(R130103) - UPI QP BANK

(R130103)

M.Phil.lPre-Ph.D. (Part-I) DEGREE EXAMINATION, APRIL 2017.

(Supplementary)

Biotechnology

Paper II - MICROBIAL 13l0TECHNOLOGY

Time: Three hours Maximum: 100 marks

Answer ALL questions.

(5 X 20 = 100)

UNIT I 1. (a)

(b)

Write about batch fermentation, fed-batch fermentation and continuous fermentation with suitable examples for the production

Or Define bioreactor. Explain design and operation of continuous stirred tank reactor.

UNIT II 2. (a)

(b)

Explain various methods for descrip ting microbial cells. Discuss gram scale purification of recombinant proteins.

Or Describe various chromatography techniques used for large scale purification. Add a note on stabilization of proteins.

UNIT III

;1. (a) Explain the industrial production of organic

acids.

Or

(b) Give a detailed account on Vitamin B 12

.

UNIT IV

1. (a) Define environmental pollution. Enumerate

the types of soil and air pollutants. Describe various methods for the measurements of air pollution.

Or

(h) Give a detailed account on bioremediation. Add a note on biopcsticides in integrated pest management.

UNIT V

5. (a) Mention industrially important enzymes

used in food processing. Explain various methods of immobilization of enzymes.

Or

(h) Discuss in detail about design and operation of immobilized enzyme system and bioreaction.

2 (RI30103)

(R130201) UNIT In

M.Phil./Pre-Ph.D. (Part-I) DEGREE EXAMINATION, APRIL 2017.

Supplementary

Chemistry

Paper I - RESEARCH METHODOLOGY


Answer ALL questions, choosing ONE from each unit.

Each question carries 20 marks. (5 x 20 == 100)

UNIT I

1. (a) Explain the criteria for the selection of area of research. Write about the design of experimental program.

Or

(b) Discuss the steps involved in developing new method and how do you validate it .

UNIT II

a

2. (a) Discuss the use of software jn literature collection. How do you collect literature from web.

Or

(b) What is the need of Explain the collection Scopus.

literature survey? of literature from

:l. (a) Describe the use of modeling in Research. Explain various types of models available for use in chemistry.

Or

(b) Explain the designing of engineering experiments. Write about randomization and blocking.

UNIT IV

4. (a) How do you write the preamble of a thesis? Add a note on the organisation of report.

Or

(b) Discuss the importance of graphs and charts in the data representation of a research work.

UNIT V

5. (a) How do you make your results with logical discussion and conclusion? Write about the procedure to be followedin these lines. "

Or

(b) Write about the formats of publication of results in Research Journals. How research findings are useful for the needs of society?

2 (R130201)

(R130301)

M.PhiIlPrc-Ph.D (Part-I) DEGREE f<~XAMINATION, APRIL 2017.

(Supplementary)

Commerce and Management



.Answer ALL questions.

1. (a) Define research. Explain the significance and process of research.

Or

(b) Give your understanding of a good research design. Is single research design suitable in all research studies?

2. (a) Explain and illustrate the procedure of selecting a random sample.

Or

(b) "The procedure of testing hypothesis requires a research to adopt several steps". Describe in brief all such steps.

:l. (a) What arc the guiding considerations -in the construction of questionnaire? Explain.

Or

(b) Explain the following scales

(i) Likert scale

(ii) Guttman scale

(iii) Serna ntic differential scale.

4. (a) What is statistical table? What are the principles of table construction?

Or

(b) Explain the place of non- parametric tests in research.

5. (a) Define a research report.' Explain the characteristics and functions of research report.

Or

(b) What are the purposes of foot notes? What are the kinds of foot notes?

2 (R130301)

(R130302)

M.PhiI./Pre.Ph.D. (Part-I) DEGREE EXAMINATION, APRIL 2017.

(Supplementary)


Paper III - MANAGEMENT PROCESS AND ORGANISATIONAL BEHAVIOUR



1. (a) Discuss the measures of managerial performance and their relevance in the present day world.

Or

(b) Discuss social responsibility of business with the help of examples from the corporate world.

2. (a) Organizational analysis and managerial planning involves the development of policies, procedures, programmes, budgets and schedules. Comment and discuss the nature, role and objectives.

Or

(b) What is delegation of authority? Explain the principles of delegation.

