Algebra MCQs Test 03 - Page 2 of 9 - PAKMATH Primary categor

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1. Let G be a finite group. Let H be a subgroup of G . Then which of the following divides the order of G

order of H

order of G

All of these

index of H

2. The symmetries of rectangle form a

optic Group

Dihedral group of order 8

Permutation group of order 3, S3

Kleins four group D4

3. Let G be a cyclic group of order 24. Then order of $a^9$ is

4. Let $D_4=\left \{ <a,b>;a^4=b^2=(ab)^2=1) \right \}$ be a dihedral group of order 8. Then which of the following is a subgroup of D4

$\left \{ <a,b>;(ab)^2=1) \right \}$

$\left \{ <a,b>;a^4=b^2=1) \right \}$

$\left \{ <a,b>;b^2=1 \right \}$

$\left \{ <a^3,b>;(a^3b)^2=1) \right \}$

5. Any group G van be embedded in a group of bijective mappings of certain sets is a statement of

Lagrang’s theorem

Cayley’s theorem

Isomorphism theorem

Cauchy’s theorem

6. Which of the following is abelian

$S_2$

$S_4$

$S_3$

$S_5$

7. The union of all positive even and all positive odd integers is

Z†

8. Let An be the set of all even permutations of Sn is a subgroup of Sn. Then order of An is

n!/2

n!/3

n+1/2

9. The set of cube roots of unity is a subgroup of

R†

C-{0}

10. If X and Y are two sets, then X∩(XUY)’=0

X∩Y