Loyola College Supplementary Statistics April 2006 Mathematical Statistics Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006

B.Sc. DEGREE EXAMINATION

                                                 ST 4201 – MATHEMATICAL STATISTICS

 

 

 

Date & Time : 28/06/2006/9.00 – 12.00        Dept. No.                                                       Max. : 100 Marks

 

 

Part A

      Answer all the questions.

  1. Define probability set function.
  2. If A and B are two events , show that P(AnBc) = P(A) –P(AnB)
  3. If p(x) satisfies the conditions of a pdf of a random variable X, find the constant C where P(x) = C(2/3)x, x = 1,2,3,…
  4. If the mgf of a random variable is (1-2t)-1. Find the mean and variance.
  5. Let the random variables X1 and X2 have the joint pdf f(x1, x2) = 2, 0<x1<x2<1, zero elsewhere. Find the conditional pdf of X1 given X2 =x2.
  6. Define and unbiased estimator.
  7. If X1 and X2 are independent random variables with X1 ~ N(10,16) and X2 ~ N(15, 9). Find the distribution of X1 + X2.
  8. Let the new random variable Y be defined as Y = 8X3. Find the Jacobian of transformation.
  9. If the random variable X has a poisson distribution such that P[X=1] = P[X=2]. Find P[X=4].
  10. Define Type I and Type II errors.

Part B

Answer any five questions.

  1. Derive the mgf of Binomial distribution. Hence find the mean and variance.
  2. Let X and Y have the joint probability function.

(x, y):     (1, 1)     (1, 2)     (1, 3)     (2, 1)     (2, 2)     (2, 3)

P(x, y):   2/15       4/15       3/15       1/15      1/15      4/15

Find the correlation coefficient.

  1. If the skulls are classified as A, B and C according as the length is under 75, between 75 and 80, or over 80, find approximately assuming Normal distribution the mean and standard deviationa of a data in which A are 58 % and B are 38% and C are 4%.
  2. Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys, and 1 girl and 3 boys. One child is selected at random from each group. Show that the chance that the three selected consists of 1 girl and 2 boys is 13/32.
  3. Let the pdf of a random variable be

f(x) =  3( 1 – x2) / 4 , -1<x<1, zero elsewhere. Find b2.

  1. Let X and Y have joint p.d.f.:

e-(x + y) x3y4

f(x, y) =                         ,  x > 0, y > 0

G4 G5

Find the p.d.f. of U = X / (X + Y).

    1. Discuss the properties of chi-square distribution.

 

  1. Obtain the method of moments estimator for the distribution with the p.d.f.

1/ (b-a),  a ≤ x ≤ b

f(x) =

0         , otherwise.

 

Part C

Answer any two questions

  1. a). Derive the recurrence relation for the moments of Poisson distribution. Obtain b1 and b2.

b). State and prove the additive property of Gamma distribution with parameter a and p.  ( 12 + 8 = 20)

 

  1. a). Derive the m.g.f. and hence find the mean and variance of Normal distribution.

b). Two random variables X and Y have the following joint probability density function

k (4 – x – y) ; 0 ≤ x ≤ 2; 0 ≤ y ≤ 2

f(x, y) =

0 ,  otherwise.

 

Find i). the constant k

ii). Marginal density functions of X and Y.

iii). Conditional density functions, and

iv). Var(X), Var(Y) and Cov (X, Y).      (8 + 12 = 20)

 

  1. a). State and prove Bayes theorem

b). Let A, B and C are three events then derive the result for P(AUBUC).

c). A factory produces a certain type of outputs by three types of machine. The respective daily production figures are:

Machine I: 3,000 Units; Machine II: 2,500 Units; Machine III : 4,500 Units.

Past experience shows that 1 percent of the output produced by Machine I is defective. The corresponding fraction of defectives for the other two machines are 1.2 percent and 2 percent respectively. An item is drawn at random from the day’s production run and is found to be defective. What is probability that it comes from the output of

i). Machine I                ii). Machine II             iii). Machine III ?                                                                                                               (7 + 7 + 6 = 20)

 

  1. a). Derive the pdf of F-distribution.

b).  Obtain the mean and variance of Beta distribution.

