Growth of textile industry in medieval Europe

Write a note on the medieval empires of Morocco.

Give a brief account of the prominent trading communities of the medieval period.

Describe the general debate on the decline of feudalism

Compare nature of Sufyanid and Marwanid Ummayad Caliphates. How did Malik bin Marwan change the nature of Ummayad Caliphate from loose organization to a centralizing state

Name some religious sects/cults in the Roman world before the dominance of Christianity. Why was the Roman world called as a ‘civilization of borrowings’?

How long will it take a given sum of money (Say in Rupees) to increase 4 times its present value when compounded half yearly at 7% rate of interest

If the demand function for a good is Q=140 – 5P, what is the price elasticity of demand at P = 15 rupees?

Evaluate the Limits of

. Find the integral of

(y² -1) dx-2dy = 0

What is a point of inflexion ? Does f(x) = x³ have a point of inflexion at x = 0?

Find the Euclidean distance between

(i) (2, 5) and (4, 2)

(ii) (1, 3, 4) and (4, 2, -5)

Create a truth table for

(a) A  B

(b) the converse of ‘A implies B’.

Given A= { 1, 2, }, B= { 3, 4, 5 } and C= { 3, 5, 6, 7, 8 }, show that

(i) A B= B A

(ii) (A B )  C= A (B C )

Let 

Find, X U Y and the Cartesian Product of X and Y

Given the aggregate consumption function C = 0.9Y + 100(where C is aggregate consumption and Y is aggregate income)

(a) Find the marginal propensity to consume (MPC) and average propensity to consume (APC)

(b) Find the elasticity of consumption with respect to income, and show that it equals MPC/APC

Given the total cost function TC = 18q ² + 4q + 16,200

(a) Find marginal cost (MC) and average coat (AC) as functions of q

(b) Show that when MC < AC, AC is falling, and when MC > AC, AC is rising

Given the demand function P_D = 27 – Q ² and supply function Ps = 2Q + 3. Assuming perfect competition, find (i) the consumers’ surplus, (ii) the producers’ surplus.

A firm in a perfectly competitive market has the following cost function: C = 1/3q³ – 5q² + 30q +10 If the market-clearing price is 6, obtain the profit maximising level of output

A monopolist firm has the following total revenue and total cost functions

     R = - mQ² + nQ                                ( m,n > 0)

     C = aQ² + bQ + c                                   (a,b,c > 0)

Suppose that the government plans to levy an excise tax on the product of this firm and wishes to maximise the total tax revenue T from this source. What tax rate t ( rupees per unit of output) should the government choose?