UPSC Mains 2024 — All Papers & Questions

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each :

Discuss the following in about 150 words each:

Discuss the following in about 150 words each:

Write notes on the following in about 150 words each :

Write notes on the following in about 150 words each :

Write short notes on the following in about 150 words each :

Write short notes on the following in about 150 words each :

Write short notes on the following in about 150 words each:

Write short notes on the following in about 150 words each:

(a) (i) Determine the distance from the nucleus at which the electron is most expected in the hydrogen atom in its ground state. [Given: The normalised radial function for hydrogen-like systems is R10(1s) = 2 (Z/a0)3/2 e−ρ/2 where ρ = 2Zr/na0 and a0 is the first Bohr orbit radius. Other notations have their usual meanings.] (ii) Sodium bromide and sodium iodide have higher lattice energies than expected from theoretical calculations. Justify. (b) (i) The 235U isotope undergoes fission when bombarded with neutrons. However, its natural abundance is only 0·72 percent. To separate it from more abundant 238U isotope, U is first converted to UF6 which is easily vaporised above room temperature. The mixture of 235UF6 and 238UF6 gases is then subjected to many stages of effusion. Calculate the separation factor, that is enrichment of 235U relative to 238U after one stage of effusion. (ii) Define ‘unit cell’. Draw all the Bravais lattices for a cubic system. (c) Use the following data to determine the normal boiling point of mercury. What assumptions must you make in order to do the calculations? Hg(l) ΔHf° = 0, S° = 77·4 J K−1 mol−1 Hg(g) ΔHf° = 60·78 kJ mol−1, S° = 174·7 J K−1 mol−1 (d) (i) The compound dichlorodifluoromethane (CCl2F2) has a normal boiling point of –30 °C, a critical temperature of 112 °C, and a corresponding critical pressure of 40 atm. If the gas is compressed to 18 atm at 20 °C, will the gas condense? Give your answer on the basis of graphical presentation. (ii) Define overvoltage. Mention the applications of overvoltage. (e) The activation energy for the decomposition of hydrogen peroxide 2 H2O2(aq) → 2 H2O(l) + O2(g) is 42 kJ mol−1, whereas when the reaction is catalysed by enzyme catalase it is 7·0 kJ mol−1. Calculate the temperature that would cause the uncatalysed reaction to proceed as rapidly as the enzyme-catalysed decomposition at 20 °C. Assume the frequency factor A to be the same in both cases.

(a) State Heisenberg’s uncertainty principle. Show that for a particle in a one-dimensional box having length from 0 to L, the two normalised eigen functions corresponding to the eigenvalues E1 and E2 (quantum numbers 1 and 2 respectively) are orthogonal to each other. (b) (i) Calculate the bond order for the following: (I) Oxygen, (II) Superoxide, (III) Peroxide, (IV) Dioxygenyl ion. Which of them has the highest stability? (ii) Draw the molecular orbital diagram for CO. (c) (i) Calculate the limiting radius ratio for crystals with coordination numbers 3 and 6. (ii) Explain stoichiometric defects with an example.

(a) (i) Calculate the coefficient of viscosity of air at (I) 298 K and (II) 0 K. Assume that the collision cross-section (πσ2) of air is 0·28 (nm)2 and the average molar mass of air is 29 g mol−1. (ii) Arrange Boyle’s temperatures of the gases Ar, CH4 and C6H6 in increasing order and give reasons. (b) (i) Which of the following liquids has greater surface tension: Ethanol or Dimethyl ether? Explain with reasons. (ii) Calculate the difference in pressure across the liquid–air interface for a water droplet of radius 150 nm. (c) (i) Calculate the change in Helmholtz energy for a reversible isothermal compression of 1 mol of an ideal gas from 100·0 L to 22·4 L at 298 K. (ii) Why does a tyre get hot when air is pumped into it? Can a tyre be inflated without a rise in temperature?

Answer ALL the parts (a) to (e):

Answer the following:

The mass spectral data of diethyl ether is as under: m/z 74, m/z 59, m/z 45, m/z 31, m/z 29. Explain the fragmentation pattern.

Using the following data, calculate the bond length of HCl : I = 2.70 × 10^−47 kg m^2 ; 1 a.m.u. = 1.661 × 10^−27 kg.

Design only the flexural reinforcement for a T-beam section to resist a service moment of 200 kNm. The details of the section are given below: Breadth of flange bf = 1400 mm Breadth of web bw = 300 mm Effective depth of the T-beam d = 455 mm Overall depth of the T-beam D = 500 mm Depth of flange Df = 125 mm Use M25 grade concrete and Fe 500 grade steel. Relevant portion of IS 456 : 2000 is enclosed.

A prestressed concrete T-beam having the cross-section of flange 1500 mm wide and 200 mm thick, rib 300 mm wide and 1200 mm deep. The beam carries a live load of 20 kN/m apart from its dead load, over a simply supported span of 20 m. The beam is prestressed with a straight cable having constant eccentricity ‘e’. Assume the losses of prestress as 16 %. Determine the initial prestressing force ‘Pi’ and its eccentricity ‘e’, if the permissible stresses are equal to zero tension and 5 MPa respectively at top and bottom fibres of the beam. The unit weight of concrete is 25 kN/m³.

A 125 mm diameter vertical cylinder rotates concentrically inside a fixed cylinder of diameter 130 mm. Both cylinders are 325 mm long. If a torque of 0·92 Nm is required to maintain a speed of 70 r.p.m., find the dynamic viscosity of the liquid that fills the space between the cylinders.

The resistance force F of a ship is a function of its length L, velocity V, acceleration due to gravity g and fluid properties like density ρ and viscosity μ. Write this relationship in a dimensionless form.

A canal is to be excavated through a soil with c = 20 kN/m², φ = 20°, e = 0·80 and G = 2·70. The side slope is 1 in 1. The depth of the canal is to be 8 m. Determine the factor of safety with respect to cohesion when the canal runs full. What will be the factor of safety if the canal is rapidly emptied? For β = 45°, the stability number for various φ values are as given above.

Answer the following questions in about 150 words each:

A Ltd. has acquired the business of B Ltd., whose Balance Sheet as at 31st March, 2024 is as under: I – Equity and Liabilities : 1. Shareholders’ Funds (a) Equity Share Capital (₹ 100 each) ............................................... 16,00,000 6% Preference Share Capital (₹ 100 each) .............................. 8,00,000 Sub-total 24,00,000 (b) Reserves and Surplus Capital Reserve ................................................................. 2,00,000 Profit and Loss Account ...................................................... 1,00,000 Workmen Compensation Reserve (expected liability ₹ 10,000) ............ 16,000 Sub-total 3,16,000 2. Non-Current Liabilities : 6% Debentures ....................................... 4,00,000 3. Current Liabilities : Trade Payables ................................................................. 2,40,000 Other Current Liabilities (Interest payable on debentures) ................. 24,000 Sub-total 2,64,000 Total Equity & Liabilities 33,80,000 II – Assets : 1. Non-Current Assets (a) Property, Plant and Equipment Land and Building ............................................................ 8,00,000 Plant and Machinery ........................................................ 12,00,000 Sub-total 20,00,000 (b) Intangible Assets Goodwill .................................................................. 4,80,000 Patents .................................................................... 1,00,000 Sub-total 5,80,000 2. Current Assets (a) Inventories ................................................................. 3,00,000 (b) Trade Receivables ............................................................ 3,60,000 (c) Cash and Cash Equivalents ................................................... 1,40,000 Sub-total 8,00,000 Total Assets 33,80,000 A Ltd. was to take over all assets (except cash) and liabilities (except for interest due on debentures) and to pay the following amounts : (i) ₹ 4,00,000, 7% Debentures (₹ 100 each) in A Ltd. for the existing debentures in B Ltd.; for the purpose, each debenture of A Ltd. is to be treated as worth ₹ 105. (ii) For each preference share in B Ltd., ₹ 10 in cash and 9% preference shares of ₹ 100 each in A Ltd. (iii) For each equity share in B Ltd., ₹ 20 in cash and one equity share in A Ltd. of ₹ 100 each having market value of ₹ 140. (iv) Expenses of liquidation of B Ltd. are to be reimbursed by A Ltd. to the extent of ₹ 20,000. Actual expenses amounted to ₹ 25,000. A Ltd. valued Land and Building at ₹ 11,00,000, Plant and Machinery at ₹ 13,00,000 and Patents at ₹ 40,000 of B Ltd. for the purpose of amalgamation. Pass necessary journal entries in the books of A Ltd. and B Ltd.