:~ . (a)' How does each of the motivation theory you know contribute to the prediction of performance, satisfaction and other outcome variables?

Or

(b) What are the assumptions of theory X and Theory Y? Is an autocratic manager likely to view his employees from theory X or theory Y perspective? Discuss.

1. (a) What influence do you think an employee's age, experience and physical abilities have on his/her performance at work?

Or

(b) Bring out with comments, the essence of social learning theory of personality.

5. (a) Define the term "Group". What are the types of groups? What purpose do groups serve?

Or

(b) What are major sources of interpersonal conflict? Which do you think is most relevant in today's organizations?

2 (R130302)

3. (u) Distinguish between training and education.(R130303) Arc you trained or educated in your college.

M.Phil./Pre-Ph.D. (Part-I) DEGREl~ EXAMINATION, APRIL 2017.

(Supplementary)


Paper III - HUMAN RESOURCE MANAGEMENT



1. (a) What are the important approaches to designing of a job? What is the relevance of each approach to the present industrial situation in India?

Or (b) "Job analysis is a formal and scientific study

undertaken to identify the job contents and qualities that are required in job holder". Elucidate this statement and bring out the uses of job analysis.

2. (a) "Recruitment is a true sales function" Discuss this statement and identify the role of recruitment in the acquisition process of Human Resources.

Or

(b) What are the objectives of compensation management? Discuss the steps involved in compensation management process.

Or

(b) "Accurate appraisal of performance is very difficult? Do you agree with this? Explain what are the pitfalls in effective appraisal system and how can these be overcome.

4. (a) What is the importance of collective bargaining? What are the essential conditions for the successful functioning of collective bargaining?

Or

(b) Explain the strategies and technique adopted by management to keep their plants union-free. .

5. (a) Briefly explain the emotional effects of cultural shock on the expatriates while undertaking foreign assignments.

Or

(b) Discuss the approaches to International Human resources Management.

2 (R130303)

(R130304) :l. (a) Diseuss the role and importance of channels of distribution.

M.PhiI./Prc-Ph.D. (Part-£) DEGREE EXAMINATION, APRIL ~017.

(Supplementary) (b)

Or

Explain the concept of integrated marketing communication.


Paper III MARKE,TING MANAGEMENT

4. (a) Discuss the growth of consumer movement in India. What are the unique problems of Indian consumers?

(Regulation 2012-2013)

Time: Three hours Maximum: 100 marks (b)

Or

Discuss the marketing mix implications E - Marketing.

m

1. (a)


How do macro environmental forces provide opportunities and poses threats to a company?

Or

5. (a)

(b)

Explain the marketing research process in detail.

Or

"Marketing research is not free from limitations" Explain.

(b) Explain about the perspectives challenges in international marketing.

and

2. (a) What is target marketing? What different levels of target marketing?

are the

Or

(b) Explain the stages development process.

in new product

2 (R130304)

(R130401)

M.PhiI./Pre-Ph.D. (Part I) DEGREE EXAMINATION, APRIL 2017.

(Supplementary)

Computer Science ,



PART A - (10 x 2 = 20 marks)

Answer the following questions.

1. What are the dimensions of research?

2. What are the tools used for research?

3. Why it is important to define research problems appropriately?

4. What is quantitative approach in research methodology?

5. What is simulation? How it is performed in computer science?

6. What is the significance of writing a research paper?

7. What do you mean by sample design?

~. Write about research hypothesis.

!) . 'For any research to be successful it must be well

defined'. -Justify this statement.

10. What is the significance of report writing?

PART 13 (5 x16 =80 marks)


] 1. (a) What are the characteristics of research?

Discuss about different types of research in detail.

Or

(b) What are the tools used for research? Describe about different tools and

measurements used in computer science for data analysis.

12. (a) What are the techniques involved in defining

a research problems? Elaborate in detail.

Or

(b) What is the purpose of literature survey?

Explain how do you identify and present literature survey findings?

I:\. (a) What are the important concepts relating to research design? Explain the basic principles of environmental designs.

Or

(b) What do you mean by 'sample design'? What points should be taken into consideration by a researcher in sample design for any computer science research?

14. (a) Write a brief note on 'task of interpretation' in the context of research methodology. 'Interpretation is fundamental component of research process'. Explain why so?.

Or

(b) Explain the techniques and importance oral presentation of research findings.

of

(c) "Report writing is more than an art that rings upon practice and experience". Discuss.

