NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 14 - 19 of 101

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Question number: 14

» Points of Continuity

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Appeared in Year: 2012

Essay Question▾

Describe in Detail

List the let of points of discontinuity, if any for the following function

a) Defined by

b) Defined by

c) Defined by

Where is the largest integer less than, or equal to .

Explanation

(a) Two cases arise

Case I: is irrational

Left hand limit

Here can be rational or rational

can be

L. H. L d

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Question number: 15

» Binomial Series

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Appeared in Year: 2013

Essay Question▾

Describe in Detail

Find the sum of the infinite series

Explanation

……. . eq. (A)

Comparing eq. (A) with the standard form i. e.

… (127 more words) …

Question number: 16

» Geometry in Complex Plane.

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Appeared in Year: 2014

Essay Question▾

Describe in Detail

Find the area of the triangle in the complex plane whose vertices are the points representing the number , the cube roots of unity.

Explanation

Let then

Or

Or

So the cube roots of unity are

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Question number: 17

» Maxima and Minima

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Appeared in Year: 2014

Essay Question▾

Describe in Detail

A right circular cylinder is inscribed in a sphere of radius . What is the height of the cylinder when its volume is maximal?

Explanation

Let be the radius and height of the inscribed cylinder respectively.

A right circular cylinder

A Right Circular Cylinder

A right circular cylinder

In

……………eq. (1)

Volume o

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Question number: 18

» Radius of Convergence

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Appeared in Year: 2015

Short Answer Question▾

Write in Short

Find the Radius of Convergence of the series

Question number: 19

» Geometry in Complex Plane.

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Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let be the polygon in the complex plane with vertices situated at the nth Roots of unity. Let be the area and let be its perimeter. Evaluate .

Explanation

The points represented by nth roots of unity are located at the vertices of a regular polygon of n sides, inscribed in a unit circle having center at the origin, one vertex being on the positive real axis (in figure below)

The positive real axis

The Positive Real Axis

The positive real axis

But when n approaches to infinity, the n sided polygon will approach to circ

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