 

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Loyola College Supplementary Physics April 2006 Quantum Mechanics – I Question Paper PDF Download

 

 

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006

M.Sc. DEGREE EXAMINATION

                                               PH 2806/2801 – QUANTUM MECHANICS – I

 

 

 

Date & Time : 27/06/2006/9.00 – 12.00        Dept. No.                                                       Max. : 100 Marks

 

PART A ( 10 X 2 = 20 )

 

ANSWER ALL QUESTIONS. EACH QUESTION CARRIES 2 MARKS.

 

  1. State two phenomena which can not be explained by classical  physics.

 

 

  1. What is meant by wave-particle duality ?

 

 

  1. What is an observable ?

 

 

  1. What are stationary states ?

 

 

  1. What is meant by self-adjointness ?

 

  1. State the expansion postulate.

 

 

  1. Define the creation and annihilation operators.

 

  1. Express the angular momentum operator in spherical polar coordinates.

 

 

  1. What is the effect of an electric field on the energy levels of an atom ?

 

  1. What is the principle of the variation method ?

 

 

 

 

PART B ( 4 X 7.5 = 30 )

 

ANSWER ANY FOUR QUESTIONS.EACH QUESTION CARRIES 7.5 MARKS.

 

  1. State and explain the Uncertainity principle.

 

  1. (a) Explain Born’s interpretation of the wave function.

(b) Explain the significance of probability current and the equation of continuity.

 

13.(a) State and explain the superposition principle.

(b) Show that any two eigen-functions belonging to distinct eigen-values are mutually orthogonal.

  1. Solve the eigenvalue equation for L2 by the method of separation of variables.

 

  1. Discuss the effect of an electric field on the energy levels of an atom.

 

 

PART C ( 4 X 12.5 = 50 )

 

ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 12.5 MARKS.

 

  1.  Explain Compton effect. Obtain an expression for the shift in wave-length of the scattered X-rays due to Compton effect.

 

  1. State and prove Ehrenfest theorem..

 

  1.  (a) Prove the relation which states the uncertainity relation for any pair of observables A and B..
  • Explain the property of closure.

 

  1. Solve the Schrodinger equation for the simple harmonic oscillator. Sketch the first two eigen-functions of the system.

 

  1. Explain the variation method for the estimation of the ground state energy. Discuss the result for the case of the hydrogen molecule.

 

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Loyola College Supplementary Physics April 2006 Mathematical Physics Question Paper PDF Download

 

 

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006

M.Sc. DEGREE EXAMINATION

                                            PH 2803/PH 2900 – MATHEMATICAL PHYSICS

 

 

 

Date & Time : 27/062006/9.00 – 12.00         Dept. No.                                                       Max. : 100 Marks

 

                                                                PART – A                                       (10´ 2=20 marks)

      Answer ALL questions.

 

  1. Starting from the general equation of a circle in the xy plane, A(x2 +y2) + Bx + Cy +D=0 arrive at the zz* representation for a circle.
  2. State Cauchy’s integral formula for derivatives
  3. Develop Taylor’s series of about z = -1.
  4. Express in the form of a+ib
  5. Show that the Dirac delta function .
  6. State convolution theorem.
  7. Solve the differential equation ’ + .
  8. Obtain the orthonormalising constant for the series in the interval     (-L, L).
  9. Evaluate using the knowledge of Gamma function.
  10. Generate L3 (x) and L4(x) using Rodrigue’s formula for Laugerre

 

 

 

                                                                PART – B                                      (4´ 7.5=30 marks)

      Answer any FOUR.

