1
GATE CSE 2016 Set 1
+2
-0.6
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

A
$$(i)$$ only
B
$$(ii)$$ only
C
$$(i)$$ and $$(ii)$$ only
D
neither $$(i)$$ nor $$(ii)$$ only
2
GATE CSE 2016 Set 1
+2
-0.6
If $$f\left( x \right) = 2{x^7} + 3x - 5,$$ which of the following is a factor of $$f(x)$$?
A
$$\left( {{x^3} + 8} \right)$$
B
$$\left( {x - 1} \right)$$
C
$$(2x-5)$$
D
$$(x+1)$$
3
GATE CSE 2016 Set 1
+2
-0.6
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 ________.
A
$$40.00$$
B
$$46.02$$
C
$$60.01$$
D
$$92.02$$
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