Algebra mcqs tests 06 - PAKMATH Algebra MCQs

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1. which of the following is even permutation

$\bigl(\begin{smallmatrix} 1 & 2 & 3 & 4\\ 2 & 4 & 1 & 3 \end{smallmatrix}\bigr)$

None

$\bigl(\begin{smallmatrix} 1 & 2 & 3 & 4\\ 2 & 1 & 4 & 3 \end{smallmatrix}\bigr)$

$\bigl(\begin{smallmatrix} 1 & 2 & 3 & 4\\ 2 & 3 & 1 & 4 \end{smallmatrix}\bigr)$

2. Let G be a group and a,b ∈ G then order of $a^{-1}$ =

$b^{-1}$

$bab^{-1}$

3. Let G be a cyclic group . Then which of the following cab be order of G.

1000000007

107

all of these

4. Let X has n elements. The Set Sn of all permutations of X is a group w.r.t to mappings

inverse

addition

multilpication

composition

5. The group in which every element except the identity element has infinite order is called

a-periodic

all of these

torsion free

locally infinite

6. Number of non-empty subsets of the set {1,2,3,4}

7. R+ is a group of non-zero positive real number under multiplication. Then which of the following group under addition is isomorphic to R+

8. Let G be a cyclic group of order 17. The number of subgroups of G are

9. If X and Y are two sets s.t n(x)=17, n(Y)=23 and n(X∪Y)=38 then n(X∩Y)=?

10. Let G be an infinite cyclic group . Then the number of generators of G are