 

  1. Obtain Cauchy Rieman equations from first principles of calculus of complex numbers.
  2. State and prove Cauchy’s residue theorem
  3. Develop half-range Fourier sine series for the function f (x) = x ; 0 < x < 2. Use the results to develop the series .
  4. Verify that the system y11 + ; y1(0) = 0 and y (1) = 0 is a Sturm-Liouville System. Find the eigen values and eigen functions of the system and hence form a orthnormal set of functions.
  5. (a) If f (x) = obtain Parseval’s Identity
    where  Pk (x) stands for Legendre polynomials.
  • Prove that  (x) = 2n – 1 Hn (x) where Hn (x) stands for Hermite polynomials.(4+3.5)

 

 

                                                               PART – C                                      (4´12.5=50 marks)

Answer any FOUR.

 

  1. Show that u (x, y) = Sin x Cosh y + 2 Cos x Sinhy + x2 +4 xy – y2 is harmonic Construct f (z) such that u  + iv is analytic.
  2. (a)  Evaluate  using contour integration.

(b)  Using suitable theorems evaluate  c : .             (7+5.5)

  1. (a) The current i and the charge q in a series circuit containing an inductance L and
    capacitance c and emf E satisfy the equations L  and i = . Using
    Laplace Transforms solve the equation and express i interms of circuit parameters.
  • Find , where L-1 stands for inverse Laplace transform.                 (3.5)
  1. Solve the boundary value problem . with Y (0, t) = 0; yx (L, t) = 0
    y (x, 0) = f (x) ;  yt (x, 0)  = 0  and
  2. Solve Bessels differential equation using Froebenius power series method.

 

 

 

 

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Loyola College Supplementary English April 2006 English & New Technologies Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006

B.A. DEGREE EXAMINATION

                                             EL 2074 – ENGLISH & NEW TECHNOLOGIES

 

 

 

Date & Time : 28/06/2006/9.00 – 12.00        Dept. No.                                                       Max. : 100 Marks

 

 

  1. Write an essay (in about 300 words) on any one of the technologies that was presented in the class or you have studied about, based on the guidelines below: 15 marks
  2. Define the Technology
  3. Origin and its development
  4. Advantages and disadvantages
  5. Ethical issues related to the technology
  6. Conclusion

 

  1. Write an essay in about 300 words on the symptoms (disadvantages) of technological influences on mankind illustrating them from the text materials you have learned at the class as well as from various writings on the same theme.                                                            15 marks

 

  1. Write an essay in about 200 words for the following question.

 

“ The mankind is at a constant warfare with the machine. The fears of humanity for the overpowering technologies presented in various Hollywood and regional movies (eg. Terminator and Matrix series, Starwars etc)”.  Explain with examples.         10 marks

 

04.    Imagine you receive the following email from e-CVs.net requesting you to complete filling in your details for CV/Biodata. Try to make a complete profile/CV/biodata about you and forward to e-CVs.net.                      15 marks

Hi santhosh,

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Debbie Mitchell
Jobseeker Advisor

  1. Write an essay in about 200 words the need for blending (merging / combining) the High Tech and High Touch according to John Naisbitt’s article titled “High Tech. High Touch”.                                                            10 marks

 

  1. Read the following ad and subscribe the product through email explaining the purpose and expectation. 10 marks

 

 

Googel AdSense

 

Discover your site’s full revenue potential.

 

Google AdSense is a fast and easy way for website publishers of all sizes to display relevant Google ads on their website’s content pages and earn money. Because the ads are related to what your visitors are looking for on your site — or matched to the characteristics and interests of the visitors your content attracts — you’ll finally have a way to both monetize and enhance your content pages.

 

It’s also a way for website publishers to provide Google web and site search to their visitors, and to earn money by displaying Google ads on the search results pages.

 

  1. Write a short story in about 200 words on the theme if all the cars / automobile vehicles were to fly on the space owing to the advancement of science and technologies to avoid traffic jam on the roads.                           10 marks
  2. Read the following article “Good Teachers = High Academic Achievement”, by Karena O’Riordan and simplify it in your own words. The simplified answer should be in 150 words.                                                                                         15 marks.

