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Note: Except for the following questions, all the remaining questions have been asked in Set-I D.B., 2006.

SECTION - B

(ADVANCED WRITING SKILLS)

Q. 3. You plan to sell your old car. Draft a suitable advertisement in not more than 50 words to be inserted in areputed national daily giving all necessary details of the car. (5)

Or

Repeated earthquakes in India and elsewhere have resulted in unprecedented dam age and destruction to bothlife and property. Educating people on the precautions to be taken is the need of the hour Prepare a poster, innot more than 50 words, for creating this awareness

Q. 4. You are Seetha/Surya living in Bangalore You and your friends are planning a week long holiday You come

across the following advertisement Select a destination of your choice Write a letter making necessary enquiriesfrom the tour operator before you make your final decision. (10)

Or

A leading news channel recently gave a live coverage of some young slum dwellers being beaten up mercilesslyby the police for crimes not committed by them. Such atrocities shake the very faith of people. Write a letter to theCommissioner of Police urging him to adopt effective measures to curb such brutality against innocent people.You are Nita/ Nitesh, a resident of Guwahati.

Q. 5. There were many vacant spaces in your colony which were lying unattended and uncared for. You and yourfriends decided to beautify and develop those areas into green parks or playgrounds for the benefit of all. Withpractically no money but lots of enthusiasm of the children of the colony, your project became a roaring success.It has now even caught media attention. You have been approached by a local newspaper to share your successstory. Write a brief report in 100 - 125 words on how you organized the entire project. You are Neha/Nitin, aresident of Chandigarh. (10)

Or

In order to promote book reading habit amongst school children, your school organ ized a Book Week. Duringthis week a number of exciting activities including interaction sessions with eminent authors took place As HeadBoy! Head Girl of the school you were actively involved in making all the arrangements. Write a report in 100 -125 words. You are Manju/Mihir, a resident of Chennai.

Q. 6. Indian TV is doing a great service to the general public Write an article giving your views on the above topicin 150 - 200 words for a leading magazine. You are Arth/Arti, a citizen of Patna. (10)

Or

A recent survey showed that there are still many communities in India which do not welcome the birth of a girlchild. Can a country which does not give equal rights to all its citizens ever dream of becoming great? Write anarticle in 150 - 200 words giving your views on the above subject and the steps we should take to solve thisproblem. You are Simran/Yusuf, a citizen of Hyderabad.

SECTION - C

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(LITERATURE)

Q. 7.

a. Read the extract given below and answer the questions that follow: (4)

Had he and I but metBy some Old ancient inn,We should have sat us down to wetRight many a nipperkin !

i. Who are the two characters in the above lines referred to as he and I (1) ii. What is the significance of the line, Had he and I but met...? (2) iii. What does a nipperkin mean? (1)

Or

One day there fell in great Benares temple-court

A wondrous plate of gold, whereon these words were writ;To him who loveth best a gift from Heaven

iv. Where did the plate of gold faIl (1) v. What was written on it (1) vi. What message does the poet give through this poem? (2)

b. Answer the following questions in 30 - 40 words each: (3 x 2 = 6)i. What, according to Tagore, has the burden of ages done to our motherland?ii. Why does Ben Jonson call the lily a flower of light?iii. Wordsworths he art was filled with wonder and sadness at the same time when he was

reclining under a tree What made him think SO

Q. 8. Answer the following questions in 30- 40 words each: (5 x 2 = 10)

a. As she was going out she asked the cashier in a low voice, Is that gentle man an Indian? Why didMaggie ask this question?

b. How do machines deprive us of two important ingredients of happiness?c. The Brahmo Samaj movement for emancipation of women has been de scribed as a false dawn. Why?d. What is Muellers view about t he study of Sanskrit?e. What objection did Lady Bracknell have in giving her consent to Gwendolens wedding with Mr.

Worthing?

Q. 9. Answer the following in 125 - 150 words: (10) A confinement in Andaman Islands was worse than a death sentence. Explain.

Or

There is light at the end of the tunnel but oniy for those who see it. Bring out the relevance of this statement bytaking examples from the story, A Man Who Had No Eyes.

