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CSIR NET Mathematics 2022| Algebra (27 OCTOBER)
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Question 1
For a positive integer p, consider the holomorphic function
for z ∈ 
. For which values of p does there exist a holomorphic function such that f(z)=g’(z) for z ∈ 
?
for z ∈ . For which values of p does there exist a holomorphic function such that f(z)=g’(z) for z ∈ ?
Question 2
What is the solution of the following system of congruences, x ≡ 3(mod 4), x ≡ 4(mod 5), x ≡ 6(mod 7)
Question 3Multiple Correct Options
If 
. Then which of the following statements is/are true.
. Then which of the following statements is/are true.Question 4Multiple Correct Options
Let 
denote the number of those permutations 
on 
such that 
is a product of at least three disjoint cycles. Then
denote the number of those permutations on such that is a product of at least three disjoint cycles. Then
Question 5Multiple Correct Options
Which of the following is/are true?
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