15. (a) Write short notes on the following:

(i) Bibliography and its importance.

(ii) Rewriting and polishing of report.

(iii) Result visualization techniques.

Or

(b) Explain the layout of a research report.

(c) Explain different types of research reports.

2 (R130401) a (R130401)

\.

15. (a) Suppose the scheme R ~ (A, E, C, D, E)

decomposed into III (A, n, C) and

R:2,(A, D, E). The following set of functional

dependencies hold.

A-)BC CD --) E

B~D

E--)A

Give a lossless-join, dependency preserving decomposition of the scheme R into BCNF.

(b) Show, that if a relation scheme is in BCNF, then it is also in 3 NF.

Or

(c) Discuss the merits and demerits of hash-join, sort-merge join and block-nested loops join.

(d) . Give algorithms for inserting a new key into a H-tree.

1 (R130402)

(R130402)

M.Phil./Pre-Ph.D. (Part-I) DEGREE EXAMINATION, . APRIL 2017.

(Supplementary)

Computer Science

Paper 1I - BROAD AREA OF RESEARCH IN COMPUTER SCIENCE


PART A-- (10 x 2 = 20 marks)


1. What are the applications of linked lists?

2. Compare quick sort and merge sort methods.

:3. Define partial order and total order of relations.

4. What is the minimal set of connectives required for a well formed formula?

5. What is Pipeline Register? What is the use of it? Explain.

6. What are the reasons for process terminations? Explain.

7. What is Serial Interfaces? What are the various standard interfaces?

8. Explain how flow control is different from congestion control.

9. Explain the differences between weak entity and strong entity.

10. Explain how B trees are advantageous over IY trees.

PART B - (5 x 16 =80 marks)


11. (a) Distinguish between linear and binary search methods.

(b) Explain the Knapsack algorithm in detail.

Or

(c) Describe different tree traversal methods.

(d) Derive the time and space complexity for bubble sort and selection sort.

12. (a) Derive the (i) Breadth first tree (ii) Depth first search spanning trees for the following graph:

1'

Or

2 (R130402)

(b) Are (p ~ q) ~ I' and p ~ (q ~ r) logically

equivalent? -Iustify your answer by using the rules of logic to simplify both expression and also by using truth tables.

13. (a) Explain various instruction formats of a general purpose CPU with examples.

(b) Explain the strategies involved in deadlock detection and how it is recovered.

Or

(c) Why do we need some bits currents micro instructions to generate address of the next micro instruction? Support with a live example.

(d) How deadlocks can be avoided? Explain with the help of necessary diagrams.

14. (a) What are the types of data communication protocols and give the frame format of these protocols.

(b) Explain about exact-count encoding method used for error detection.

Or

(c) What is parity? What are the types of parity methods? Explain.

(d) Discuss about bandwidth balancing mechanisms.

3 (R130402)

(R130503)

M.Phil.lPre-Ph.D. (Part-I) DEGREE EXAMINATION, APR£L 2017.

(Supplementary)

English

Paper II - ENGLISH LANGUAGE TEACHING



Each question carries equal marks. (5 x 20 == 100)

UNIT I

1. (a) Summarize the features of the National Approach. Which procedures of this approach are still used in the classroom? Wha tare their advantages?

Or

(b) What is the general goal of CLI? Do you agree this should be the objective in language learning? Why or why not?

UNIT 11

2. (a) How does age affect second language acquisition? What does the critical period hypothesis argue about age and acquisition?

Or

(b) Account for how both form focused and meaning focused instruction contribute to second language acquisition in the classroom.

UNIT III

:~. (a) Consider ways for improving or refining existing methodologies in second language acquisition.

Or

(b) Examine the data collection methods used in formal, generative SLA Research.

UNIT IV

4. (a) Outline the current assumptions and practices concerning the teaching of listening and speaking skills.

Or

(b) What are the essential elements improving reading vocabulary?

of

2 (R130503)

UNITV

5. (a) What are the different kinds of tests to assess the student's skills in language? Explain.

Or

(b) How do you classroom?

test speaking and writing in a

:~ (R130503)

(R130601)

M.Phil/Prc-Ph.D. (Part-I) DEGREE EXAMINATION, APRIL 2017.

(Supplementary)

Journalism and Mass Communication




Each question carries equal marks.

(5 x 20 =100)

UNIT I

1. (a) Examine the status of Mass Communication research in India.

