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

Consider the following grammar $$G$$

$$\eqalign{ & \,\,\,\,\,\,\,S \to \,\,\,\,\,\,\,F|H \cr & \,\,\,\,\,\,F \to \,\,\,\,\,\,\,p|c \cr & \,\,\,\,\,\,H \to \,\,\,\,\,\,\,d|c \cr} $$

where $$S, F$$ and $$H$$ are non-terminal symbols, $$p, d,$$ and $$c$$ are terminal symbols. Which of the following statement(s) is/are correct?

$$\,\,\,\,\,\,\,S1.\,\,\,\,\,\,\,LL\left( 1 \right)\,\,$$ can parse all strings that are generated using grammar $$G$$
$$\,\,\,\,\,\,\,S2.\,\,\,\,\,\,\,LR\left( 1 \right)\,\,$$ can parse all strings that are generated using grammar $$G$$

Among simple $$LR (SLR) ,$$ canonical $$LR,$$ and look-ahead $$LR$$ $$(LALR),$$ which of the following pairs identify the method that is very easy to implement and the method that is the most powerful , in that order?

Two hosts are connected via a packet switch with $${10^7}$$ bits per second links. Each link has a propagation delay of $$20$$ micro-seconds. The switch begins forwarding a packet $$35$$ microseconds after it receives the same. If $$10000$$ bits of data are to be transmitted between the two hosts using a packet size of $$5000$$ bits, the time elapsed between the transmission of the first bit of data and the reception of the last bit of the data in microseconds is____________.