#Q176 Which of the following is/are true?
Anonymous Quiz
44%
(Q ,+) is infinitely generated
15%
(P(N),โ) is finitely generated.
30%
ZรZ is Cyclic
11%
Z_(m )รZ is cyclic,mโ 1
#Q177 Set of Rational numbers with odd denominator with addition is a group which is
Anonymous Quiz
8%
non-abelian
24%
Cyclic
38%
Finitely generated
30%
Infinitely generated
#Q178 Let A be any subgroup of (Q ,+) such that |A|= countably infinite. Then number of choices for A is equal to
Anonymous Quiz
23%
Q
29%
N
29%
R
19%
ZรZ
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#Q179 Which of the following statements is/are true for (Q ,+)?
Anonymous Quiz
34%
Every infinitely generated subgroup is cyclic
47%
Every finitely generated subgroup is cyclic
16%
Every finitely generated subgroup need not to be cyclic
3%
None of these.
#Q180 Let G=(C*,โ) is a group. Then
Anonymous Quiz
2%
G is Cyclic
24%
G is finitely generated
39%
G has uncountable no. of elements of finite order.
36%
G has unique cyclic subgroup of order for each nโN.
#Q181 No. of subgroups of order 6. Which one abelian in (C* ,โ) is
Anonymous Quiz
16%
2
47%
1
31%
Infinite
7%
6
#Q182 Which of the following is/are true for (C* ,โ)?
Anonymous Quiz
19%
(C* ,โ) has uncountable No. of subgroups of finite order.
33%
(C* ,โ) has uncountable No. of subgroups of infinite order.
42%
H={zโยข ; |z|=1} , every element of H is of finite order.
5%
โ nโN ,โ ฯ(n) elements of order n
#Q184 No. of subgroups of order 8 in S'={zโ| |z|=1} with multiplication is
Anonymous Quiz
7%
5
39%
2
21%
3
33%
1
Dear Friends , Today Quiz will start at 9:00 AM. Total 10 Questions - Part B - Mathematical Science. Thanks
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#Q185 Which of the following true?
Anonymous Quiz
11%
(R^* ,โ )โ
(C^* ,โ )
25%
(R^* ,โ )โ
(Q^* ,โ )
48%
(R^* ,โ )โ (C^* ,โ )
16%
(R^*,โ )โ
(P(N) ,โ )
#Q186 Collection of Nth root of unity with multiplication forms a subgroup which is of
Anonymous Quiz
37%
Order โ
(n) and Cyclic
30%
Order โ
(n) and non-Cyclic
22%
Order n and only abelian
12%
Order n and Cyclic
#Q187 Which of the following is/are true? H={zโC ;z(2n )=1 ;n=0,1,2,โฆ..}
Anonymous Quiz
23%
Every proper subgroup of (H ,โ ) need not to be Cyclic
51%
Every proper subgroup is finitely generated
13%
โ cyclic group of Infinite order.
13%
Group (H ,โ ) is finitely generated.
#Q188 For (R* ,โ ) , which of the following is/are true?
Anonymous Quiz
18%
Every subgroup is infinitely generated.
38%
Every subgroup is finitely generated.
43%
There exist infinite subgroups of infinite order.
2%
None of these.
#Q189 No. of subgroups of finite order in (R^* ,โ) which are cyclic
Anonymous Quiz
14%
1
18%
2
52%
Countable
15%
Uncountable
#Q190 Let =(C ,+) . Then No. of elements of finite order in GรG is
Anonymous Quiz
14%
1
24%
2
41%
No element of finite order
21%
Uncountable.
#Q191 ZรZ can be generated by
Anonymous Quiz
35%
<1,1>
24%
{<1,2> ,<2,1>}
38%
{( 1 ,0 ),( 0 ,1 )}
3%
{(3 ,0 ),( 0 ,3 )}
#Q192 Let 0(G)= 27 ,and G is non-abelian. Then number of conjugate classes with cardinality 1 is
Anonymous Quiz
20%
9
25%
8
24%
4
31%
3
#Q193 Let A5 be alternating group over 5 elements then, the total no. of conjugate classes for A5 is
Anonymous Quiz
24%
5
42%
4
24%
6
10%
3
#Q194 Let n=2m+1 ,where mโN . Then the number of conjugate classes for D_n is
Anonymous Quiz
38%
(2m+1)/2
31%
(2n+1)/2
17%
(n+2)/2
14%
(n+3)/2