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Answer : C

$g$ is called a Generator of a Group $(G,*)$ if Every element of $G$ can be expressed in terms of $g,*$. 

So, this way, We can say that for the given Group $G = \left \{ a,a^2,a^3,a^4,a^5 = e \right \}$ :

$a$ is One Generator as every other element can written as $a^n,$ where $n$ is an integer. 

$a^2$ is also a Generator. as $a^2$ can generate $a$ and $a$ is a generator. $(a^2)^3 = a$.

$a^3$ is also a Generator. as $a^3$ can generate $a$ and $a$ is a generator. $(a^3)^2 = a$.

$a^4$ is also a Generator. as $a^4$ can generate $a$ and $a$ is a generator. $(a^4)^4 = a$.

$a^5$ is NOT a Generator. as $a^5$ is the Identity element and Identity element can be a Generator Only for the Group $(e,*)$.

So, the answer for the given question will be Option C.

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