Answer the following questions in about 150 words each:

Answer each of the following questions in about 150 words:

Answer each of the following questions in about 150 words:

In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

Write an essay of about 600 words on ANY ONE of the following topics: (a) Democracy and the Freedom of Nature (b) Is the problem of drinking water about to become acute in India? (c) Preservation of International Culture: Efforts and Possibilities (d) Empty Columns Make the Loudest Noise

Read the following prose passage carefully and answer ALL the questions that follow, briefly, completely and in clear language. (12 × 5 = 60) [Passage in Bengali beginning with "সমালোচনা, সাহিত্যের একটি অংশ হিসেবে বিবেচ্য..." continues across two pages.]

Write a summary (precis) of the following passage in your own words, reducing it to about one-third of its length. No title is required. (60 marks) [Passage in Bengali beginning with "এই উদ্ধৃতির সঙ্গে বোঝা দরকার, চিরী কোনও নির্দিষ্ট ব্যক্তিসম্প্রেষণে প্রতিও…"]

Translate the following passage into ENGLISH: (20 marks) [Passage in Bengali about the contemporary relevance of cottage and small-scale industries, beginning with "কুটির শিল্প এবং ক্ষুদ্র শিল্পের মধ্যে আজ ভারতের আবার…" and ending with "ফলে সময় দেশে আজ কুটির শিল্পের প্রতি লক্ষ করা যাচ্ছে।"]

Translate the following passage into BENGALI: (20 marks) "In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning."

Write an essay of about 600 words on any ONE of the following topics:

Read the following passage carefully and answer the questions that follow (12×5 = 60):

Write a précis of the following passage in your own words and give it a suitable title.

Write a composition on the following topic:

In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

Write an essay in about 600 words on any one of the following topics: (a) Paper books are more attractive than their electronic formats. (b) Ethics in sports. (c) War as a policy instrument for nations today. (d) There is no place like home.

Read carefully the passage given below and write your answers to the questions that follow in clear, correct and concise language: British rule in India was a relationship of economic and political domination between an imperial power and its colony. It was based on conquest, consolidated after several wars and followed economic policies designed to serve British interests. Both the parties knew it was unequal, exploitative and based on force. As such it raised moral questions and needed justification. Their self-respect, sense of morality and morale required the British to convince themselves that they were right to rule over India. In order to ensure its orderly and continued existence and secure the co-operation and support of the Indians without whom they simply could not run the country, they also needed to convince their subjects that British rule was in their ‘real’ interest. It was, of course, possible for them to justify it to themselves in one way and to their subjects in another. However, they knew that such a strategy was open to the charge of inconsistency, even hypocrisy, and inherently precarious. In order to achieve the dual objective of justifying their rule to themselves and their subjects in a single and consistent language, the British needed to show that they had something to give to the Indians which the latter badly needed, were unable to acquire unaided and was so precious as to compensate for whatever economic and political price they were required to pay. The logic of justification required a perfect match between British gifts and Indian needs, the British strength and the Indian deficiency. Following the fashion of the time, the British wrapped their gifts in the language of civilisation, which had latterly replaced Christianity as the unifying principle in Europe, taken over its universalist and proselytising mission and built up an ambiguous and uneasy relationship with it. Although modern civilisation was a co-operative European product, the British role in its creation and dissemination was considerable. They were one of the first to industrialise themselves, more or less to recast their religion, ways of life and thought and major political, economic and other institutions in the light of the dominant liberal culture and to roam all over the world as if possessed by its inherently restless and universal spirit. They claimed to ‘represent’ or ‘embody’ it to a greater degree than any other country and saw themselves as its transcendentally or historically accredited ‘vehicle’. Since their civilisation had, in their view, attained the highest possible level of human existence and cultivated capacities which all men qua men ought to develop, they had no doubt that it was universally desirable. All societies had a common destiny and destination, namely to become civilised in the British way and were to achieve this destiny by the same route. Hence the more ‘advanced’ among them, that is, those whose journey had brought them closer to the universal destination, provided the models for and had the moral duty to guide those who had not yet started, become stuck, were proceeding in a wrong direction or at an extremely slow pace. The British could not show that they represented the highest level of civilisation without so defining it that it broadly corresponded to their own ways of life and thought. Like all ideological systems they abstracted, reified and absolutised the distinctive features of their ways of life and thought and presented them as a universal norm for evaluating all societies, including their own. Their facts became values for others, an illicit logical move lying at the heart of every ideology. Other societies were therefore always deficient whereas the British was necessarily more or less perfect. The British argued that they had brought to India the unique and most precious gift of civilisation. Since this civilisation was deemed to be universally desirable, India obviously needed it. All they had to do was show that India lacked it and was unable to acquire it unaided. Unlike some of the other British colonies, India had a well-developed literati tradition, a long history of civic life and considerable philosophical, artistic, scientific and other achievements. Since these were supposed to be some of the indices of civilisation, obviously it could not be contemptuously dismissed as uncivilised. Some British writers and leaders did so dismiss it; most, however, acknowledged its great achievements, but contended that they were all in the past and did not redeem its contemporary degeneration. Its social structure and practices were oppressive, unjust and sometimes inhuman; its religions were incomprehensible, replete with meaningless rituals, polytheist, lacking a single authoritative text, and not really religions in the ‘proper’ sense of the term; its modes of thought were ‘mystical and mythological’ and largely irrational; and its people were emotional, excitable, undisciplined, unambitious, lacking in self-control, unreliable and very like women and children. The British view of India did, of course, change over time, largely as a result of their increased knowledge of its past and the changes in their conceptions of themselves and the yardsticks they employed. Throughout their rule, however, they continued to think of it as neither wholly uncivilised nor fully civilised but ‘semi-civilised’ or ‘only half-civilised’, and of the Indians as a moderately talented people who needed to be disciplined, guided and trained in the ways of civilisation.

Make a précis of the following passage in about one-third of its length. Do not give or suggest a title to it. The précis should be written in your own words: The mad rat race among nations over the globe for development jeopardised the health of man itself. Progress in agriculture and industry is taken a general criterion of development of any country. This craze resulted into unlimited exploitation of every bit of natural resource. The splendid plentifulness of nature is a heritage that should be conserved for future generations and not be spoiled. Such activities of man had adverse effect on all forms of living organisms in the biosphere. The earth planet along with the atmosphere (air, land, water) that sustains life is called the biosphere. Biosphere extends into about 7 km of the earth surface itself, downward into the ocean to depths of about 10-67 km and vertically into the air to about 10 km, where life is found to exist. Unlimited exploitation of nature by man disturbed the delicate ecological balance between living and non-living component of the biosphere. The unfavorable conditions created by man himself threatened the survival not only of man himself but also other living organisms. The number of the species likely to become rare, threatened, endangered or near extinction in the Red Data Book of the IUCN is increasing with time. It is very common to find warnings at public places, reading as "Air unfit for breathing", "Water unfit for drinking", "Do not eat fish caught here" and so on. India today is one of the first ten industrialised countries of the world. Today we have a good industrial infrastructure in core industries like metals, chemicals, fertilisers, petroleum, food etc. What has come out of these? Pesticides, detergents, plastics, solvents, fuels, paints, dyes, food additives etc. are some examples. Due to progress in atomic energy, there has also been an increase in radioactivity in the biosphere. Besides these, there are a number of industrial effluents and emissions particularly poisonous gases in the atmosphere. Mining activities also added to this problem particularly as solid waste. Thus, pollution is a necessary evil of all development. Due to lack of development of a culture of pollution control, there has resulted a heavy backlog of gaseous, liquid and solid pollution in our country. It is to be cleaned. Thus pollution control in our country is a recent environmental concern. Not only in India, but in developed Western World also, pollution is a scare-word. Pollution is a man-made problem, mainly of effluent countries. The developed countries have been in a mad race to exploit every bit of natural resource to convert them into goods for their comfort, and to export them to needy developing world. In doing so, the industrialised countries dump lot of materials in their environment which becomes polluted. In one way pollution has been in fact "exported" to developing countries. What is pollution? Pollution is an undesirable change in the physical, chemical or biological characteristics of air, water and soil that may harmfully affect the life or create a potential health hazard of any living organism. Pollution is thus direct or indirect change in any component of the biosphere that is harmful to the living component(s), and in particular undesirable for man, affecting adversely the industrial progress, cultural and natural assets or general environment. What are pollutants? Any substance which causes pollution is called a pollutant. A pollutant may thus include any chemical or geochemical (dust, sediment, grit etc.) substance, biotic component or its product, or physical factor (heat) that is released intentionally by man into the environment in such a concentration that may have adverse harmful or unpleasant effects. A pollutant has also been defined as "any solid, liquid or gaseous substance present in such concentration as may be or tend to be injurious to the environment". Pollutants are the residues of things we make, use and throw away. There are many sources of such pollutants. The lakes and rivers are polluted by wastes from chemical and other factories, and the air by gases of automobile exhausts, industries, thermal power plants etc. There has grown up a serious concern all over the world about the rivers turning murky, fish rotting on sea shores, trees withering, cities choking with foul air, toxic chemicals being cycled into food stuffs and disease epidemics appearing so frequently. (697 words approximately)

