Obtain seasonal Indices by the “Moving average” method from the following data:
| Quarterly output of a Factory | ||||
| Year | I | II | III | IV |
| 2010 | 65 | 58 | 56 | 61 |
| 2011 | 68 | 63 | 63 | 67 |
| 2012 | 70 | 59 | 56 | 52 |
| 2013 | 60 | 55 | 51 | 58 |
Define the binding energy of nuclei. Draw a graph between binding energy per nucleon as a function of mass number. Write the main features of the curve.
See Answer →The mean life of a radioactive element is 17.31 months. Calculate the time required for 75% of the element to decay.
See Answer →A solicitors’ firm employs typists on hourly price-rate basis for their daily work. There are five typists and their charges and speed are different. According to an earlier understanding only one job is given to one typist and the typist is paid for a full hour even if he works for a fraction of an hour. Find the least cost allocation for the following data:
| Typist | Jobs | ||||
| P | Q | R | S | T | |
| A | 85 | 75 | 65 | 125 | 75 |
| B | 90 | 78 | 66 | 132 | 78 |
| C | 75 | 66 | 57 | 114 | 69 |
| D | 80 | 72 | 60 | 120 | 72 |
| E | 76 | 64 | 56 | 112 | 68 |
The annual sales revenue (in lakhs of Rs) of a product as a function of sales force (number of salesmen) and annual adverting expenditure (in Thousands of Rs) for the past 10 years are summarised in following table:
| Annual Sales Revenue Y(in Lakhs) | Sales Force X1 (in Number) | Annual Advertising Expenditure X2 (in Thousand) |
| 100
115
125
135
105
145
110
120
135
175 | 40
65
40
90
115
80
50
60
70
100 | 140
115
190
80
100
140
115
150
130
160 |
Obtain a regression model to forecast the annual sales revenue of the product using Matrix Method.
See Answer →What is the probability that it will take him or her more than 10 minutes altogether to wait for the phone and complete his or her call?
See Answer →What is the average length of the queen that forms from time to time?
See Answer →A reactor is producing energy at the rate of 32 106 watts. How many atoms of U235 undergo fission per second? Assume that on the average, energy of 200 Me V is released per fission.
The telephone department will install a second booth when convinced that an arrival would expect waiting for at least 3 minutes for phone call. By how much should the flow of arrivals increases in order to justify a second booth?
See Answer →What is the probability that a person arriving at the booth will have to wait?
See Answer →How are radioisotopes produced? Describe three examples of their use as tracers.
See Answer →At what potential difference must an X-ray tube operate to produce X-rays with a minimum wavelength of 2 ?
Arrivals at telephone booth are considered to be Poisson with an average time of 10 minutes between are arrival and the next. The length of phone call is assumed to be distributed exponentially with mean 3 minutes
See Answer →Write down the electronic configuration of Ca20 and Sr38 and their ground state spectral terms.
See Answer →The production department for a company requires 3600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs 36 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price is Rs10 per kg. The purchase manager wishes to determine an ordering policy for raw material
See Answer →For a simple harmonic oscillator, show that the expectation value of x, defined as
for the n = 0 and m =1 states. Use the result
.
Let X is the advertisement expenditures (in Lakh Rs.) and Y is the sales (in Lakh Rs.). Let the data are
| X: | 1182 | 1172 | 1264 | 1493 | 1571 | 1711 | 1804 | 1840 | 1956 | 1956 |
| Y: | 129 | 135 | 147 | 160 | 171 | 184 | 198 | 223 | 240 | 293 |
Estimate the parameters and find the estimated linear equation. Whether the advertisement influences the sale of product? Test and comment on the goodness of fit of the model.
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