Let P (w , w ) = 1 2 be a portfolio of two securities X and Y. Find the values of w1 and w2 in the following situations: i) ρxy = −1 and P is risk free. ii) σx = σy and variance P is minimum.

Variance P is minimum and ρxy = − ,5.0 σx = 2 and σy = 3

Return distributions of the two securities are given below:

 Find which security is more risky in the Markowitz sense. Also find the correlation coefficient of securities X and Y.

Tumour is developing from the organ of a human body with concentration 9 2.3 ×10 with growth and decay control parameters 9.2 and 2.7 respectively. In how many days the size of the tumor will be twice?

Let G )t( be the amount of the glucose in the bloodstream of a patient at time t. Assume that the glucose is infused into the bloodstream at a constant rate of k /g min . At the same time, the glucose is converted and removed from the bloodstream at a rate proportional to the amount of the glucose present. If at t = ,0 G = G )0( then

i) formulate the model.

ii) find )t(g at any time t.

iii) discuss the long term behavior of the model.

If D+ and D ̶ denote presence and absence, respectively, of a disease and T+ and T ̶ denote test result as positive and negative, respectively, then on the basis of the following information:

			Total
	145	2000	2145
	15	48000	48015
Total	160	50000	50160

Find: (i) sensitivity (ii) specificity (iii) positive and negative predictive values.

A company manufacturing soft drinks is thinking of expanding its plant capacity so as to meet future demand. The monthly sale for the past 5 years are available. State, giving reasons, the type of modelling you will use to obtain good estimates for future demand so as to help the company make the right decisions. Also state four essentials and four non-essentials for the problem.

Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?

In a parallel-line assay, total 18 guinea pigs, 4 guinea pigs each from 3 different breeds were selected and classified into 4 groups for each breed. Two groups were administered with two doses of the standard preparation and remaining two groups with two doses of the test preparation. The responses of these doses are recorded in the following table:

(i) Determine the dose-response regression models for both preparations.
(ii) Test whether the dose-response curves of both preparations are linear and parallel to each other or not.
(iii) Interpret whether the relative potency and its confidence interval can be computed or not. 

The data on population and number of deaths for different age groups of Districts A and B in the year 2001 were collected in the following table:

Calculate standardised death rate by direct method, taking population of District A as the standard population.

Briefly explain the major components of research report.

Explain the various types of sampling

Discuss the various aspects of Evaluation

What is Project Proposal? Explain the various steps in project proposal formulation.

Define Globalisation indicators. What are its limitations?

What are the major significances of second wave of globalisation?

Discuss any two environmental issues due to colonisation.

Write an essay on social changes due to global conventions

What are the major factors contributing to effective community ownership and engagement?

Explain the meaning and concept of quality of life. Discuss the role of CSR in enhancing the quality of life.

Discuss any five CSR related sections of Companies Act

Write an essay on historical perspectives of CSR.