4.(a) Rewrite the following sentences after making necessary corrections. Do not make unnecessary changes in the original sentence: (i) Little learning is dangerous thing. (ii) You are requested to kindly grant me leave. (iii) Could you please advised me what I should do. (iv) I envied he his success. (v) If people feel good of coming to work, they will work better. (vi) How terribly sad? (vii) Spanish is more widely used outside of Europe. (Add a question tag) (viii) He played the piano one night in the village hall. (ix) Many a men has succumbed to this temptation. (x) If she gets the right grades, she'd go to university. 4.(b) Supply the missing words: (i) Don't walk ________ the grass. (ii) I lived in Uttarakhand ________ five years. (iii) He stood tall ________ all his friends in the college. (iv) The cat jumped ________ the well to escape from the dog. (v) She walked ________ the forest to reach her village. 4.(c) Use the correct form of the verb given in brackets: (i) Two plus two ________ four. (make) (ii) We need rain, the garden ________ so dry. (be) (iii) She ________ with a baby girl last week. (bless, passive voice) (iv) I just ________ even talking to him. (bear) (v) ________ you just shut up for a minute! (can) 4.(d) Write the antonyms of the following: (i) Optimist (ii) Gali (iii) Zest (iv) Profit (v) Quick

5.(a) Rewrite the following sentences as directed without changing the meaning: (i) The mangoes are too cheap to be good. (Remove ‘too’) (ii) The French surrendered Quebec to the English in 1759. (Change the Voice) (iii) Mumbai is richer than most other cities in India. (Use superlative degree) (iv) What though we happen to be late? (Change to Assertive)

Translate the following passage into Gujarati: In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

Answer the following as directed.

In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

Q1. 600 ಪದಗಳ ಮಿತಿಯಲ್ಲಿ ಕೆಳಗಿನ ವಿಷಯಗಳ any one ಮೇಲೆ ಪ್ರಬಂಧ ಬರೆಯಿರಿ : (a) ಧರ್ಮ, ಪ್ರಜಾಪ್ರಭುತ್ವ ಮತ್ತು ಅಭಿವ್ಯಕ್ತಿ ಸ್ವಾತಂತ್ರ್ಯ (b) ಭಾರತದಲ್ಲಿ ಕುಡಿಯುವ ನೀರಿನ ಸಮಸ್ಯೆ ಗಂಭೀರವಾಗಿದೆಯೆ? (c) ಬುಡಕಟ್ಟು ಸಂಸ್ಕೃತಿ ರಕ್ಷಣೆ : ಪ್ರಯತ್ನಗಳು ಮತ್ತು ಸಾಧನೆಗಳು (d) ಹಸಿರು ಗ್ರಹ (GREEN EARTH) ರಕ್ಷಣೆಯ ಮರುಸಂರಚನೆ – ಅವಶ್ಯಕತೆ ಹಾಗೂ ಸವಾಲುಗಳು

Q2. ಕೆಳಗಿನ ಕೊಟ್ಟಿರುವ ಗದ್ಯಭಾಗವನ್ನು ಮನಗಂಡು ಓದಿ, ಕೆಳಗಿನ ಪ್ರಶ್ನೆಗಳಿಗೆ ಸರಳ, ಸ್ಪಷ್ಟ ಮತ್ತು ಸಂಕ್ಷಿಪ್ತವಾಗಿ ಉತ್ತರಿಸಿ : (ಪ್ರತಿ ಪ್ರಶ್ನೆಗೆ 12 ಮಾರ್ಕ್; ಒಟ್ಟು 60) [ಗದ್ಯಭಾಗ – ಒಟ್ಟು ಮೂರು ಪುಟಗಳು]

Q3. ಕೆಳಗಿನ ಗದ್ಯಖಂಡವನ್ನು ուշದಾಗಿ ಓದಿ. ಅದರ ಸಂಗತಿಯನ್ನು 300 ಪದಗಳ ಮಿತಿಯಲ್ಲಿ own summary (ಸಾರಾಂಶ) ರೂಪದಲ್ಲಿ ನಿರೂಪಿಸಿ. (ಒಟ್ಟು 60 ಮಾರ್ಕ್) [ಗದ್ಯಖಂಡ – ಸುಮಾರು 351 ಪದಗಳು; ಪುಟ ಸಂಖ್ಯೆ 4-6]

Translate the following Kannada prose passage into English: ಗುಡಿ ಕೈಗಾರಿಕೆಗಳು ಮತ್ತು ಸಣ್ಣ ಪ್ರಮಾಣ ಉದ್ಯಮಗಳನ್ನು ಕಡಿಮೆ ಚಟುವಟಿಕೆಯ ದಿನಗಳಲ್ಲಿ ಭಾರತದಲ್ಲಿ ಮತ್ತೊಮ್ಮೆ ಮಹತ್ವ ಪಡೆದುಕೊಂಡಿವೆ. ಅಂತಹ ಕೈಗಾರಿಕೆಗಳ ಕೇಂದ್ರದಲ್ಲಿರುವುದು ಚಿಕ್ಕ ಯಂತ್ರಗಳು, ಕಡಿಮೆ ಬಂಡವಾಳ ಹೂಡಿಕೆ ಮತ್ತು ಕಡಿಮೆ ಕೌಶಲ್ಯ ಅಗತ್ಯವಿರುವ ಸಣ್ಣ ಕೃಷಿಾಧಾರಿತ ಉದ್ಯಮಗಳು. ಈ ಮಾದರಿಯ ವ್ಯವಹಾರಗಳನ್ನು ಮಾಲೀಕರು ಹಾಗೂ ತಯಾರಕರು ಅವಲಂಬಿಸುತ್ತಾರೆ ಮತ್ತು ಅವರಿಗೆ ತಾವು ಜೀವನಾಧಾರವನ್ನು ಗಳಿಸುವ ಅವಕಾಶವನ್ನು ಒದಗಿಸುತ್ತದೆ. ಆ ಮೂಲಕ ಉತ್ಸಾಹಭರಿತ ಉತ್ಪಾದನೆಯ ತತ್ವವನ್ನು ಸಾಧಿಸುತ್ತದೆ. ಜೊತೆಗೆ ಇದು ನಿರ್ದಿಷ್ಟ ಸಾಮರ್ಥ್ಯವನ್ನು ನಿರ್ಮಿಸುತ್ತದೆ. ಗಾಂಧಿಯವರು ಸ್ವಾತಂತ್ರ್ಯ ಸಂಗ್ರಾಮದ ಕಾಲದಲ್ಲೇ ಭಾರತದಂತಹ ದೇಶದ ಅನೇಕ ಹಿತಾಸಕ್ತಿಗಳಿಗೆ ಸಣ್ಣ ಗೃಹ-ಕೈಗಾರಿಕೆಗಳು ಕಾರಣಕಾರಿತ್ವವೆಂದು ಕಂಡುಕೊಂಡಿದ್ದರು. ಸಣ್ಣ ಉದ್ಯೋಗಾವಕಾಶಗಳನ್ನು ಸ್ವಾವಲಂಬಿ ಹಾಗೂ ಸಂರಕ್ಷಣಾತ್ಮಕ ಗೃಹ-ಕೈಗಾರಿಕೆಗಳು ಅವಲಂಬಿಗಳಾಗಿವೆ. ಈ ಮೂಲಕ ಸ್ವಾವಲಂಬ್ಯವನ್ನೇ ಕಂಡುಕೊಳ್ಳಲು ಬೃಹತ್ ಉದ್ಯಮಗಳಿಗೆ ಅಡಚಣೆ ನೀಡಲಾಗುತ್ತದೆ. ಬೃಹತ್ ಉದ್ಯಮಗಳು ಶ್ರಿಮಂತ ವರ್ಗದ ಬಾನಿಯ ಆಶ್ರಯವಾಗುತ್ತವೆ. ಜನಸಂಖ್ಯೆ, ಶಿಕ್ಷಣದ ಪ್ರಸಾರ, ಜನಸಾಮಾನ್ಯರಲ್ಲಿ ಜಾಗೃತಿ, ತಮ್ಮ ಹಕ್ಕುಗಳನ್ನು ಗುರುತಿಸಿಕೊಂಡು ಬೆಳೆದಂತೆ, ನಿರ್ಧಾರಗಳ ಹಟ್ಟೋತ್ತರ ಇದು ಸಾಲ – ಇವೆಲ್ಲವೂ ತತ್ತ್ವವಾಗಿ ರೂಪುಗೊಳ್ಳುತ್ತವೆ. ಹಿನ್ನಡೆಯಿಂದ ತೆಗೆದ ಪ್ರಜ್ಞಾವಂತ ಚಿಂತಕರು ಗಾಂಧೀ ತತ್ವಗಳನ್ನು ಮರುವಿಚಾರಣೆಗೆ ಒಳಪಡಿಸಿದ್ದಾರೆ. ಇಷ್ಟು ಸಣ್ಣ ಕೈಗಾರಿಕೆಗಳನ್ನು ಅಷ್ಟಪಡಿಸದೇ ಇರುವುದು ರಾಷ್ಟ್ರದ ಉದ್ದೇಶಗಳಿಗೆ ಪರಾಕ್ರಮಾತ್ಮಕ ಎಂಬುದನ್ನು ಎಚ್ಚರಿಸುತ್ತದೆ. ಪರಿಣಾಮವಾಗಿ, ದೇಶಾದ್ಯಂತವೂ ಗುಡಿ ಕೈಗಾರಿಕೆಗಳ ಜಾಲ ವಿಸ್ತರಿಸಿಕೊಂಡಿದೆ.