Q. 10. Answer the following in 125 - 150 words: (7)

The writer says that, truth is vastly stranger than fiction. Do you agree? Explain with reference to the story, TheFace on the Wall.

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Or

Mrs. Wang wins our sympathy and admiration through her wisdom and simplicity. Explain the truth of thisstatement with examples from the story, The Old Demon.

Q. 11. Answer the following in30 - 40 words each: (4 x 2 = 8)

i. Each one of us misses out on some success or happiness , says Dr. Stromer. What is the point hewants to make?

ii. At one point in the play, Baldwin says, ...never thought this day would come. What is he referring to?iii. The winner of the, bet eventually did not collect his bet money. Why? When the glass kept near the wall

of the compartment was vibrating, Barin became almost paralyzed with fear. Why?

General Instructions: See in the Set - I , O.D., 2006.

Note: Except for the following questions, all the remaining questions have been asked in Set - I O.D., 2006.

SECTION - B

(ADVANCED WRITING SKILLS)

Q. 6. Water is very precious. Some scientists even go to the extent of saying that the third world war may befought on the issue of water. Keeping in view the need for saving each drop of water, write an article in 150 - 200words. You are Natasha / Rohan, a resident of Lucknow. (10)

Or

Television is termed as an idiot box in many countries. Keeping in view this opinion, write an article in 150 - 200words, showing the influence of T.V. on young minds. You are Susan / John, a resident of Mumbai.

SECTION - C

(LITERATURE)

Q. 7. (b) Answer the following questions in 30-40 words each: (3 x 2 = 6)

i. What, according to Tagore, has the burden of ages done to our motherlandii. What is the central idea of the poem, Written in Early Spring?iii. The poem, Once upon a Time, is a satire on modern life. Explain how.

Q. 8. Answer the following questions in 30 - 40 words each: (5 x 2 = 10)

a. Markwardts blindness fails to evoke the readers sympathy. Why?b. What were some of the doubts that Gandhiji initially had about womens ability to play a proactive role in

the national movement. How did the women surprise him?c. What is Muellers view about the study of Sanskrit?d. The prevention of destitution (poverty) does not entirely depend upon machines. Do you agree?e. Why did Lady Bracknell advise Mr. Worthing to produce one parent ol either sex before the season was

over?

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Q. 9. Answer the following in 125 - 150 words: (10)How does the author describe the Jailor of the Silver Jail?

Or

Maggie was an ordinary girl with extraordinary qualities. Discuss.

General Instructions: See in the Set - I , O.D., 2006.

Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set Il, O.D.,2006.

SECTION - B

(ADVANCED WRITING SKILLS)

Q. 5. Keeping in view the frequent occurrence of earthquakes in the country, your school arranged a talk ondisaster management. Identifying the areas of your state most prone to earthquakes, the speaker explained theprecautionary measures to be taken by the public and the government in case of emergency. As a studentreporter, Ravi / Rani, send a report of the event, in 100 - 125 words, to a national daily. (10)

Or

Your school celebrated a green week in which a number of programmes including the plantation of trees, guestlectures on environment, nukkad nataks (street plays) etc. were organized. Write a report in 100 125 words for anational daily, for creating awareness. You are Roshan/Rachna, Secretary, Youth Club of your school.

SECTION - C

(LITERATURE)

Q. 7. (b) Answer the following questions in 30-40 words each: (3 x 2 = 6)

i. What, according to Tagore, has the burden of ages done to our motherland?ii. Why did Wordsworth suddenly become sad though he was in a sweet mood?iii. Modern society has double standards. How does the poet bring out this idea through his poem, Once

upon a Time?

Q. 8. Answer the following questions in 30 -40 words each: (5 x 2 = 10)

a. Markwardts blindness fails to evoke the readers sympathy. Why?b. What were some of the doubts that Gandhiji initially had about womens ability to play a proactive role in

the national movement? How did the women surprise him?c. According to Max Mueller, what happened to a hundred and seventy two gold coins found on the bank

of a river?d. A machine is like a Djinn in the Arabian Nights. Do you agree?e. Why did Jack invent Earnest?

