Mathematics
GATE MA topic:algebra PYQs
Build your understanding with focused practice from past exam papers.
Questions 41–50 of 54. Imported answers require independent review unless marked reviewed.
Question 32
Open questionMAMCQ2 marksNeeds review
Consider the following statements:
I. If
denotes the additive group of rational numbers and
is a non-trivial homomorphism, then
is an isomorphism.II. Any quotient group of a cyclic group is cyclic.
III. If every subgroup of a group
is a normal subgroup, then
is abelian.IV. Every group of order 33 is cyclic.
Which of the above statements are TRUE?
Your answerChoose one option.
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Open questionMAMCQ2 marksNeeds review
Consider the following statements:
I. The ring
is a unique factorization domain.II. The ring
is a principal ideal domain.III. In the polynomial ring
, the ideal generated by
is a maximal ideal.IV. In the polynomial ring
, the ideal generated by
is a prime ideal.(
denotes the set of all integers,
denotes the set of all integers modulo
, for any positive integer
)Which of the above statements are TRUE?
Your answerChoose one option.
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Open questionMANAT2 marksNeeds review
The number of elements of order 15 in the additive group
is ______.
(
denotes the group of integers modulo
, under the operation of addition modulo
, for any positive integer
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Open questionMANAT2 marksNeeds review
Let
be the ring of integers modulo 125 under the operations of addition modulo 125 and multiplication modulo 125. If
is the number of maximal ideals of
and
is the number of non-units of
, then
is equal to ______.Log in to check the answer
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Open questionMAMCQ1 markNeeds review
In the permutation group
, the number of elements of order 8 isYour answerChoose one option.
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Open questionMAMCQ1 markNeeds review
Let
be a commutative ring with 1 (unity) which is not a field. Let
be a proper ideal such that every element of
not in
is invertible in
. Then the number of maximal ideals of
isYour answerChoose one option.
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Open questionMANAT1 markNeeds review
Let
be a field with
elements and let
be a subfield of
with 49 elements. Then the dimension of
as a vector space over
is ________.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 29
Open questionMAMCQ2 marksNeeds review
Consider the polynomial
in the ring
of polynomials in the variable
with coefficients in the field
of rational numbers. ThenYour answerChoose one option.
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Open questionMAMCQ2 marksNeeds review
Which one of the following statements is true?
Your answerChoose one option.
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Open questionMAMCQ2 marksNeeds review
For an odd prime
, consider the ring
. Then the element 2 in
isYour answerChoose one option.
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