Algebra mcqs tests 06 - Page 4 of 9

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1. If aN={ax|x∈ N} then 3N∩5N=

12N

15N

2. The number of subgroups of a group is

One

at most two

at least two

two

3. A mapping $\Phi : G \rightarrow \rightarrow G'$ is called homorphism if a, b belongs to G

$\Phi(ab)=\Phi(a)-\Phi(b)$

$\Phi(ab)=\Phi(a)+\Phi(b)$

$\Phi(ab)=\Phi(a) \Phi(b)$

$\Phi(ab)=\Phi(a) \Phi(b)^{-1}$

4. which binary operation is not defined in the set of natural number

subtraction

multiplication

None

addition

5. Which of the following is the representation of $C_4= \left \{1,-1,i,-i \right \}$

$<x:x^4=1>$

$<a,b:a^4=b^2=1>$

$<a,b:a^2=b^2=(ab)^2=1>$

$<a,b:a^3=b^2=(ab)^2=1>$

6. Let H,K be the two subgroups of a group G. Then set HK={hk|h∈H ^ k∈ K} is a subgroup of G if

All of these

G is abelian

G is cyclic

G is a prime number

7. A group G is abelian then

|G|≤ 3

|G|≤ 9

|G|≤ 12

|G|≤ 5

8. The symmetries of square form a

Group of quarternian

Kaleins four group, V4

Dihedral group of order 8, D4

permutatation group of order 3

9. In $S_3,a=\begin{pmatrix} 1 & 2 & 3\\ 2& 3 & 1 \end{pmatrix} ,then \,\ a^{-1}=$

$\begin{pmatrix} 1 & 2 & 3\\ 3& 1& 2 \end{pmatrix}$

$\begin{pmatrix} 1 & 2 & 3\\ 2& 3 & 1 \end{pmatrix}$

None

$\begin{pmatrix} 1 & 2 & 3\\ 3& 2 & 1 \end{pmatrix}$

10. Let G be a group of order 36 and let a belongs to G . The order of a is