Or

(b) Discuss different problems involved communications research in India.

in

UNIT II

2. (a) Discuss various methods and techniques of research.

Or

(b) Differentiate hypothesis and null-hypothesis.

UNIT III

3. (a) Explain about the importance experimental and field research.

Or

of

(b) Detail the methods of sampling with suitable examples.

UNIT IV

4. (a) Discuss the application of research electronic media with suitable examples.

in

Or

(b) Explain the ethical issues involved in media research.

UNIT V

5. (a) Discuss the process of Data Analysis.

Or

(b) Write short following.

notes on any TWO of the

(i)

(ii)

Tabulation

Application of statistics

(iii) Questionnaire

(iv) Bibliography.

2 (R130601)

-1

(e) Write short notes on the following: (R130405) (i) Project organization

M.PhiVPre-Ph.D (Part-I) DEGREE EXAMINATION,(ii) Metrics automation APRIL 2017.

(iii) Path testing (Supplementary) (iv) Quality indicator.

Computer Science

Paper III - SOFTWARE ENGINEERING AND PROJECT MANAGEMENT


PART A - (10 x 2 =20 marks)


1. What is software engineering? Define:

2. Explain the incremental development model.

~3. What do you mean by flow-oriented modeling?

4. Differentiate between SIW architectural style and pattern.

5. What is the difference between coupling and cohesion?

6. What is cyclomatic complexity? Explain.

7. Differentiate between reverse and forward engmeermg.

8~ What is process discriminates? Explain.

4 (R130405)

10.

!) .

What are the roles and responsibilities of project manager?

What are the mct.rics used for source code'? 1:3. (a)

(b)

Describe the pattern based software design in detail.

Define and explain abstraction and refinement.

PART B (5 x 16 == 80 marks) Or

Answer ALL questions. (c) What is refactoring? Why it is done?

11. (a) Differentiate spiral model.

between waterfall model and (d) What are the approaches testing? Discuss.

used for static

(b)

(c)

Elaborate on the evolution of software.

Or

Describe software quality attributes detail.

In

14. (a)

(b)

Describe the framework for software product metrics.

Write the significance of Restructuring in SE.

12.

(d)

(a)

Explain the evolutionary process models in detail.

.Discuss about

engineering relationships.

principal activities

requirements

and their

(c)

(d)

Or

Explain different basic building blocks of process automation.

What are the metrics used for S/W testing and maintenance? Discuss.

(b)

Or

Differentiate between data modeling class-based modeling techniques.

and

15. (a)

(b)

Discuss about useful management indicators.

Write about software tools used for project and process metrics.

• Or

2 (R130405) 3 (R130405)

(R130501) UNIT III

M.Phil./Pre-Ph.D. (Part - I) DEGREE EXAMINATION, APRIL 2017.

(Supplementary)

English

Paper I - RHETORIC RESEARCH METHODOLOGY



All- questions carry equal marks. (5 x 20 = 100)

UNIT I 1. (a) What are

Research? the aims 'and - objectives of

Or

(b) What is Research? steps involved in research proposal.

What are the various the preparation of a

UNIT II

2. (a) Write a detailed essay on consulting source material, collecting relevant information and preparing a working bibliography.

Or

(b) Do you consider the computer indispensible research tool? Explain.

as an

3. (a) Outline the criteria of selecting a topic.

Or

(b) What is the essential selection criterion to be followed in making use of quotations in thesis writing?

UNIT IV

4. (a) What are the rules and conventions expected of scholarly writing?

Or

(b) What is thesis?

the style suitable' for a literary

UNIT V

5. (a) What are the procedures for editing, evaluating and proof reading a thesis?

Or

(b) Why is the study of Research Methodology important for a researcher?

2 (RI30501)

(R130504)

M.Phil./Pre-Ph.D. (Part.-1) DEGREE EXAMINATION, APRIL 2017.

(Supplementary)

English

Paper - III: TOPIC OF RESEARCH IN ENGLISH LANGUAGE/LITERATURE

Time: Three hours Maximurn : 100 marks

Answer ALL questions. Each question carries equal marks.

(5 x 20 = 100)

UNIT I

1. (a) Comment on the significance of your area of

your research and the particular topic of

study.

Or

(b) Briefly outline the literary theory you

propose to use in your research and state its

relevance to your area of study.

