Question 1. $A(S)$ is commutative if $S$ has     elements.

	i)	$2$
	ii)	$3$
	iii)	$4$
	iv)	$5$

Question 2. There are     subgroups of $S_3$ which are not normal in $S_3$.

	i)	$2$
	ii)	$3$
	iii)	$4$
	iv)	$5$

Question 3. In a group of order $72$, $c_e=$    .

	i)	$1$
	ii)	$8$
	iii)	$9$
	iv)	$72$

Question 4. For subgroups $H,K$ of a group $G$, if $o(H)=\underline{}$ and $o(K)=$     , then $HK$ is cyclic.

	i)	$2,2$
	ii)	$2,3$
	iii)	$3,3$
	iv)	$3,5$

Question 5. The smallest possible order of a group $G$ in which converse of the Lagrange’s theorem fails is     .

	i)	3
	ii)	6
	iii)	9
	iv)	12

Question 6. The order of $5$-Sylow subgroups of $S_{25}$ is     .

	i)	$5^6$
	ii)	$6^5$
	iii)	$5^2$
	iv)	$2^5$

Question 7. If $G=N_1\cdot N_2\cdot N_3$, a direct product, then $N_2$     .

	i)	is nonabelian
	ii)	$\cap (N_1\cdot N_3)=\{e\}$
	iii)	is abelian
	iv)	is finite

Question 8. Number of nonisomorphic abelian groups of order 672 is     .

	i)	$5$
	ii)	$7$
	iii)	$9$
	iv)	$32$