Q. 9. Answer the following in 125 - 150 words: (10)

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Describe the train journey of the convicts to Calcutta.

Or

Describe the character of Maggie.

Mathematics 2006 (Set I Outside Delhi)

SECTION A

Q. 1. Express the matrix as the sum of a symmetric and a skew-symmetric matrix.

Q. 2 . Using properties of determinants, prove the following:

Q. 3. Solve the following differentia equation:

Q. 4. Verify that is solution of the differential equation

Or

Solve the following differential equation:

Q. 5.

Or

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Q. 6.

Q. 7. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find theprobability distribution of number of jacks.

Q. 8. A and B toss a coin alternately till one of them gets a head and wins the game. If A starts first, find theprobability that B will win the game.

Q. 9. Shove that the following argument is in valid:

Or

Construct an input/output table for the following circuit:

Q. 10.

Q. 11. Differentiate w. r. t. x from first principle.

Q. 12.

Or

Q. 13.

Q. 14.

Q. 15. Find the intervals in which the function f (x) = x 3 - 12x 2 + 36x + 17 is (a) increasing, (b) decreasing.

Q. 16. Using matrices, solve the following system of equations:

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Q. 17. An open box, with a square base, is to be made out of a given quantity of metal sheet of area C2

. Show

that the maximum volume of the box is

Or

A window is in the form of a rectangle surmounted by a semi-circle. If the total perimeter of the window is3O m,find the dimensions of the window so that maximum light is admitted.

Q. 18. Find the area of the region bounded by the parabola x 2 = 4y and the line x = 4y 2.

Or

SECTION B

Q. 19. Find the angle between the vectors

Q. 20. Using vectors, prove that in a

where a, b and c are lengths of the sides opposite, respectively, to the angles A, B and C of

Q. 21. Find the coordinates of the point where the line

meets the plane x + y + 4z = 6.

Q. 22. Find the image of the point (1, 2, 3) in the plane x + 2y + 4z = 38.

Q. 23. Find the radius of the circular section of sphere by the plane .

Q. 24. The resultant of two forces acting at an angle is equal to and when

they act an angle , the resultant is equal to , Show that

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Q. 25. A body of mass 10 kg hags by a string from a fixed point. The string is drawn out of the vertical by applyinga force 49 N to the body. In which direction should this force be applied in order that, in equilibrium, the deflectionof the string from the vertical may be of 300? Also find the tension in the string.

Q. 26. A particle is projected so as to graze the tops of two walls, each of height 10m, at distances 15 m and 45

m respectively from the point of projection. Find the angle of projection.

SECTION C

Q. 19. In a bolt factory, machines A, B, C manufacture 25%, 35% and 40% respectively of the total bolts. Of theiroutput 5%, 4% and 2% respectively are defective bolts. A bolt is drawn at random and is found to be defective.Find the probability that it is manufactured by machine B.

Q. 20. The mean and variance of the binomial distribution are 4 and 4/3 respectively. Find the distribution and

Q. 21. The bankers discount and bankers gain on a certain bill of exchange, due after a certain time, are

respectively Rs.1,250 and Rs.50. Find the face value of the bill.

Q. 22. A bill for Rs.5,050 is drawn on April 13, 2005. It is discounted on July 4,2005 at 5% per annum. If thebankers gain in the transaction is Rs. 0.50 find the nominal date of maturity of the bill.

Q. 23. A machine costs a company Rs 5,75,000 and its effective life is estimated to be 20 years. A sinking fund iscreated for replacing the machine at the end of its life-time when its scrap realises a sum of Rs.75,000 only.Calculate what amount should be provided every year out of profits, for the sinking fund if it accumulates aninterest of 5% per annum, compounded annually. [Use(1.05)20 = 2.6551]

Q. 24. A and B are partners sharing profits and losses in the ratio 5 : 3. C pays Rs.96,000 as premium for the

goodwill of the business and is admitted for 1/5th share. Show how this amount will be shared by A and B,assuming that the share of C is contributed by A and B in their profit sharing ratio. Find also the new profitsharing ratio.