Translate the following English passage into Kannada: In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

Write an essay in about 600 words on any ONE of the following topics:

Read the following prose passage carefully and, in your own words, answer the questions that follow:

Summarise the following prose passage in about one-third of its length. Do not give it a title. The summary should be written in your own words.

Translate the following prose passage into English:

In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

पुढीलपैकी कोणत्याही एका विषयावर 600 शब्दांत निबंध लिहा : (a) लोकशाही आणि अभिव्यक्तिस्वातंत्र्य (b) भारतातील पिण्यासाठी पाण्याचे संकट (c) आदिवासी संस्कृतीचे जतन : प्रयत्न आणि शक्यता (d) विक्रया भांड्याला खडखडाट फार

पुढील उतारा काळजीपूर्वक वाचा आणि उताऱ्याच्या शेवटी दिलेल्या प्रश्नांची उत्तरे सुग्रथित, योग्य व संक्षिप्त भाषेत लिहा :

पुढील उताऱ्याचा अंदाजे एक-तृतीयांश शब्दांत सारांश लिहा. उताऱ्यात ग्रंथाळ देऊ नये. सारांश मराठीत लिहा.

पुढील उताऱ्याचे इंग्रजी भाषांतर करा :

पुढील उताऱ्याचे मराठीत भाषांतर करा :

Use any FIVE of the following idiomatic phrases in sentences of your own (one sentence for each): हावा खाने, तीन न देखेको, आँखा फुट्नु, पेट काट्नु, इर्ष्या हुनु, काँधको फेरु, कुर्सीको काम.

Write the one-word equivalent (precise term) for any FIVE of the following expressions:

Change the gender of any FIVE of the following words:

Complete any FIVE of the following proverbs/phrases:

In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

Write an essay in about 600 words on any ONE of the following topics: (a) ଗ୍ରାମଜୀବନ ଓ ଅନ୍ତର୍ଗତ ଅଭିଜ୍ଞାନ (b) ଭାରତରେ ପାଣ୍ଠା ଜନସଂଖ୍ୟାର ଆହ୍ବାନ କି? (c) ଜନତାଙ୍କ ସଂସ୍କୃତି ସଂରକ୍ଷଣ : ପ୍ରୟାସ ଓ ଯଥାର୍ଥତା (d) ପର୍ଯ୍ୟାଟନ ମାଧ୍ୟମର ଅର୍ଥନୈତିକ ବିକାଶ

Read the following passage carefully and answer, in your own words, the questions that follow.

Write a précis of the following passage in Odia, reducing it to about one-third of its length (approximately 140 words) and give it an appropriate title.

Translate the following passage into English.

Translate the following passage into Odia: In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

Write an essay of about 600 words on any ONE of the following subjects:

Read the following passage carefully and answer, in coherent and correct Punjabi, the questions given below:

Write the summary of the following passage in about one-third of its length (approximately 210-215 words). Do not give a title to the summary. Write the condensed version in your own words.

Translate the following passage into English:

Translate the following passage into Punjabi: In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

निम्नलिखितेषु विषयेषु कतमेकं विषयमवलम्ब्य यथाशक्ति (600 परिमितशब्दैः) निबन्धः लेखनीयः : (a) लोकतन्त्रः : अभिनवत्वं, स्वातन्त्रता च (b) किं भारते पेयजलस्य संकटः आसन्नः अस्ति ? (c) जनजातीय संस्कृतिसंरक्षणम् : प्रयासः, समस्याः च (d) निःसंसारस्य पदस्य प्रयोगात्मकः महान्

अधोलिखितं गद्यांशं सावधानं पठित्वा तत्सरस्यम् अंशः प्रदत्तानां प्रश्नानामुत्तराणि स्पष्टता-समस्तस्य शुद्धियुत्तया दीयताम् :

अधोलिखितगद्यांशस्य संक्षेपे मूलभावस्य तृतीयांशपरिमितः स्वशब्दैः संक्षेपः स्वयमेव लेखनीयः (श्लोकं वा न उद्धृतम्) ।

अधोलिखितगद्यांशस्य आङ्ग्लभाषायाः अनुवादः करणीयः ।

अधस्तनगद्यांशस्य संस्कृतभाषानुवादः करणीयः ।

हेठियन मां कोईहिक विषय ते 600 लफ्जनि में मग़मू लिखो : (a) लोकतशाही ऐं इज़हार-ए-खयाल जी आज़ादी (b) छा पाकिस्तान जो हुहुम्रु भारत में जल्दु अच्छण बारे आहे ? (c) क़लमाइली सफ़र जो रहनुमु : कोशिशूं ऐं इंक़लाकात (d) व्हले चणे वधे घणे

हेठि डिनल टुक्क ध्यान में पधो ऐं उन जे ठो लिखियल सुझावलनि जा जवाब सापू , सही ऐं जुच लफ्जनि में लिखो : 12×5 = 60

हेठि डिनल टुक्क जो साग अटिकल टुकं हिस्से जितिको लिखो. उन जो उन्वाअ लिखण जी जरूरत न आहे. साग अचन जे पन्धैंसी बोलियों में हुवणु तुहिंजे. (625 शब्द)

हेठि डिनल टुक्कर जो अंग्रेजी में तर्जुमो करयो :

हेठि डिनल टुक्कर जो सिंधी में तर्जुमो करयो : (In our democratic system, the press has a vital role … to be followed by those involved in public functioning.)

Write an essay of about 600 words on any ONE of the following topics:

Read the following passage carefully and answer the questions given below clearly, correctly and concisely. (12 × 5 = 60)

Summarise the following passage to one-third of its length in your own words. No title is necessary.

In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

ఈ క్రింది అంశాలలో ఏదైనా ఒకదానిని ఎంపికించుకొని దాని గురించి ఆరు వందల (600) పదాలలో వ్యాసరచన చేయండి :

ఈ క్రింది గద్యభాగాన్ని శ్రద్ధగా చదివి, దిగువ ఇచ్చిన ప్రశ్నలకు సరైన సమాధానాలను సుస్పష్టమైన, సరళమైన భాషలో వ్రాయండి : (12 × 5 = 60) [గద్యభాగం 361 పదాలు – పేజీల 2-3లో ముద్రితంగా ఉంది]

ఈ క్రింది గద్యభాగాన్ని మీ స్వంతమాటల్లో మూలం విత్త పందికొరకు కుదించండి, దీనికి సరైన శీర్షిక ఇవ్వండి : [గద్యభాగం – పేజీలు 4-5లో సుమారు 361 పదాలు.]

ఈ క్రింది తెలుగు వచనాన్ని ఆంగ్లానికి అనువదించండి : [వచనం – పేజీ 6లో ముద్రితం]

Translate the following passage from English into Telugu: In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and efficient public servants and organizations, according special attention to developments in the remote and backward areas of our country. Our media is free and unfettered. It should be able to expose cases and incidents involving irregular and unlawful exercise of authority and abuses of all kinds. The existing ills in our socio-political environment will, on present reckoning, take considerable time to remedy. The Department of Personnel and Administrative Reforms should focus on establishing institutions responsible for all personnel matters — appointments, postings, transfers etc. — without any external interference. Also, there is a need for adoption of a robust code of ethics to be followed by those involved in public functioning.