Good Teachers = High Academic Achievement

by Karena O’Riordan

Recognizing that a school technology program is only as successful as the teachers who use it, the Milken Exchange on Education Technology has introduced the Professional Competency Continuum (PCC), a road map for educators to use to assess their skills in integrating technology in the classroom..

In order to answer a question many states, districts and schools are struggling to answer — What are the skills for the digital age classroom? — the Milken Exchange gathered a panel of experts to identify areas where teachers’ professional skills should be developed in order to become effective users of technology. The experts’ recommendations grew into the key elements of the PCC.

The goal of the Milken Exchange has always been to promote higher academic achievement in schools. “Using technology for technology’s sake has little academic value,” says Edward Coughlin, author of the PCC. “We think that education systems should first set high academic standards that are appropriate for their students, and then work towards those goals using technology as one tool in the process. There is no question that technology helps move students forward academically, but it must be used wisely.”

The PCC is part of the Milken Exchange’s series, Seven Dimensions for Gauging Progress with Technology in Schools and represents the third of the seven dimensions: professional competency.

“Our seven dimensions are being used all over the country in training programs, school districts and staff development initiatives,” says Cheryl Lemke, executive director of the Milken Exchange. “The PCC helps those efforts by prescribing the specific steps educators can take to effectively integrate technology in their classrooms.”

The PCC includes a set of introductory scenarios describing “how it could be” in technology-rich classrooms. While some of the scenarios depict situations that seem futuristic or expensive, all the technologies described — as well as the contexts in which they are used and the research supporting their credibility — are available. Yet few of them are encountered in our nation’s school districts. “The goal of creating the PCC is to encourage teachers to think beyond the traditional classroom with its antiquated structure and learning style,” says Coughlin. “But many cannot begin to do so without knowing what the possibilities are. We hope this document and its accompanying activities can help to expand their thinking.”

The PCC also describes various “stages” of progress for educators. For example, in acquiring “core technology skills,” an educator might be at stage one: Entry — educators, students and the community are aware of the possibilities technology brings, yet learning, teaching and the system remain relatively unchanged by technology. Hopefully, the skills described by the PCC will lead that educator to Stage Two: Adaptation; and ultimately, Stage Three: Transformation, in which technology becomes a catalyst for significant changes in teaching learning practices.

The PCC is available in several formats. The first is the print publication described here. The second is the Web site, which will be dedicated to updating and evaluating progress with the PCC. And the third is an assessment tool, available both in print and online. The assessment tool is a matrix on which educators can plot their progress in various levels of technology integration and a tool to support the professional development planning process. The assessment tool consists of five parts:

  1. 20-question survey assessing educators’ individual levels of comfort with technology.
  2. A more in depth survey with at least 15 items per area which provides a more specific picture of areas of need.
  3. Database of “advice essays” linked to the survey. Each advice essay corresponds to the levels of comfort described in the survey and recommends ways for educators to improve.
  4. Database of resources — Web sites, articles, books and training — deemed valuable to the levels of comfort described in the survey.
  5. Comprehensive reports. Reports are available both for individual teachers and for groups of teachers. Individual teachers can access comprehensive reports in each of 26 areas of competency. Professional developers working with groups of teachers can create “project groups” for whom they can develop summary reports for the group or for any subgroup within the project. The assessments can be taken multiple times and progress can be charted over time for individuals and groups.

 

 

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Loyola College Supplementary English April 2006 English For Self-Enhancement Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034

B.A. / B.Sc. / B.Com.  SUPPLEMENTARY EXAMINATION

EL 2056 – ENGLISH FOR SELF-ENHANCEMENT

 

Date:   27-06-2006                                                                                  Max Marks: 100

Time:   1.00 – 4.00 p.m.                                                                              Duration: 3 hrs

 

 

 

I The ten words underlined in the passage are grammatically incorrect. Substitute with the correct alternatives. (Note: Write the number and the correct word only. Do not rewrite the passage.)