UNIT II UNIT V

2. (a) What are the source materials available for

supporting your research work.

Or

(b) What is your hypothesis? and how can it help

for better outcome of research?

UNIT III

3. (a) How far can you claim that you

progressed in your research work?

have

Or

(b) Write a detailed essay on

your research study.

the relevance of

UNIT IV

4. (a) What would be a suitable background study

for your topic of research?

Or

(b) What is your knowledge base in your area of

research? Explain.

2 (R130504)

5. (a) How far is a study of the literature of the Diaspora relevant in today's world?

Or

(b) . What is the relevance of using a critical approach or method in the context of thesis writing? Discuss.

3 (R130504)

(R130803) UNIT [T[

M.Phil.lPre-Ph.D. (Part - I) DEGREE EXAMINATION, APRIL 2017.

3. (a) What do you know of

(i) carrier gases in GC

(Supplementary) (ii) column efficiency parameters.

Pharmacy Or

Paper III RESEARCH SPECIALISATION IN PHARMACY

(b) Discuss the applications pharmaceutical analysis.

of GC In


1.

Answer ALL questions each question carries equal marks.

UNIT I

(a) How do you formulate and evaluate extended release tablets?

1. (a)

(b)

UNIT IV

Describe the various degradation pathways by which drugs undergo degradation.

Or

Write briefly on :

(i) Accelerated stability testing

Or (ii) ICH guidelines.

2.

(b)

(a)

List out different types of emulsions and discuss methods by which these emulsions can be obtained.

UNIT II

Explain with schematic diagram the principle and instrumentation of HPLC.

Or

5. (a)

(b)

UNIT V

Discuss the importance Pka of drugs.

Or

Write the importance dissolution rate of drugs.

of lipohilicity

of solubility

and

and

(b) Write briefly on :

(i) Detectors in HPLC

(ii) Mobile phase selection.

2 (R130803)

8. (a) Define a spanning tree. Prove that every connected graph has atleast one spanning tree.

(b) Define a graceful labeling of a graph. If a tree T with m edges has graceful labelling, then prove that K Zm d has a decomposition

into 2m -j 1 copies of T.

UNIT V

9. (a) Derive. the equation of continuity for homogeneous incompressible fluid flow.

a

(b) At a point in an incompressible fluid having spherical polar coordinates (r, 0, If) ,

the velocity components are· [2Mr- 3cosO, Mr-3 sin O, 0] where M is a

constant. Find the velocity potential and the equations of the stream lines.

Or

10. (a) Derive the Euler's equation of motion.

(b) Show that at any point P of a moving inviscid fluid, the pressure p is the same in aU directions.

1 (R141003)

(R141003)

M.Phil./Pre-Ph.D. (Part-I) DEGREE EXAMINATION, APRIL 2017.

(Supplementary)

Mathematics

Paper III - RESEARCH SPECIALIZATION


Answer ONE question from each Unit.

All questions carry equal marks.

UNIT I

1. (a) If p is a prime number of the form 4n + 1,

then show that p = 0,2 + b2 for some integers

a, b. (b) Show that x 2 + 1 is irreducible over the

integers mod 7.

Or

2. (a) Let R be a ring with unity and let M be an R-module. Then prove that the following statements are equivalent: (i) (ii)

M is simple M * (0) and M is generated by and

O1'xEM.

(iii) M ~ R II, where I is a maximal left ideal of R.

(b) ]f I .M -) N is an R-homomorphism of an R-module M to an R-module N, then show that (i) ker f is an R-submodule of M. (ii) 1m f is an R-submodule of N.

UNIT II

~3. (a) If V is the internal direct sum of its subspaces VI' V z, ... , Un then prove that V is isomorphic to the external direct sum of VI' V z, ... , V n ·

(b) If V is a finite dimensional vector space and . W is a subspace of V such that

"dim V:= dim W, prove that V:= W.

Or

4. (a) State and prove the Eisenstein criterion.

(b) Show that x 3 ~ Z E Q[x] is irreducible over Q. Find an extension K of Q, if it exists, having all roots of x 3

- 2 such that [K: Q]:= 6.

UNIT III

5. (a) Find the general .solution of the Legendre's eq uation (1 - X

Z )y" - Zxy' + p(p + l)y := 0 on

the interval Ix I < 1 .

(b) The equation xZy" - 3xy' + (4x + t1)y:= 0 has a regular singular point and only one Frobenius series solution. Find them both.

