Question 1 |
Which of the following statements is/are TRUE for a group G?
MSQ
MSQ
If for all x,y \in G, (xy)^2=x^2y^2, then G is commutative. | |
If for all x \in G, x^2=1, then G is commutative. Here, 1 is the identity element of G. | |
If the order of G is 2 , then G is commutative. | |
If G is commutative, then a subgroup of G need not be commutative. |
Question 1 Explanation:
Question 2 |
Let G be a group of order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?
Both G and H are always cyclic. | |
G may not be cyclic, but H is always cyclic. | |
G is always cyclic, but H may not be cyclic. | |
Both G and H may not be cyclic. |
Question 2 Explanation:
Question 3 |
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is _______.
34 | |
35 | |
5 | |
7 |
Question 3 Explanation:
Question 4 |
(G,*) is an abelian group. Then
x=x^{-1} for any x belonging to G | |
x=x^{2} for any x belonging to G | |
(x * y)^{2}=x^{2} * y^{2} , for any x,y belonging to G | |
G is of finite order |
Question 4 Explanation:
Question 5 |
Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is ________.
42 | |
21 | |
24 | |
84 |
Question 5 Explanation:
Question 6 |
f (G,.) is a group such that (ab)^{-1}=a^{-1}b^{-1},\forall a,b \in G, then G is a/an
Commutative semi group | |
Abelian group | |
Non-abelian group | |
None of these |
Question 6 Explanation:
Question 7 |
There are two elements x,y in a group (G,*) such that every element in the group can be
written as a product of some number of x's and y's in some order. It is known that
x * x = y * y = x * y *x * y = y* x * y *x = e
where e is the identity element. The maximum number of elements in such a group is _______.
x * x = y * y = x * y *x * y = y* x * y *x = e
where e is the identity element. The maximum number of elements in such a group is _______.
3 | |
4 | |
5 | |
6 |
Question 7 Explanation:
Question 8 |
Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L\neqG and that the size of L is at least 4. The size of L is _______.
4 | |
5 | |
6 | |
7 |
Question 8 Explanation:
Question 9 |
The arithmetic mean of attendance of 49 students of class A is 40% and that of 53 students of class B is 35%. Then the percentage of arithmetic mean of attendance of class A and B is
27.20% | |
50.25% | |
51.13% | |
37.40% |
Question 9 Explanation:
Question 10 |
Consider the set S = {1, \omega ,\omega ^{2}}, where \omega and \omega ^{2} are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms
A group | |
A ring | |
An integral domain | |
A field |
Question 10 Explanation:
There are 10 questions to complete.
Please add a feature to BOOKMARK questions for revision. It would be really helpful.
check question 20 ,answer should be option c
For the Q24, The answer is option C