Q. 25. The manufacturing cost of an item consists of Rs. 900 as overheads, the material costs Rs.3 per item andIabour cost is x 2 /100 for x items produced. How many items must be produced to have minimum average cost?

Q. 26. David wants to invest at most Rs. 12,000 in bonds A and B. According to the rule, he has to invest at leastRs. 2,000 in Bond A and at least Rs.4,000 in Bond B. If the rates of interest on Bonds A and B respectively are8% and 10% per annum, formulate the problem as L.P.P. and solve it graphically for maximum interest. Alsodetermine the maximum interest received in a year.

Mathematics 2006 (Set II Outside Delhi)

SECFION A

Q. 1.

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Q. 2. If a, b, c, are in A.P. show the following:

Q. 3. Solve the following differential equation:

Q. 4.

Q. 9. Differentiate from first principle.

Q. 10.

Q. 11. Verify Rolles Theorem for the following function:

Q. 18. Using matrices, solve the following sys tem of equations:

Mathematics 2006 (Set III Outside Delhi)

SECTION A

Q. 1. If , find the values of a and b such that A 2 + Aa + bi = 0. Hence find A -1.

Q. 2. Using properties of determinants, prove the following:

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Q. 3. Solve the following differential equation:

Q. 4.

Q. 9. Differentiate from first principle.

Q. 10.

Q. 11. Verify Lagranges Mean Value Theorem for the following:

Q. 17. Using matrices, solve the following system of equations:

Physics 2006 (Set I Outside Delhi)

Q. 1. Define the term electric dipole moment. Is it a scalar or a vector quantity? 1

Q. 2. The variation of potential difference V with length I in case of two potentiometers P and Q is as shown.Which one of these two will you prefer for comparing emfs of two primary cells. 1

Q. 3. de Brogue wavelength associated with an electron accelerated through a potential difference .What will be its wavelength when the accelerating potential is increased to 4 V?

Q. 4. Give any one difference between FAX and e-mail systems of communication. 1

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Q. 5. Steel is preferred for making permanent magnets whereas soft iron is preferred for making electromagnets.Give one reason. 1

Q. 6. You are given a resistors, each of resistance r. These are first connected to get minimum possibleresistance. In the second case, these are again connected differently to get maximum possible resistance.

Compute the ratio between the minimum and maximum values of resistance so obtained. 2

Q. 7. Two capacitors of capacitance of are connected in series with a battery. The voltage

across the capacitor is 2 V. Compute the total battery voltage. 2

Or

A parallel plate capacitor with air between the plates has a capacitance of 8 pF. The separation between thepates is now reduced by half and the space between them is filled with a medium of dielectric constant 5.Calculate the value of capacitance of the capacitor in the second case. 2

Q. 8. Draw a labelled ray diagram to show the image formation in a refracting type astronomical telescope. Whyshould the diameter of the objective of a telescope belarge?

Q. 9. Draw a circuit diagram using a metre bridge and write the necessary mathematical relation used todetermine the value of an unknown resistance. Why cannot such an arrangement be used for measuring very lowresistances? 2

Q. 10. Which one of the two, an ammeter or a milliammeter, has a higher resistance and why? 2

Q. 11. An alternating voltage of frequency f is applied across a series LCR circuit. Let f r be the resonance

frequency for the circuit. Will the current in the circuit lag, lead or remain in phase with the applied voltage when(i) (ii) Explain your answer in each case. 2

Q. 12. A point charge q is placed at O as shown in the figure.

Q. 13. Using Gausss theorem, show mathematically that for any point outside the shell, the field due to auniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the centre.

Why do you expect the electric field inside the shell to be zero according to this theorem? 3

Q. 14. Distinguish between frequency modulation and amplitude modulation. Why is an FM signal lesssusceptible to noise than an AM signal? 3

Q. 15. Write the order of frequency range and one use of each of the following electromagnetic radiations. 3

(i) Microwaves(ii) Ultra-violet rays(iii) Gamma rays

Q. 16. Sketch a graph between frequency of incident radiations and stopping potential for a given photosensitivematerial. What information can be obtained from the value of the intercept on the potential axis?