Or

s. (a) State and establish the orthogonality property of the Legendre polynomials.

(b) With the usual notation, show that

(i) JI(X)=~ Z sinx - ;rrxz

(ii) r(t)=J;·

UNIT IV

7. (a) Define a bipartite graph. Show that the complete graph K; can be expressed as the

union of k bipartite graphs if and only if

n ~ Zk.

(b) When do we say that two simple graphs GI(Vl> E

1) and GZ(V2 , E z) are isomorphic?

Examine whether the simple graphs with the following adjacency matrices are isomorphic:

0 1 0 1] [0 1 1 1]1,0011001.

0001'1001[ 11101110

Or

2 (R141003) 3 (R141003)

(R141002)

r\1.Phil./Pre-Ph.D. (Part-I) DEGREE EXAl\lINATION, APRIL 2017.

(Supplementary)

Mathematics

Paper II - BROAD AREA OF RESEARCH


Answer ONE question from each unit.

All questions carry equal marks.

UNIT I

1. (a) Let ¢ be a homomorphism of G onto G with Kernel K. Then prove that G / K ~ G.

(b) Show that every subgroup of an abelian group is normal and that the intersection of

two normal subgroups of a group G is a normal subgroup of G.

Or

2. (a) Prove that a finite integral domain is a field.

(b) Let R be a commutative ring with unit element whose only is deals are (0) and R

itself. Then prove that R is a field.

UNIT II

3. (a) Let II and L' be real valued functions defined on a subset S of the complex plane. Let u

and u be differentiable at an interior point C of S and that the partial derivatives

satisfy the Cauchy-Riemann equations at c. Then show that f =: u + iu has a derivative

(h) Let f be a function having a derivative f' at each point in R' and let g be defined on

1 . 222R by the equation g(x,Y,z) =: x + y + Z . If h = fog, then show that

'12 . 2II oc ..,vh(x,y,z)1 4g(x,y,z){['[g(x, y, z)J}

Or

4. (a) If the partial derivatives Dr! and Dd exist in an n-ball B(c; d) and if both are

differentiable at c then prove that Dr,k{(C) = Dkr!(c).

(b) Using Taylor's formula, express the function {(x,Y) = x 2 + xy + y2 in powers of (x -1)

and (y 2).

UNIT III

5. (a) Define a harmonic function. Show that U IS harmonic III some domain and

find a harmonic conjugate u when u(x,y) = y/(x2 + y2).

(b) State and prove the Cauchy's integral formula using their, evaluate f zdz ---:::-?--

C (9 - z: Hz + i)

where c is the circle Izl = 2 taken in the positive sense.

Or

6. (a) State and prove Cauchy's residue theorem. Using this, evaluate Y cos2e de. 05 4cose

(b) '" 2

Using the Cauchy's residue theorem, evaluate f 4 2x

-:; 1 dx. oX + 5x- + 4

UNIT IV

7. (a) Use the classical (fourth order) Runge-Kutta method to find a numerical solution at

x = 0.4 for ~~ =~x + Y , y(O.4) = 0.41 with h = 0.2.

(b) Find the solution at t = 0.3 for the differential equation y' = t y2, yeO) = 1 by the

Adams-Bashforth method of order two with h = 0.1. Determine the starting values

using the Euler's method.

Or

8. (a) Classify the equation and find its

characteristics.

(b) Solve the partial differential equation V2u = x 2 -1, Ixl:-s; 1, Iyl:-s; 1 with u = 0 on the

boundary of the square. Formulate the five point difference scheme with mesh size h in

both directions and solve it for h =~ . 2

2 (R141002)

UNIT V

9. (a) State the existence theorem for Laplace transforms. Find L[x cos ax] . Using this result,

1 1 findr [ 2. 2 9 ]

(p +0 t '

(b) Using Laplace transforms, solve the initial value problem y" + 2y' + 5y =3e- x sinx;

yeO) = 0 and y'(O) = 3 .

Or

10. (a) Define a Storm-Liouville problem. Show that the solutions of it form an orthonormal set

of functions. Obtain the characteristic values of the problem y" + A.y = 0, yeO) = 0 and

Y(Jr /2) = O.

(b) Find the Fourier series of the function [(x) = Isin xl in the interval - Jr < X < Jr .

3 (R141002)

(R130103) - UPI QP BANK

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