometimes
$$\,\,\,\,\,{\rm I}V.\,\,\,\,\,\,\,\,$$ R always loses to Q

Which of the following can be logically inferred from the above statements?

$$\,\,\,\,\,\,\,\,\,\left( i \right)\,\,\,\,\,\,\,\,$$ P is likely to beat all the three other players
$$\,\,\,\,\,\,\,\,\left( ii \right)\,\,\,\,\,\,\,$$ S is the absolute worst player in the set

Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation’s diversity, nothing else is. Which of the following can be logically inferred from the above sentences?

If $$f\left( x \right) = 2{x^7} + 3x - 5,$$ which of the following is a factor of $$f(x)$$?

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of $$80$$ units, it takes $$100$$ cycles for failure. When the load is halved, it takes $$10000$$ cycles for failure. The load for which the failure will happen in $$5000$$ cycles is ________.