[10 x 1 = 10 marks]

Give More Than You Get

It (1) was easy to succeed today. We have no competition. If you want to (2) got ahead in life, go the extra mile. There is no competition on the extra mile. Are you (3) will to do a little more than you get paid for? How many people you know (4) is willing to do a little bit more than what they get paid for? Hardly any. Most people don’t (5) wanted to do what they get paid for and there is a second category of people who only (6) wants to do what they can get by with. They fulfill (7) his quota just to (8) kept their jobs. There is a small fraction who are willing to do a little bit more than what they get paid for. Why do (9) he do more? If you fall into the last category, then (10) why is your competition?

 

II  Read the following passage and answer the questions given below:

[3 x 2 = 6 marks]

 

Horror gripped the heart of the World War I soldier as he saw his lifelong friend fall in battle. Caught in a trench with continuous gunfire whizzing over his head, the soldier asked his lieutenant if he might go out to bring his fallen comrade back. “You can go,” said the Lieutenant, “but I don’t think it will be worth it. Your friend is probably dead and you may throw your own life away.” The Lieutenant’s words didn’t matter, and the soldier went anyway. Miraculously he managed to reach his friend, hoist him onto his shoulder, and bring him back to their company’s trench. As the two of them tumbled together to the bottom of the trench, the officer checked the wounded soldier, then looked kindly at his friend. I told you it wouldn’t be worth it,” he said. “Your friend is dead, and you are mortally wounded.” “It was worth it, though, sir,” the soldier said. “How do you mean, `worth it?’ ” responded the Lieutenant. “Your friend is dead!” “Yes sir,” the soldier answered. “But it was worth it because when I got to him, he was still alive, and I had the satisfaction of hearing him say, `Jim, I knew you’d come.’ ”

 

  1. What is the meaning of the expression ‘You may throw your own life away’?
  2. What does the phrase ‘mortally wounded’ mean?
  3. Why did the lieutenant warn the soldier not to go out to help his friend?

 

 

III Read the story and state whether the statements given below are true or false. (Note: Write the letter and state ‘true’ or ‘false’. Do not write the statement)

[10 x 1 = 10 marks]

 

I have a friend named Ravi who owns a college. He has let me use his college to conduct a programme in order to raise money for visually challenged students. He is so helpful to students because he feels that this is the time student’s dream and work towards their future. By saying so he started narrating an incident from Ravi’s life.

 

It all goes back to Ravi’s college days. He was the son a watchman in a reputed college. Since he went to see his father quite often in the college, so he was much attached to the college. By sheer hard work, he entered high school. When he was in the final year, he was asked to write an assignment about what he wanted to be and do when he grew up. “That night he wrote a seven-page assignment describing his goal of owning a college. He wrote about his dream in great detail and handed over to the teacher. Two days later he received his paper back. On the front was a large red F, which meant ‘fail’, with a note that read, “See me after class.” Ravi with his dream went to see the teacher and asked, “Why did I fail?” The teacher said, “This is an unrealistic dream for a young boy like you. You have no money. You come from a poor family. You have no resources. Owning a college requires a lot of money. You have to buy the land, erect giant buildings and above all, you have to pay a huge amount for the teachers every month. There is no way you could ever do it.” Then the teacher added, “If you would rewrite this paper with a more realistic goal, I will reconsider your grade.”

 

The boy went home and thought about it long and hard. He asked his father what he should do. His father said, “Look, son, you have to make up your own mind on this. However, I think it is a very important decision for you.” “Finally, after sitting with it for a week, the boy turned in the same paper, making no changes at all. He stated, “You can keep the ‘F’ and I will keep my dream.” He still has the school paper framed safe on the wall and the mind.

