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Question:

c) Prove that the linear fractional transformation $\Phi (z)=\frac{2z-1}{2-z}$ maps the circle c : | z | =1 into itself. Also prove that f (z) is conformal in D ={z:| z| $\leq$ 1}.

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Question:

Using the recurrence relation

$(n+1)P_{n+1}(x)=(2n+1)xP_{n}(x)-nP_{n-1}(x),$

prove that

$(2n+1)^2\int_{-1}^{1}x^2$ $P_{n}^{2}(x)dx=\frac{2(n+1)^2}{(2n+3)}+\frac{2n^2}{(2n-1)}$

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Question:

(b) Departmental store and Multiple shop.

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Question:

(a) Selective distribution and exclusive distribution.

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Question:

Find the zeros and singularities of the function $f(x)=\frac{z}{4cos^{2}z-1$ in $\left | z \right |\leq 1.$ Also find the residue at the poles.

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Question:

Merchant Agents

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Question:

Digital Marketing

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Question:

Write short notes on:

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Question:

What is Green Marketing? Discuss its importance.

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Question:

Define rural marketing and challenges faced by rural marketers.

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Question:

What do you mean by services? Discuss its characteristics.

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Question:

What are the factors that determine the choice of media?

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Question:

List out the tools used in trade promotion.

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Question:

How is a retailer different from a wholesaler?

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Question:

What are the functions of channels of distribution. Explain them.

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Question:

Discuss the basic purpose of changing the package?

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Question:

Briefly explain the factors that affect the basic price of product or service?

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Question:

How is the distinction between buyer and user meaningful to a marketer?

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Question:

Expand $f(z)=\frac{1}{(z-1)^{2}(z-3)}$ in a Laurent series valid for

(i) $0< \left | z-1 \right |< 2$ and

(ii) $0< \left | z-3\right |< 2$ .

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Question:

Using Laplace transform technique, solve the following initial value problem:

$\frac{dx}{dt}+\frac{dy}{dt}=t,\frac{d^2x}{dt^2}-y=e^{-t},$

$x(0)=0,y(0)=0,\frac{dx}{dt}=0,$ for $t=0.$

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