NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 72  80 of 101
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Question number: 72
» Taylor Series Expansion (Complex)
Appeared in Year: 2009
Describe in Detail
Write down the coefficient of in the Taylor series expansion of the function about the origin.
Explanation
Taylor series expansion about the origin is given by
Now coefficient of is
… (104 more words) …
Question number: 73
» Square Root of a Complex Plane
Appeared in Year: 2012
Describe in Detail
Find all the square Roots of the complex number.
Explanation
The square roots of are
And
Here let
Comparing
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Question number: 74
» Definite Integral as Limit of a Sum
Appeared in Year: 2015
Write in Short
Evaluate
Question number: 75
Appeared in Year: 2015
Describe in Detail
Let . Evaluate the determinant
Explanation
Let
Applying , then
Taking
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Question number: 76
» Definite Integral as Limit of a Sum
Appeared in Year: 2005
Describe in Detail
Evaluate
Explanation
………. eq. (A)
Replace by by the sign of .
Lower lim
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Question number: 77
Appeared in Year: 2015
Describe in Detail
Evaluate
Explanation
This is exponential form form
Using the result
If
Then
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Question number: 78
Appeared in Year: 2011
Describe in Detail
Find the cube Roots of
Explanation
Let
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Question number: 79
» Differentiability in Complex Plane
Appeared in Year: 2007
Question
Which of the following function are differentiable at ?
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  All a. , b. and c. are correct 

Question number: 80
Appeared in Year: 2014
Question
Which of the following statements are true?
Choices
Choice (4)  Response  

a.  If , then is rational when n is even 

b.  If , then is rational when n is odd 

c.  If , then is Irrational when n is even 

d.  Question does not provide sufficient data or is vague 