 

  1. Ravi was selfish
  2. The Assignment changed his life
  3. Ravi belonged to a rich family
  4. Teacher discouraged Ravi
  5. Ravi loved his father
  6. Ravi rewrote the assignment
  7. Teacher scolded Ravi
  8. Ravi forgot the past
  9. Grade mattered much to Ravi
  10. The assignment is still with Ravi

 

 

IV Five stories are given. Neither title nor space is given for each story. Read them carefully and write appropriate titles for the five stories. In addition, read the following questions and write the answers.

[Title: 5 x 1 = 5 marks]

The five anecdotes

George Washington shocked his general one morning by merely being a gentleman. It seems Washington and his general were talking   together when a slave   passed.  “The coloured man paused, tipped his hat and said, “Good morning, your majesty”. Immediately Washington removed his hat, bowed and answered, “Good morning to you and I hope you have a pleasant day.” After a moment of shocked silence, the general asked, “Why did you bow to a slave?” Washington smiled and replied, “I would not allow him to be a better gentleman than I.” Oscar Wilde once passed by a flower shop. He asked the flower girl to pack all the flowers for him. She thought that he was a rich costumer on his way to some grand wedding! As he paid the bill the overjoyed flower seller asked him where she should deliver the basket. “Throw them away. Their faded look bleeds my sensitive heart.” So saying he went on his way. A disciple said to Mohammed, “Master, my six brothers are all asleep, and I alone have remained awake to worship Allah.” Mohammed replied, “And you too had better been asleep, if your worship of Allah consists of accusation against your brethren.” A boy was flying a kite with his father and asked him what kept the kite up. Dad replied, “The string.” The boy said, “Dad, it is the string that is holding the kite down.” The father asked his son to watch as he broke the string. Guess what happened to the kite? It came down. A boy was drowning in a river and he shouted for help. A man passing by jumped in the river and saved the boy’s life. As the man was leaving the boy said, Thank-you.” The man asked, “For what?” The boy replied, “For saving my life.” The man looked into the boy’s eyes and said, “Make sure when you grow up that your life was worth saving.”

 [Questions: 5 x 3 = 15 marks]

  1. Why was the general shocked?
  2. What comparison was made between kite and discipline?
  3. Was Mohammed happy to listen to a disciple’s complaint? Give reason/s.
  4. Comment on the nature of the man who saved the boy’s life.
  5. Why did the flower girl think that Oscar Wilde was a rich man?

 

V  Hidden is a story titled ‘Selective Listening’. Read the story and rewrite it by splitting the cluster into meaningful sentences which would become a story.                                                                                                         [1 x 14 = 14 marks]

Crab mentality

 

whatiscrabmentalitydoyouknowhowtheycatchcrabstheyplaceaboxwithonesideopenforthecrabstowalkinithasabasebutnolidwhentheboxisfulltheyclosethefourthsidethecrabscouldeasilycrawloutoftheboxandgofreebutthisdoesnthappenbecausethecrabmentalitydoesntletithappenthemomentonecrabstartscrawlinguptheotherspullitdownandnonegetsoutguesswheretheyallenduptheyallgetcooked

 

 

VI Rewrite the story in your own words. (1) Avoid the words/phrases underlined, (2) Avoid direct speech, and (3) Give another suitable title to the story.

[1 x 10 = 10 marks]

 

Genius

 

In 1914, Thomas Edison, at age 67, lost his factory. His factory was burnt to ashes. It had very little insurance. No longer a young man, Edison watched his lifetime effort go up in smoke. Even after this tragedy, he said, “There is great value in disaster. All our mistakes are burnt up. Thank God we can start anew.” In spite of the disaster, three weeks later, he invented the phonograph.

 

VII Write essays on the following in about 150 words each.

[2 x 15 = 30 marks]

  1. Write your opinion on the reservation policy in education.
  2. Write your impression on ‘Soccer Fever”

 

 

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Loyola College Supplementary English April 2006 Literary Criticism Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006

M.A. DEGREE EXAMINATION

                                                 EL 4801/EL 4808 – LITERARY CRITICISM

 

 

 

Date & Time : 28/06/2006/9.00 – 12.00        Dept. No.                                                       Max. : 100 Marks

 

 

Part A.