Write an essay of about 600 words on ANY ONE of the following topics:

Read the following passage carefully and, in clear and concise Urdu, answer the questions given below. (12 × 5 = 60)

Write a précis, in Urdu, of the following passage in about one-third of its length and give it a suitable title. (60 marks)

Translate the following Urdu passage into English. (20 marks)

Translate the following English passage into Urdu. (20 marks) "In our democratic system, the press has a vital role. While there has been large-scale expansion of the print and visual media in recent years, a focused approach to dealing with major societal and political issues has still to evolve. There is, as yet, excessive and exaggerated coverage of exposures and scandals and far too little well-informed comment or analysis of the various deep-rooted factors which generate the continuing malaise. The media could make an extremely useful contribution by devoting adequate coverage to tasks well done, highlighting the achievements of honest and..."

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each : 10×5 = 50

Answer the following questions in about 150 words each : 10×5 = 50

(c) Find the logic equations for the outputs in the concise form and write the corresponding truth table for the circuit given below :

a) In the circuit diagram given here, load resistance R_L is to be set for maximum power transfer. Draw Thevenin equivalent circuit across ab and calculate the value of R_L for maximum power transfer. Also calculate the power loss in resistance R_3, when the circuit is delivering maximum power to load R_L. b) (i) Define input bias current and input offset voltage for an OPAMP. Using an OPAMP, draw an inverting amplifier circuit with gain = –4 in such a way that the effect of bias current is minimized. (ii) In the linear regulated power-supply circuit shown here, calculate the output-voltage adjustment range and maximum power dissipation in transistor T₁ in the worst case. c) A circuit using three 2-input multiplexers is shown below. Determine the function performed by this circuit :

a) A uniform plane wave travels in vacuum along +y direction. The electric field of the wave at some instant is given as \vec{E} = 4\hat{x} + 3\hat{z}. Find the vector magnetic field \vec{H}. (Given, μ₀ = 4π×10⁻⁷ H/m, ε₀ = 1/(36π)×10⁻⁹ F/m) b) The maximum efficiency of a 200 kVA, 3300/600 V, 50 Hz, single-phase transformer is 98% and occurs at 75% full load and unity power factor. If the leakage impedance is 10%, find the voltage regulation at full load and power factor 0·8 lagging. c) A diode circuit with an L–C load is shown in the figure, with the capacitor having an initial voltage V_C(t = 0) = 120 V, capacitance C = 12 µF and inductance L = 48 µH. If switch S is closed at t = 0 s, then find : (i) Peak value of current i, and (ii) Conduction time of the diode. d) How can linear pre-emphasis and de-emphasis filters be employed to improve the performance of an FM system? Is the improvement in output S/N ratio dependent on both the frequency responses of the pre-emphasis filter and the de-emphasis filter? e) A transmission line is 25 m long. Its characteristic impedance is Z₀ = 40 Ω and it operates at 2 MHz. The line is terminated with a load of Z_L = (50 + j30) Ω. If the wave velocity is u = 0·8c (with c = 3×10⁸ m/s) on the line, determine (i) the reflection coefficient and (ii) the input impedance.

a) (i) An AM signal s(t) = A_c[1 + k_a m(t)] cos(2π f_c t) is applied to the system shown. Show that the message signal m(t) can be obtained from the square-rooter output v₃(t). Assume |k_a m(t)| < 1 for all t, that m(t) is limited to –ω_s ≤ f ≤ ω_s and that the carrier frequency f_c > 2ω_s. (ii) A narrow-band FM signal is approximately given as s(t) = A_c cos(2π f_c t) – βA_c sin(2π f_c t) sin(2π f_m t). Determine the envelope of this modulated signal. Also determine the ratio of the maximum to the minimum value of this envelope. Plot this ratio versus β for 0 ≤ β ≤ 0·4. Also determine the average power of the narrow-band FM signal as a percentage of the average power of the unmodulated carrier. b) (i) Explain why PWM inverters are preferred over square-wave inverters. Further, draw the harmonic spectrum to highlight differences between unipolar and bipolar PWM techniques. (ii) A single-phase, full-bridge inverter has a DC-link voltage V_DC = 400 V and fundamental frequency 50 Hz. Find the r.m.s. value of the voltages of the fundamental and the next two prominent harmonics for : (1) square-wave mode, and (2) voltage-cancellation mode with α = 20°.

(a) (i) Draw the neat and properly labelled output voltage waveform of a three-phase, phase-controlled rectifier having firing angle α. Also derive the relationship for average output voltage in terms of line voltage V_LL and firing angle α. (ii) A three-phase full-wave controlled rectifier is being operated from a star-connected, 415 V, 50 Hz supply. This rectifier is feeding a constant load current of 15 kW. It is required to obtain an average output voltage of 80% of maximum possible output voltage. Find the firing angle, r.m.s. value of line current and input power factor. Assume devices are ideal. (b) (i) Show that the maximum power that a synchronous generator can supply when connected to constant voltage, constant frequency busbars increases with the excitation. (ii) An 11 kV, 3-phase, star-connected turbo-alternator delivers 250 A at unity power factor when running on constant voltage and frequency busbars. If the excitation is increased so that the delivered current rises to 300 A, find the power factor at which the machine now operates and the percentage increase in the induced e.m.f., assuming a constant steam supply and unchanged efficiency. The armature resistance is 0·5 Ω per phase and the synchronous reactance is 10 Ω per phase. (c) A medium has infinite conductivity for z ≤ 0, ε_r = 7 and μ_r = 18, and σ = 0 for z > 0. The electric field for z > 0 is given as E̅ = 10 cos(3×10^8 t − 15x) ẑ. Determine the surface charge density and surface current density at location (3, 4, 0) at t = 0·8 ns. Given, μ_0 = 4π×10^−7 H/m, ε_0 = 1/(36π)×10^−9 F/m.

(a) What are the limitations of (i) Proportional (P), (ii) Integral (I), (iii) Derivative (D), and (iv) PID Controllers? What is the application of positive feedback control system? (b) Explain the operation performed by 8085 microprocessor when the following arithmetic instructions are executed: (i) ADD M (ii) ADC M (iii) DAD rp (iv) SBI d8 (v) DCR reg (c) The ohmmeter circuit has VB = 1.5 V, R1 = 15 kΩ, Rm = 50 Ω, R2 = 50 Ω and meter FSD = 50 μA. Determine the ohmmeter scale reading at 0.5 FSD. (d) Calculate the power loss in a cable insulation having capacitance 9 μF, loss angle 0.05 degree and operating at 11 kV, 50 Hz. Draw the phasor diagram and equivalent circuit also. (e) Explain the concept of a constellation diagram. Draw the PSK signal constellations for the value of M = 2, 4 and 8, if all have same transmitted signal energy Es.

(a) The open-loop transfer function of a feedback control system incorporating a dead-time element is given by G(s) = K e^{–Ts} / [ s (s + 1) ] where K > 0 and T > 0 are variable scalar parameters. For a given value of T, show that the closed-loop system will be stable for all values K < K0 where K0 = ω0 cosec (ω0 T), and ω0 is the smallest value of ω satisfying ω = cot (ω T). (b) (i) Compare I/O-mapped I/O and memory-mapped I/O interfacing techniques used in 8085 micro-processor. (ii) What are the operating modes of Port-A of 8255? Explain hand-shake operation in I/O ports. (c) In a parallel circuit, in one branch the current I1 = (100 ± 2) A and in the other branch the current I2 = (200 ± 5) A. Determine the total current considering the following errors: (i) Limiting error (ii) Probable error Comment upon the results as well.

(a) An under-damped second-order system having the transfer function M(s) = K ωn² / ( s² + 2 ξ ωn s + ωn² ) has a frequency-response plot as shown in the figure. Compute the system gain K and the damping factor ξ. (b) A CRT has an anode voltage of 3 kV and its parallel deflecting plates are 2.5 cm long and 5 mm apart. The screen is 30 cm from the centre of the plates. Assuming the amplifier gain applied to the plates is 100, calculate: (i) Beam speed (ii) Deflection sensitivity of the CRT (iii) Deflection factor of the CRT (iv) Input voltage required to deflect the beam through 5 cm (c) Write an assembly-language program to add two numbers of 8-bit data stored in memory locations 4200H and 4201H and store the result in 4202H and 4203H.

