Here we have $n$ vertices & $n$ edges. So we must have cycle.

So (C) has at least one cycle is True & (A) is false.

(D) The graph obtained by removing any two edges from $G$ is not connected $\rightarrow$ This is true, for graph of $n$ vertices to be connected, we need at least $n-1$ edges. If we remove $2$ out of $n$, we get $n-2$ edges, which can connect at max $n-1$ vertices. $1$ Vertex at least will be disconnected. So D is true.

(B) is false as if graph is cyclic graph then removing any edge will not disconnect graph.

Option (C) might not be correct because they have used the word "at least one cycle" while a graph with n vertices and n edges, graph will contain exactly 1 cycle.

But 'at least' contains the possibility of 'exactly one', hence option (C) also can be considered as true statement.

In quality exams like GATE there is nothing called “strongest” unless it is mentioned in question. If a regular language is given and if CFL is an option, that is correct. Similarly if “exactly” is correct, “at least” is also correct as exactly implies “at least”. Even “not more than 1” is correct as “exactly one” does imply “not more than one”.

yes Sir in this year’s GATE the same question came from TOC. I thought that if in option it is given as “ Language(L2) is CFL” so it is not clear that whether they are only focusing on CFL and neglecting that the language is regular as well OR they are saying that the given language is both regular and CFL. thats why i didn’t marked that option .

so unless it is mentioned in the question to select the strongest one , we have to select the superset’s of the answers as well right?

That’s always the case. You are a man but also a human being and and also a living being. Only due to solving bad questions students have these confusions.

if there are n vertices if you want to make it as a connected graph , there should be at least n-1 edges. hence if we remove two edges, it wont be a connected graph hence answer :d