Explain Pauli’s paramagnetism. Show that at T = 0 Pauli’s paramagnetic susceptibility is given by
where is the intrinsic magnetic moment of the particle of mass m.
Obtain Fermi-Dirac distribution function. Draw it for What is its physical significance?
Using the result show that the expression of density matrix
of a
free particle in box of volume V in the canonical ensemble in the coordinate representation is given by
Consider a gas in lattice-gas model, in which gas contained in volume V is assumed to be divided into fixed small cubic cells of volume V0 such that each of the (cell) can contain at most one atom. The system behaves as a set of distinguishable and independent cells in contact with a reservoir at temperature T and chemical potential .Obtain the expressions of canonical partition function and average number of particles
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Calculate relative fluctuations in the energy of the system about the mean value in canonical ensemble.
See Answer →Obtain an expression of probability of finding the system in the microstate k corresponding to energy Ek in canonical ensemble. Also, write the expression of canonical partition function.
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What is Gibb’s paradox? Derive Sackur-Tetrode equation of entropy for a classical, ideal gas.
See Answer →Consider a single classical 1-D non-relativistic harmonic oscillator. Obtain x(t) and p(t) as a function of time t. Assume that initially at t = 0, the oscillator is at the maximum displacement .Plot its phase space trajectory for fixed total energy E
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Show that for any distribution where N is large, the distribution tends to a Gaussian or a normal distribution.
See Answer →Calculate the mean, and the variance of the following probability density functions:
i) Uniform
ii) Rayleigh distribution
Select any Small or Medium Enterprise (SME) of your choice. Discuss with them about why they need to manage working capital and how it is done. What are the various barriers faced by them in optimization of working capital
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Explain the significance of trade credit. What are the factors that influence the availability of trade credit?
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How does uncertainty affect Inventory Management? Explain any one model of Inventory Management under the condition of uncertainty.
See Answer →The Profit and Loss Account for the year ended 31 March, 2024 and the Balance Sheet as on that date, for Alpha Ltd. is as follows:
Profit and Loss Account for the year ended 31st March, 2024
| Particulars | Rs. Lakhs | Particulars | Rs. Lakhs |
| Opening stock | 1.75 | Sales : Credit | 12.00 |
| Add: Manufacturing costs | 10.75 | Cash | 3.00 |
| 12.50 | |||
| Less: Closing stock | 1.50 | ||
| Cost of goods sold | 11.00 | ||
| Gross Profit | 4.00 | 15.00 | |
| 15.00 | |||
| Administrative expenses | 0.35 | Gross Profit | 4.00 |
| Selling expenses | 0.25 | Other Income | 0.09 |
| Depreciation | 0.50 | ||
| Interest | 0.47 | ||
| Income –tax | 1.26 | ||
| Net Profit | 1.26 | ||
| 4.09 |
Balance Sheet as on 31st March, 2024
| Liabilities | Rs. Lakhs | Assets | Rs. Lakhs |
| Equity shares of Rs. 10 each | 3.50 | Plant and machinery | 10.00 |
| 10% Preference shares | 2.00 | Less: Depreciation | 2.50 |
| Reserves and Surplus | 2.00 | Net plant and machinery | 7.50 |
| Long-term loan (12%) | 1.00 | Goodwill | 1.40 |
| Debentures (14%) | 2.50 | Stock | 1.50 |
| Creditors | 0.60 | Debtors | 1.00 |
| Bills Payable | 0.20 | Pre-paid expenses | 0.25 |
| Accrued expenses | 0.20 | Marketable securities | 0.75 |
| Provision for tax | 0.65 | Cash | 0.25 |
| 12.65 | 12.65 |
The market price of the shares of Alpha Ltd. on 31st March, 2024 is Rs. 45
| (Rs. Lakhs) | |
| Reserves at the beginning | 1.465 |
| Net Profit during the year | 1.260 |
| Preference dividends | 2.725 |
| Equity dividends | 0.200 |
| Reserves at the close of year | 0.525 |
| 2.000 |
Calculate the following Ratios – (1) Current ratio (2) Quick ratio (3) Debt- equity ratio (4) Interest coverage (5) Fixed charge coverage (6) Stock turnover (7) Debtors turnover (8) Average collection period (9) Gross profit margin (10) Net profit margin (11) Operating ratio (12) Return on capital employed (ROCE) (13) Earnings per share (14) Return on shareholders’ equity (15) P/E ratio and (16) Earning yield.
See Answer →Discuss the Industry Norm Approach and Economic Modelling Approach to the determination of working capital.
See Answer →What is a Virtual Cloud Network? What are its advantages and disadvantages?
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List the features of any two Programming Languages that can be used to develop Mobile Applications.
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