GATE 2015 CSE & IT PYQ

Question

Consider the equality $$\sum\limits_{i = 0}^n {{i^3}} = X$$ and the following choices for $$X$$
$$\eqalign{ & \,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\Theta \left( {{n^4}} \right) \cr & \,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\Theta \left( {{n^5}} \right) \cr & \,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,O\left( {{n^5}} \right) \cr & \,\,\,{\rm I}V.\,\,\,\,\,\,\Omega \left( {{n^3}} \right) \cr} $$
The equality above remains correct if $$𝑋$$ is replaced by

Accepted Answer

$${\rm I}$$ or $${\rm III}$$ or $${\rm IV}$$ but not $${\rm II}$$

Answer

Only $${\rm I}$$

Answer

Only $${\rm II}$$

Answer

$${\rm II}$$ or $${\rm III}$$ or $${\rm IV}$$ but not $${\rm I}$$