(a) A piezoelectric (low-voltage) transducer has capacitance 2000 pF and charge sensitivity 30 × 10^–3 C/m. Assume a 1 MΩ feedback resistor with 100 pF shunt capacitance for the charge amplifier and a connecting cable of capacitance 150 pF. Calculate: (i) Sensitivity of the cable–transducer combination (ii) High-frequency sensitivity of the complete system (iii) Maximum frequency measurable by the system with ±5 % amplitude error (iv) Value of feedback resistance that can be increased by 5 % error allowance up to 20 kHz

Answer any or all of the following sub-parts (a) to (e).

Answer the following in about 150 words each:

Answer the following in about 150 words each:

On the outline map of India provided to you, mark the location of all of the following. Write in your QCA Booklet the significance of these locations, whether physical/commercial/economic/ecological/environmental/cultural, in not more than 30 words for each entry : (i) Lunkaransar (ii) Gua (iii) Raidak River (iv) Ekta Nagar (v) Chandanwari (vi) Babina (vii) Tatipaka (viii) Along Airport (ix) Karaikal (x) Panna

Institutional factors are playing a dominant role in controlling the agricultural prosperity in India. Justify with evidences.

India has wide-ranging regional disparities in economic development. Explain the patterns, implications and challenges.

Migration is the reflection of regional disparities. What socio-economic and demographic consequences are experienced at the place of origin and destination?

How are geographic factors influencing the distribution of high annual rainfall in certain parts of India?

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each.

Answer the following questions in about 150 words each.

Identify the following places marked on the map supplied to you and write a short note of about 30 words on each of them in your Question-cum-Answer Booklet. Locational hints for each of the places marked on the map are given below seriatim: (i) Prehistoric site (ii) Area of petroglyphs (iii) Neolithic site (iv) Harappan site (v) Buddhist monastery (vi) Chalcolithic site (vii) Neo-Chalcolithic site (viii) Megalithic site with rock art (ix) One of the Mahajanapadas’ capital and associated with Buddha’s miracle (x) Hominid fossil find site (xi) Major rock edict of Ashoka (xii) Ancient trade centre (xiii) Stone inscription recording land grants with tax exemptions (xiv) Shiva temples named after family relationships (xv) Place of art-related inscription (xvi) Place of inscription of three languages (xvii) Temple site where three styles of temple architecture are found (xviii) Jain pilgrimage site (xix) Shiva temple of Gupta period (xx) Megalithic monumental site

Answer the following questions in about 150 words each:

Critically examine the following statements in about 150 words each:

Critically examine the following statements in about 150 words each:

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each. Support your answer with relevant legal provisions and Judicial pronouncements.

Answer the following questions in about 150 words each. Support your answer with relevant legal provisions and Judicial pronouncements.

Answer ANY FIVE of the following in about 150 words each.

Answer ALL THREE of the following questions.

Answer ALL THREE of the following questions.

Answer ALL THREE of the following questions.

Answer EACH of the following in about 150 words.

Explain with reference to the context any FIVE of the following passages. (Answer in about 150 words each)

Answer the following questions:

Answer the following questions:

Answer the following questions:

Explain with reference to the context any FIVE of the following passages. (Answer in about 150 words each)

Explain the contextual reference and critical meaning of ANY FIVE of the following excerpts.

Write critical notes on the following topics.

Write analytical notes on the following:

Answer the following questions explaining the inner essence of the poems mentioned.

Explain the contextual reference and critical meaning of ANY FIVE of the following excerpts.

Answer all the following passages in about 150 words each (write the answer in your own language):

Answer all the following questions:

Answer all the following questions:

Answer all the following questions:

Answer all the following passages in about 150 words each:

ಈ ಕೆಳಗಿನ ಪದ್ಯದ ಸಂದರ್ಭವನ್ನು ಸೂಚಿಸಿ, ಅಂಶದ ಭಾವ ಮತ್ತು ಸೌಂದರ್ಯವನ್ನು ಕುರಿತು ಬರೆಯಿರಿ. (ಪ್ರತಿಯೋಂದೂ 150 ಪದಗಳ ಉತ್ತರ ಮಿತಿಯಲ್ಲಿ)

ಕೆಳಗಿನ ಎಲ್ಲ ಪ್ರಶ್ನೆಗಳನ್ನು ಉತ್ತರಿಸಿ :

ಕೆಳಗಿನ ಎಲ್ಲ ಪ್ರಶ್ನೆಗಳನ್ನು ಉತ್ತರಿಸಿ :

ಕೆಳಗಿನ ಎಲ್ಲ ಪ್ರಶ್ನೆಗಳನ್ನು ಉತ್ತರಿಸಿ :

ಈ ಕೆಳಗಿನವುಗಳನ್ನು ಕುರಿತು ಚಿಟ್ಟು ಬರೆಯಿರಿ. (ಪ್ರತಿಯೋಂದೂ 150 ಪದಗಳ ಮಿತಿ ಉತ್ಕಟವಾಗಿರಲಿ) 10×5 = 50

സന്ദര്‍ഭം, ആശയം, ശൈലി എന്നിവ വിശകലനം ചെയ്യുക. താഴെ കൊടുത്തിരിക്കുന്ന ഓരോ ഉദ്ധരണവും വിലയിരുത്തി കുറിച്ചുറപ്പിക്കുക.

താഴെക്കൊടുത്തിരിക്കുന്ന എല്ലാ ചോദ്യങ്ങള്‍ക്കും ഉത്തരം എഴുതുക.

താഴെക്കൊടുത്തിരിക്കുന്ന എല്ലാ ചോദ്യങ്ങള്‍ക്കും ഉത്തരം എഴുതുക.

താഴെക്കൊടുത്തിരിക്കുന്ന എല്ലാ ചോദ്യങ്ങള്‍ക്കും ഉത്തരം എഴുതുക.

SECTION B – താഴെ കൊടുത്തിരിക്കുന്ന എല്ലാ ഉദ്ധരണങ്ങള്‍ക്കും ചുരുക്കേചിത്രവതരണം തയ്യാറാക്കുക.

Answer any five of the following in about 150 words each:

(Manipuri text – full question 2)

(Manipuri text – full question 3)

(Manipuri text – full question 4)

Answer any five of the following in about 150 words each:

Critically analyse ANY FIVE of the following passages in about 150 words each :

Write answers to the following questions :

Write answers to the following questions :

Write answers to the following questions :

Critically analyse ANY FIVE of the following passages in about 150 words each :

ନିମ୍ନଲିଖିତ ଭାଗଗୁଡ଼ିକର ସଂକ୍ଷିପ୍ତ ବ୍ୟାଖ୍ୟା (Short Notes) ଲେଖ | ପ୍ରତ୍ୟେକଟି ଉତ୍ତର 150 ଶବ୍ଦର ମଧ୍ୟରେ ହେଉ |

ନିମ୍ନ ଭିତ୍ତିକ ଆଶୟରେ ବିସ୍ତୃତ ଆଲୋଚନା କର :

ନିମ୍ନ ଭାଗଗୁଡ଼ିକୁ ଆଧାର କରି ଉତ୍ତର ଦିଅ :

ନିମ୍ନ ଭିତ୍ତିକ ପ୍ରସ୍ତୁତିକୁ ଆଧାର କର :

ନିମ୍ନଲିଖିତ ଭାଗଗୁଡ଼ିକର ସଂକ୍ଷିପ୍ତ ବ୍ୟାଖ୍ୟା (Short Notes) ଲେଖ | ପ୍ରତ୍ୟେକଟି ଉତ୍ତର 150 ଶବ୍ଦର ମଧ୍ୟରେ ହେଉ |

ਹੇਠ ਲਿਖੇ ਕਾਵਿ-ਟੁਕੜਿਆਂ ਦੀ ਪੂਰੀ ਸਹਿਤ ਆਲੇਫਨਾਤਮਕ ਵਿਆਖਿਆ ਕਰੋ ।

ਹੇਠ ਲਿਖੇ ਸਵਾਲ ਪ੍ਰਸ਼ਨ ਕਰਨੇ ਜਰੂਰੀ ਹਨ ।

ਹੇਠ ਲਿਖੇ ਸਵਾਲ ਪ੍ਰਸ਼ਨ ਕਰਨੇ ਜਰੂਰੀ ਹਨ ।

ਹੇਠ ਲਿਖੇ ਸਵਾਲ ਪ੍ਰਸ਼ਨ ਕਰਨੇ ਜਰੂਰੀ ਹਨ ।

ਹੇਠ ਲਿਖੇ ਪੰਥ ਸਾਹਿਤਕ ਭੰਡਾਰ ਦੀ ਪੂਰੀ ਸਹਿਤ ਆਲੇਫਨਾਤਮਕ ਵਿਆਖਿਆ ਕਰੋ ।

Each answer along with examples of the following questions is to be written within 150 words :

Enumerate the significance of the following questions :

Analyse in detail the following questions :

The answers of the following questions must be written in Sanskrit language and in Devanāgari script only :

Explain each of the following verses in Sanskrit language and in Devanāgari script only (within 150 words) :

Write critical notes (about 150 words each) on ANY FIVE of the following passages:

Answer ANY TWO of the following questions:

Write answers to ANY TWO of the following:

Write answers to ANY TWO of the following:

Write critical notes (about 150 words each) on ANY FIVE of the following passages:

Answer the following five questions on the given verses in not more than 150 words each. (10×5 = 50)

Answer ALL of the following:

Answer ALL of the following:

Answer ALL of the following:

Answer the following five questions on the given passages in not more than 150 words each. (10×5 = 50)

“Well differentiated products create a significant competitive advantage and a distinctive aura for themselves.” Analyse the statement and discuss the various attributes on the basis of which products can be successfully differentiated.

