NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 35 - 43 of 101

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Question number: 35

» Indeterminate Forms

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Appeared in Year: 2012

MCQ▾

Question

Let be a sequence of functions defined on . Determine . For each the following.

Choices

Choice (4)Response

a.

b.

c.

d.

All a. , b. and c. are correct

Question number: 36

» Geometry in Complex Plane

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Appeared in Year: 2013

Essay Question▾

Describe in Detail

Find the area of the polygon whose vertices are represented in the complex plane by the eighth roots of unity.

Explanation

Figure of the area of the polygon

Figure of the Area of the Polygon

In triangle OAB

area of triangle

Area of polygon whose vertices are represented in the complex plane by the eighth roots of unity

… (15 more words) …

Question number: 37

» Indeterminate Forms

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Appeared in Year: 2011

Essay Question▾

Describe in Detail

Evaluate

Explanation

And

This is exponential form

Using the Result:

If

Then

Now

… (141 more words) …

Question number: 38

» Maxima and Minima

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Appeared in Year: 2007

Essay Question▾

Describe in Detail

Find the Minimum value of the function:

Explanation

Here

Step I:

Step II: Let us solve

i. e

and

we get

is the only critical point

Step III:

… (121 more words) …

Question number: 39

» Nth Roots of Unity

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Appeared in Year: 2005

Essay Question▾

Describe in Detail

Let denote the seventh roots of unity. Evaluate

Explanation

Let x be nth root of unity. Then

(Where k is an integer)

Let . Then nth roots of unity

… (277 more words) …

Question number: 40

» Maxima and Minima

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Appeared in Year: 2006

Essay Question▾

Describe in Detail

What is the relation between the height and radius of a right circular cylinder of fixed volume and Minimal Total surface area?

Explanation

Here given that is the radius of the base of right circular cylinder and its height. is the volume and Let be the total surface area.

Also

Now

… (92 more words) …

Question number: 41

» Geometry in Complex Plane

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Appeared in Year: 2012

Essay Question▾

Describe in Detail

Find the area of the pentagon whose vertices are the fifth root of unity in the complex plane.

Explanation

To find fifth root of unity.

Let

Figure of the area of pentagon

Figure of the Area of Pentagon

Putting we get

… (215 more words) …

Question number: 42

» Definite Integral

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Appeared in Year: 2015

Essay Question▾

Describe in Detail

Does the integral exist? If it exists give its value.

Explanation

Yes, its value is…

Note that is not defined for . Here we can write;

(Integration by parts)

………eq. (A)

Now

… (92 more words) …

Question number: 43

» Convergence of Positive Series Test

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Appeared in Year: 2014

Essay Question▾

Describe in Detail

Which of the following series are convergent?

a)

b)

c) , Where

Explanation

Option (a) The given series is where

Take

Which is finite and non –zero

By comparison test

behave alike

But is divergent by p –test

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