Write short notes on five of the following key terms/concepts choosing not less than two from each section:                                                              (5×8=40 marks)

Section-1.

  1. Definitions of Romanticism and Classicism
  2. Eliot an concept of Tradition
  3. “Close Reading” in New Criticism
  4. Socialist Realism.

Section-2.

  1. Pragmatic theories
  2. Two motivating wishes of fantasizing
  3. Limitations of structural analysis
  4. ‘Objectivity’ in fiction.

Part-B.

 

Answer the following questions in about 300 words each:                (2×20=40marks)

  1. a) The uniqueness of Structuralist literary criticism according to Barthes

Or

  1. Attempt a critique of Derrida’s Deconstruction.

 

  1. a) Write an essay oh the central pattern of Tragic and comic vision in
    Literature

Or

  1. Cull out the features of Richards’ Theory of Meaning.

 

PART-C

III. Attempt a practical criticism of the following poem employing the critical theories and tools at your disposal. ( 20 marks)

THE PAINTER MUNCH

The painter caught the dumb mouth,

Fixed wide, in a man out walking

Down a road. One moment past,

Pleasantly, he was musing,

With the sun shining south

Behind him. Air and hill

Were drawn together

In blue and green paste

When the painted mouth is stilled .

Afflicted by knottier

Pigment, the eye, off-guard,

Suffers and goes mad,

In rigor mortis.

Shirley Lim

 

 

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Loyola College Supplementary English April 2006 Power Communication In English Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006

B.A. DEGREE EXAMINATION

                                        EL 2062 – POWER COMMUNICATION IN ENGLISH

 

 

 

Date & Time : 28/06/2006/9.00 – 12.00        Dept. No.                                                          Max. : 75 Marks

 

 

Answer the following questions:

  1. Identify the elements and various types of communication. (10 marks)
  2. What are the various communication factors and skills necessary for communicating effectively? (10 marks)
  3. Draft a speech on the following topic with an arresting introduction, relevant elaboration with four main points and an apt conclusion.

“The Media has no right to offend religious sentiments claiming the right to free speech”.           (15 marks)

  1. Why should every good speaker know about audience psychology? How does it help him/her?  (10 marks)
  2. What are the factors that contribute to Group-worthiness? (10 marks)
  3. Why is listening difficult for most of us? Elaborate on the importance of listening skills for success in a group discussion.                                                                       (10 marks)
  4. List out the decisive factors for success in a job interview. (10 marks)

 

 

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Loyola College Supplementary Mathematics April 2006 Measure And Integration Question Paper PDF Download

 

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006 M.Sc. DEGREE EXAMINATIONMT 2801 – MEASURE AND INTEGRATION
Date & Time : 27/06/2006/9.00 – 12.00 Dept. No. Max. : 100 Marks
ANSWER ALL :-                                                                                                                                                    MARKSI      a  (1)  Define outer measure and show that it is translation invariant (8)                                      (OR)
(2)  State and prove countable sub additive theorem for outer measures.
b  (1)   Prove that there exists a non measurable set                                                                 (17)                                                                                                                               (OR)
(2)   Show that the following statements are equivalent for a set E :                (i)     E is measurable(i)      0 , G an open set ,G  E, such that m(G – E)  , (ii)     G, Gδ  -set, G  E, such that m (G – E) = 0(iii)      0 , F a closed set, F  E, such that m (E – F)   ,(iv)     F, an Fσ–set, F  E, such that m (E – F) = 0 .
II.  a.   (1)   If  is a measurable simple function ,then in the usual notations prove                            (8)  (i)    dx =  aį  m ( A      0 for any measurable set E.
(ii)      dx =   dx +   dx for any disjoint measurable sets A and B.
(iii)      a  dx  = a   dx if a  0.
(OR)
(2)    Let f and g be non negative measurable functions.Then prove                                                             f dx +   g dx =  (f  + g) dx