Sunder Ltd. is planning an expansion programme which will require ₹30 crores and can be funded through one of the three following options: 1. Issue equity shares of ₹100 each at par 2. Raise a 15% loan, and 3. Issue 12% preference shares The present paid-up capital is ₹60 crores and the annual EBIT is ₹12 crores. The tax rate may be taken at 30%. After the expansion plan is adopted, the EBIT is expected to be ₹15 crores. Calculate the EPS under all the three financing options indicating the alternative giving the highest return to the equity shareholders. Also determine the indifference point between the equity share capital and the debt financing (i.e. option 1 and option 2 above).

Directors of ABC Ltd. wish to diversify. Presently, ABC Ltd. is into selling finished goods from its own godown. ABC Ltd. issued debentures on 07-04-2022 and purchased fixed assets on the very same day. The purchase prices are assumed to have remained stable during the concerned period. Following financial information is available to you: INCOME STATEMENT (₹) 2021-22: Cash sales 30,000; Credit sales 2,70,000; Less: Cost of goods sold 2,36,000; Gross profit 64,000; Less: Operating expenses – (i) Warehousing 13,000 (ii) Transport 6,000 (iii) Administrative 19,000 (iv) Selling 11,000; Net profit 15,000. 2022-23: Cash sales 32,000; Credit sales 3,42,000; Less: Cost of goods sold 2,98,000; Gross profit 76,000; Less: Operating expenses – (i) Warehousing 14,000 (ii) Transport 10,000 (iii) Administrative 19,000 (iv) Selling 57,000; Net profit 19,000. BALANCE SHEET (₹) Assets & Liabilities 2021-22 2022-23 Fixed Assets (Net Block) – 30,000 – 40,000 Receivables 50,000 82,000 Cash at Bank 10,000 7,000 Stock 60,000 94,000 Total Current Assets (CA) 1,20,000 1,83,000 Payables 50,000 76,000 Total Current Liabilities (CL) 50,000 76,000 Working Capital (CA-CL) 70,000 1,07,000 Net Assets 1,00,000 1,47,000 Represented by: (i) Share capital 75,000 75,000 (ii) Reserve & Surplus 25,000 42,000 (iii) Debentures – 30,000 1,00,000 1,47,000 You are required to calculate the following ratios for the years 2021-22 and 2022-23: (i) Gross Profit Ratio (ii) Operating expenses to sales ratio (iii) Operating profit ratio (iv) Capital turnover ratio (v) Stock turnover ratio (vi) Net profit to Net worth ratio (vii) Receivables collection period Ratio relating to capital employed should be based on the capital at the end of the year. Give the reasons for change in the ratios for two years. Assume opening stock of ₹10,000 for the year 2021-22. Ignore taxation.

Answer all the following sub-parts.

Answer all the following sub-parts.

Answer all the following sub-parts.

Answer all the following sub-parts.

Answer all the following sub-parts.

(a) A 2 gm quantity of air undergoes the following sequence of quasi-static processes in a piston-cylinder arrangement: (i) An adiabatic expansion in which the volume doubles. (ii) A constant pressure process in which the volume is reduced to its initial value. (iii) A constant volume compression back to the initial state. The air is initially at 150°C and 5 atm. Calculate net work on the air in the sequence of processes. (b) Consider a nozzle of inlet area 'A1' and outlet area 'A2'. The velocity is 'V1' at inlet and 'V2' at outlet. This nozzle accelerates the incompressible fluid (V2 > V1) and decreases the pressure. Can this nozzle in any condition, deaccelerate the fluid? If yes, then justify your answer with the help of continuity, momentum and energy equations. (c) Deduce an expression for the temperature distribution in an infinite long slab of thickness "L" m under one-dimensional steady-state heat conduction. The slab uniformly generates heat of q̇ W/m³. One of its surfaces is perfectly insulated and the other surface is maintained at a constant temperature of Tw °C. Also plot the temperature profile clearly mentioning the maximum and minimum temperatures and the location. (d) For special cases of axial-flow reaction turbines with degree of reaction in the form R = 1/(k + 1), where k is an integer, a special relationship exists between the blade velocity 'u' and fluid inlet velocity or velocity for maximum utilization. Show that this relationship is given by u / V1 = (k + 1)/(2k) cos α. Here α is the angle between inlet velocity V1 and blade velocity u. (e) Incompressible fluid having free-stream velocity of "u" m/s and temperature of T °C flows over a flat plate maintained at a constant temperature of Tw °C (T ≠ Tw). Flow is within the laminar region. Draw the relative thicknesses of thermal and hydrodynamic boundary layers developed on the flat plate for three fluids having (i) Pr < 1, (ii) Pr = 1 and (iii) Pr > 1. Justify your answer appropriately. (Draw three diagrams for the three fluids for better clarity.)

(a) Air flows through a 5 cm diameter pipe with inlet velocity 70 m/s, temperature 80 °C and pressure 1 MPa. For a pipe length of 25 m, assuming adiabatic flow with mean friction factor 0·005, determine the exit temperature, pressure and Mach number using the attached Fanno table. (b) Saturated liquid refrigerant at –7 °C flows through a horizontal copper tube (inside diameter 25 mm, thickness 2·5 mm, length 10 m) exposed to air at 20 °C. For a mass flow rate of 0·0012 kg/s and latent heat of evaporation 400 kJ/kg, find the exit dryness fraction. Property values of air at 280 K: ρ = 1·271 kg/m³, k = 0·0246 W/mK, ν = 1·4 × 10⁻⁵ m²/s, Pr = 0·717. Use the correlation Nu_f = (0·48)[Gr·Pr]^0·25 and neglect temperature drop in the tube wall and tube thermal resistance. (c) (i) Explain how Stefan–Boltzmann law is obtained from Planck’s law. Compute the total emissive power of a black sphere of 5 cm diameter maintained at 500 K, taking σ = 5·67 × 10⁻⁸ W/m²K⁴.

(b) (i) A 55-year-old female presented with haematemesis. On physical examination, she was afebrile and pale. No organomegaly was noted. Serological tests for hepatitis B were positive. 1. What is the most likely diagnosis? 2. Describe the microscopic findings. 3. What is the pathogenesis? (ii) Describe the clinical features and microscopic findings in acute lymphoblastic leukaemia. (c) (i) State the role of diuretics in the management of hypertension. (ii) Discuss how excess dose of paracetamol causes acute hepatocellular toxicity and how you will manage the condition. (iii) Elaborate the advantages and disadvantages of Sodium-Glucose Cotransporter-2 (SGLT-2) inhibitors in the management of diabetes mellitus.

(a) (i) What is enteric fever? What are its causative agents? Give a detailed presentation of a case according to the time of the disease and the respective tests used for diagnosis. (ii) Draw a diagram of HIV virion depicting the various antigens and proteins. Give the serological pattern in an HIV infection according to the time of presentation. List the various diseases associated with AIDS. (b) (i) What is virtual autopsy? State its methodology. What are its merits? (ii) Define brain death. Describe its medicolegal importance. (c) (i) Discuss why infliximab is considered as an immunosuppressant. Mention its therapeutic uses. (ii) Describe briefly the pharmacological characteristics of natriuretic peptides and their clinical uses.

(a) Discuss in short the role of a Chest X-ray in the diagnosis of pulmonary tuberculosis. (b) Describe the clinical features for diagnosing a case of Depression. (c) What are the key differences between Kwashiorkor and Marasmus? Which is the easiest method which can help in the early detection of Protein Energy Malnutrition (PEM) in children? (d) During the initial phase of stabilization in a severe acute malnourished child, map out the dietary plan. State the type, amount and frequency of feed that the child requires and for how long that would be necessary. In this phase, what is the vitamin and mineral supplementation given? (e) In a confirmed case of scabies in an adult: (i) What are the primary manifestations of the disease and what is the pattern of distribution of lesions on the body? (ii) What are the complications seen in scabies?

