For the (M/M/K) : (∞ / FIF )0 queuing model with arrival rate λ and service rate per service channel µ, obtain the steady-state probability of n customers in the system, P . n Hence or otherwise, find the probability that an arrival has to wait.

Consider the following system considering of two switches I and II between two points A and B:

A signal is sent from the point A to point B and is received at B if both the switches I and II are closed. It is assumed that the probabilities of I and II being closed are 0.8 and 0.6 respectively and that P [II is closed] I is closed] = P [II is closed].

Find:

i) The probability that signal is received at B.

ii) The conditional probability that switch I was open, given that the signal was not received at B,

iii) The conditional probability that switch II was open, given that the signal was not received at B.

In a certain state, 58 landfills are classified according to their concentration of three hazardous chemicals: arsenic, barium and mercury. Suppose that the concentration of each one of the three chemicals is characterized as either high or low. If a landfill is chosen at random from among 58 landfills, given the following configuration:

Find the probability that it has:

i) high concentration of Barium,

ii) high concentration of mercury and low concentration of both Arsenic and Barium and

iii) high concentratin of any one of the chemicals and low concentration of the other two.

A study about a population showed that the mobility of population of a state to a village, town and city is in the following percentages:

What will be the proportion of population village, town and city after one year and two years, given that the present proportion of the population in the village, town and city are respectively 0.50, 0.40 and 0.10?

What is sampling? Explain the different methods of probability sampling.

List the different operational process that need to be done to bring data into a presentable form and explain each process with suitable examples.

Describe the various steps adopted in test construction in order to arrive at accuracy in the result.

Explain the different components of a project proposal.

Describe the concept of community ownership in CSR activities with suitable examples.

Analyse the role of CSR in achieving women's empowerment in India.

Discuss the different sections under Companies Act of 2013 related to CSR?

Write Essay on the perspective of CSR in global context, with special reference to developed countries.

Explain any two key international conventions and financing mechanisms for the conservation and sustainable management of aquatic ecosystems, with special reference to developing countries.

Identify the measures for research and capacity building initiated by government for achieving sustainable use of freshwater and marine aquatic ecosystems in India.

Discuss any two major drivers for the degradation and loss of integrity in wetland ecosystem, with special reference to India.

Explain the structure and ecology of various types of river systems.

Appreciate the role and significance of technological interventions in metering, billing and collection for the utility's revenue protection.

Explain the metering techniques used for LT and HT consumer metering.

 Explain various long term plans for technical loss reduction in distribution systems.

Write down provisions laid out in Indian Electricity Rules regarding:

(i) Clearance from buildings of low and medium voltage lines and service lines, and

(ii) Intimation of Accidents