b.   (1)    State and prove Fatou’s Lemma  for measurable functions                                         (17)                                                                                                        (OR)
(2)     Show that if f  is a non negative  measurable function., then  a sequence               of measurable simple functions such that  (x)     f (x) .                                                                                                                    III   a   (1)   Show that with a usual notations the outer measure  on H(),and the                        (8)           outer measure defined   by  on S(   and  on S  are the same.
(OR)
(2)    Let ‘s’ be a non negative measurable simple function defined on a measure  space                          (X, S ,   ) Define  (E)  =   s d then  is a measure on  (X, S )  and if ‘t’  is another                non negative measurable simple function defined on a measure space              (X, S,  )  then prove that    (s + t) d =  s d +   t d  .                                                                              .                                                               b  (1)     State and prove Holder’s’s inequality for convex functions                                              (17)
(OR)
(2)   (i)   State and prove Jensen’s inequality for convex functions       (8+9)
(ii)  If f, g LP (, are complex numbers then  prove that,
(fg)   LP (  and    (fg)  d =   f d +   g d                                                                                                                               IV.  a  (1)  Show that if  be a sequence of sets in a ring  R then there exisists                      a sequence    of  disjoint sets of  R such that    Bi    Ai for each i and                       A  =    B   for each N ,so that    A i =    Bi  .                                                                        (OR)
(2)   State and prove ‘Egorov’s theorem for almost uniform convergence.
b.       (1)   State and prove ‘Completeness theorem’ for convergence in measure.                            (17)                       .                                                                                                                                                                   (OR)
(2)      (i)    State and prove  Reisz-Fisher’s theorem                                                                   (8+9)
(ii)   State and prove Jordan’s lemma.

 

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Loyola College Supplementary English April 2006 British Literature (1670 – 1832) Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006

M.A. DEGREE EXAMINATION

                                    EL 3805/EL 3800 – BRITISH LITERATURE (1670 – 1832)

 

 

 

Date & Time : 27/06/2006/9.00 – 12.00        Dept. No.                                                       Max. : 100 Marks

Part – A

  1. Interpret the following lines in about 50 words each. (10 x 2 = 20 marks)
  1. Though round his breast the rolling clouds are spread Eternal sunshine settles on his head.
  2. The song began from Jove
  3. In tasks so bold, can little men engage
    And in soft bosoms dwells such mighty rage?
  4. The paths of glory lead but to the grave
  5. So twice five miles of fertile ground
    With walls and towers were girdled round:
  6. “I love everything that’s old: old friends, old manners, old looks…  Comment on the attitude of the speaker.
  7. The greatness of hear is not in corporal dimension, but in intellect.  Explain.
  8. I reverence theses young Africans of our own growth.  Explain the metaphor.
  9. Spirits and fairies cannot be represented… only be believed.  Comment.
  10. … and immediately awaking I found myself seated … with the faithful Bridget unchanged by my side.  Explain the autobiographical element.

Part – B

  1. Write paragraph answers to any FIVE of the following in about 150 – 200 words each. (5 x 8 = 40 marks)
  1. Show how in the final analysis, the little black boy is in a better position than his white counterpart.
  2. What are the various blessings of the evening according to Collius?
  3. What is tale and the message connected up with ‘The Castaway’?
  4. How does Jane Austen employ various types of love in pride and prejudice?
  5. Write a short note on Johnson’s views on Milton’s epics.
  6. How does Dryden establish Chancer as the father of English Poetry in Preface to Fables?
  7. Write a short note on two themes swift develops in Gulliver’s Travels.

Part – C

III. Answer the following in about 350 – 400 words each.                        (2 x 20 = 40 marks)

  1. How does Trinothens influence Alexander the great by the powr of his music?

(or)

  1. Bring out the most impressive features which make ‘The School for Scndal’ a very successful play.
  2. Tintern Abbey traces the evolution of Wordsworth as a poet. – Illustrate.

(or)

  1. She stoops to conquer is a play about Appearance and Reality – Elucidate.

 

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