(a) (i) Discuss in short about the different modalities used in the diagnosis of Extra-Pulmonary Tuberculosis. (ii) Describe the clinical features of malabsorption syndrome. (b) (i) Write in brief the ten steps of Baby-friendly Hospital Initiative (revised 2018). (ii) Write the advantages of breast-feeding. (c) A young adult female develops asymptomatic depigmented chalky white macules and patches with no sign of inflammation over face and around body orifices. (i) What is the diagnosis? (ii) What are the associated findings seen in this disorder? (iii) How is this disorder classified? (iv) Describe the clinical course of the disease.

(a) Describe the clinical features, diagnosis and treatment of Kala-azar. (b) What are the types of vaccines currently in use against Pneumococcus organisms? State the National Immunization Schedule for administering Pneumococcal Vaccine in infants. Enumerate the diseases that the Pneumococcal Vaccine can safeguard against. (c) A young female patient develops acute inflammatory papules and vesicles all over her scalp and tips of ears following repeated use of hair dye. (i) What is the diagnosis? (ii) How can the diagnosis be confirmed? (iii) How will this condition be treated?

(a) A sixty-year-old male develops central chest pain while walking uphill. The pain is squeezing in character, radiating to left arm, that relieves on taking rest. Discuss in short about the evaluation and treatment of this case. (b) (i) Enumerate the causes of respiratory distress in a newborn. How would you differentiate between respiratory distress of respiratory origin and that of cardiac origin? (ii) Write the complications of cyanotic congenital heart diseases. (iii) How will you manage a one-year five-month old child presenting with severe respiratory distress with a history of cough and fever for 5 days? (c) (i) What is the meaning of the term 'lichenoid'? (ii) Name the disease that is a prototype of lichenoid reaction. (iii) Describe the clinical features of the disease.

(a) (i) Enlist conditions having an increased risk of malignant disease in bone and cartilage. (ii) Briefly mention classification of bone tumours. (b) A 55-year-old male patient underwent subtotal gastrectomy for carcinoma stomach. Briefly describe early and late complications of this procedure. (c) (i) A 25-year-old infertile woman presents with menorrhagia. Ultrasound pelvis revealed multi-fibroid uterus, largest measuring 3 × 3 cm. Describe the evaluation and management of Fibroid Uterus in the above patient. (ii) Describe recent classification of Abnormal Uterine Bleeding (AUB). Briefly discuss the endometrial pattern in various types of Abnormal Uterine Bleeding.

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each:

Answer the following:

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each:

Answer any three of the following:

Answer the following:

Answer the following:

Answer the following:

(a) A particle limited to the x-axis has the wave function φ(x) = bx² between x = 0 and x = 2; the wave function φ(x) = 0 elsewhere. (i) Find the probability that the particle can be found between x = 1·0 and x = 1·5. (ii) Find the expectation value < x > of the particle position. (b) Show that the square of the orbital angular momentum operator (L²) commutes with any of the components of angular momentum operator L. Is it possible to measure L², Lx, Ly and Lz simultaneously? Give reasons for your answer. (c) How is Rydberg constant related to emission wavelength of hydrogen spectrum? (d) Explain how the hydrogen spectrum is used for imaging the universe. (e) Find the energy of the particle of mass m moving in a potential field V(x) = 2ħ²b²x² / m for which the time-independent wave function is ψ(x) = exp(–bx²). Here b is a constant.

(a) Prove that: (i) [L², Lz] = 0 (ii) [Lz, L+] = ħL+ (iii) [L+, L–] = 2ħLz (iv) L+ Ly = L² – Lz² + ħLz where ħ = h / 2π (h is Planck’s constant). (b) The ground-state wave function of a harmonic oscillator is ψ₀(x) = (mω / πħ)^{1/4} exp(–mωx² / 2ħ). (i) At which point is the probability density maximum? (ii) What is the value of the maximum probability density? (c) (i) Assuming the potential seen by a neutron in a nucleus to be schematically represented by a one-dimensional, infinite rigid-wall potential of length 10⁻¹⁵ m, estimate the minimum kinetic energy of the electron. (ii) Estimate the minimum kinetic energy of a neutron bound within the nucleus as described above. Can an electron be confined in a nucleus? Explain.

(a) How do Stokes lines appear in Raman spectrum as per classical and quantum theory of Raman effect? (b) What is Lamb shift in the fine structure of hydrogen spectrum? Discuss its theory based upon second quantization. (c) Describe Electron Paramagnetic Resonance. Highlight its differences with NMR and discuss its applications.

(i) Using free electron theory of metals, calculate the Fermi energy level of sodium atom at absolute zero. Assume that sodium has one free electron per atom and its density is 0·97 gm cm⁻³. (ii) Draw the energy level diagram and write the mathematical expressions for the following: I. En of an electron confined in a one-dimensional box, II. Linear harmonic oscillator. Make a qualitative comparison of the above two cases.

Write approximately 150 words on each one of the following:

Write approximately 150 words on each one of the following:

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each:

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each :

Answer the following in about 150 words each:

Answer the following in about 150 words each:

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each :

Answer the following questions in about 150 words each :

Consider the following five sub-questions. Answer all of them. (a) Consider a system consisting of three identical units connected in parallel. The unit reliability factor is 0·90. If the unit failures are independent of one another, and if the successful operation of the system depends on the satisfactory performance of any one unit, determine the system’s reliability. (b) Describe the procedure and some of the applications of the Cumulative Sum (CUSUM) chart for monitoring process mean. (c) Explain the following terms as used in sampling inspection plans : (i) Producer’s risk (ii) Average Outgoing Quality Limit. (d) A Linear Programming Problem (LPP) in standard form is given below : Optimise Z = CᵀX subject to AX = B, with X ≥ 0 Write down the Dual Simplex form and its iterative procedure. (e) What is Monte Carlo Simulation? State the uses and applications of Monte Carlo Simulation.

(a) Obtain the control limits for X̄-chart and R-chart and describe the significance of joint study of these charts. (b) Find the reliability and hazard functions of Weibull distribution with scale parameter θ and shape parameter β, and interpret the findings. (c) Use simplex method to solve the following Linear Programming Problem (LPP) : Maximise z = 5x₁ + 2x₂ subject to 6x₁ + x₂ ≥ 6, 4x₁ + 3x₂ ≥ 12, x₁ + 2x₂ ≥ 4, x₁ ≥ 0, x₂ ≥ 0.

(a) With respect to a given Linear Programming Problem (LPP), explain the following concepts : (i) Extreme Point Solutions (ii) Duality Theorem (iii) Complementary Slackness Principle. (b) Define a Transition Probability Matrix (TPM). When is it said to be Regular and Ergodic? Check whether the following TPM is Regular or Ergodic. Hence or otherwise obtain the limit, as n → ∞, of Pⁿ where P = [0·88 0·12; 0·15 0·85]. (c) The reliability function R(t) of a cutting assembly is given by R(t) = {(1 − t / t₀)² , 0 ≤ t ≤ t₀; 0 , t ≥ t₀} (i) Determine the failure rate. (ii) Does the failure rate increase or decrease with time? (iii) Determine the mean time to failure.

(a) A manually handled toll-booth has two tellers, who are each capable of handling an average of 60 vehicles per hour, with the actual service times exponentially distributed. Vehicles arrive at the booth according to a Poisson process, at an average rate of 100 per hour. Determine the following : (i) The probability that there are more than three vehicles in the booth at the same time. (ii) The probability that a given teller is idle. (iii) The probability that a vehicle spends more than three minutes in the booth. (b) PQR Electronics produces 300 transistors per day, which go into the inventory. It supplies 150 transistors per day to XYZ Radios. The annual demand is 37,500 units. The inventory holding cost is $0·25 per transistor per year and the set-up cost per production run is $200. Find the following : (i) Economic Order Quantity (EOQ) (ii) Production run length (iii) Number of production runs per year (iv) Maximum Inventory Level (c) (i) Explain the terms ‘chance causes’ and ‘assignable causes’ of variation in quality control. Also provide some principal advantages of statistical quality control. (ii) Describe the procedure of obtaining OC curve for a single sampling plan.

Write short notes on the following in about 150 words each :

Write short notes on the following in about 150 words each :

Write on the following in about 150 words each :

Write on the following in about 150 words each :