Mathematics
2022 · Paper 1
Take it one question at a time. Try an answer, then check your understanding.
Complete GATE MA 2022 Paper 1 overview, original pages and practice · Timed previous-paper practice
Questions 52–54 of 65. Imported answers require review unless explicitly marked reviewed.
Question 52
Open questionMAMSQ2 marksNeeds review
Let
be an orthonormal set in
such that
, where
is a constant and
is the Legendre polynomial of degree
, for each
. Then, which of the following statements are TRUE?Your answerSelect all correct options. You can choose more than one.
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Open questionMAMSQ2 marksNeeds review
Let
, where
is the smallest topology on
in which all the singleton sets are closed. Then, which of the following statements are TRUE?Your answerSelect all correct options. You can choose more than one.
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Open questionMAMSQ2 marksNeeds review
Consider
, where
is the topology generated by sets of the form
, for
and
. Then, which of the following statements are TRUE?Your answerSelect all correct options. You can choose more than one.
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