Mathematics
GATE MA concept:field-extensions PYQs
Build your understanding with focused practice from past exam papers.
How to practice concept:field-extensions
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–4 of 4. Imported answers require independent review unless marked reviewed.
Question 29
Open questionMANAT1 markNeeds review
Let
, where
is the ring of all polynomials with coefficients in
. Then the degree of the field extension
of
is equal to ________. (answer in integer)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 60
Open questionMAMSQ2 marksNeeds review
Let
and
be field extensions which are not algebraic. Let
be algebraic over
and
. Let
be the subfield of
generated over
by the coefficients of the monic polynomial of minimal degree over
which has
as a zero. Then, which of the following is/are TRUE?Your answerSelect all correct options. You can choose more than one.
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 59
Open questionMANAT2 marksNeeds review
Let
be the field extension of
obtained by adding all the roots of the polynomial equation
. The number of distinct fields
such that
is equal to
(answer in integer)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 21
Open questionMANAT1 markNeeds review
Let
be a primitive complex cube root of unity and
. Then the degree of the field extension
over
(the field of rational numbers) is _____.Log in to check the answer
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