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A source of light of frequency greater than the threshold frequency is placed at a distance of 1 m from thecathode of a photo-cell. The stopping potential is found to be V. If the distance of the light source from thecathode is reduced, explain giving reasons, what change will you observe in the

(i) photoelectric current,

(ii) stopping potential. 3

Q. 17. Define the terms half-life period and decay constant of a radioactive substance. Write their S.I. units.Establish the relationship between the two. 3

Q. 18. A neutron is absorbed by a nucleus with the subsequent emission of an alpha particle.

(i) Write the corresponding nuclear reaction.(ii) Calculate the energy released, in MeV, in this reaction. 3

Q. 19. When an inductor L and a resistor R in series are connected across a 12 V, 50Hz supply, a current of 0.5

A flows in the circuit. The current differs in phase from applied voltage by radian. Calculate the value of R.3

Or

A 0.5 long metal rod PQ completes the circuit as shown in the figure. The area of the circuit is perpendicular tothe magnetic field of flux density 0.15 T. If the resistance of the total circuit is , calculate the force needed tomove the rod in the direction as indicated with a constant speed of 2 ms -1.

Q. 20. State Faradays laws of electrolysis. Express these in mathematical notation. Name any two applicationsof electrolysis. 3

Q. 21. What are eddy currents. How are these produced? in what sense are eddy currents consideredundesirable in a transformer and how are these reduced in such a device? 3

Q. 22. A beam of light converges to a point P. A lens is placed in the path of the convergent beam 12 cm from P.At what point does the beam converge if the lens is

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(i) a convex lens of focal length 20 cm,(ii) a concave lens of focal length 16 cm ? 3 Do the required calculations.

Q. 23. Consider an optical communication system operating at nm. Suppose, only 1% of the optical

source frequency is the available channel band-width for optical communication. How many channels can beaccommodated for transmit ting

(a) audio-signals requiring a band-width of 8 kHz,(b) video TV signals requiring an approximate band-width of 4.5 MHz? Support your answer with suitablecalculations. 3

Q. 24. Explain (I) forward biasing, (ii) reverse biasing of a P-N junction diode. With the help of a circuit diagram,explain the use of this device as a half - wave rectifier. 3

Q. 25. Draw a neat and labelled diagram of a cyclotron. State the underlying principle and explain how a

positively charged particle gets accelerated in this ma chine. Show mathematically that the cyclotron frequencydoes not depend upon the speed of the particle. 5

Or

State the Biot - Savart law for the magnetic field due to a current carrying element. Use this law to obtain aformula for magnetic field at the centre of a circular loop of radius R carrying a steady current I. Sketch themagnetic field lines for a current loop clearly indicating the direction of the field. 5

Q. 26. What are coherent sources of light? State two conditions for two light sources to be coherent.Derive a mathematical expression for the width of interference fringes obtained in Youngs double slit experimentwith the help of a suitable diagram. 5

Or

State Huygens principle. Using the geometrical construction of secondary wave - lets, explain the refraction of aplane wave front incident at a plane surface. Hence verify Snells law of refraction. Illustrate with the help of diagrams the action of (i) convex lens and (ii) concave mirror on a plane wave frontincident on it. 5

Q. 27. What are energy bands? How are these formed? Distinguish between a conductor, an insulator and asemiconductor on the basis of energy band diagram. 5

Or

Explain the function of base region of a transistor. Why is this region made thin and lightly doped?Draw a circuit diagram to study the input and output characteristics of n-p-n transistor in a common emitter (CE)configuration. Show these characteristics graphically. Explain how current amplification factor of the transistor iscalculated using output characteristics. 5

Physics 2006 (Set I Compartment Outside Delhi)

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Q. 1. Write two properties of a material used as a suspension wire in a moving coil glvanometer. 1

Q. 2. Name the experiment which establishes the wave nature of a particle. 1

Q. 3. Write the S.I. unit for the activity of a radoactive nuclide. 1

Q. 4. The a.c. current gain of a transistor is 120. What is the change in the collector current in the transistor

whose base current changes by 1

Q. 5 . Name the underlying principle of the working of an optical fibre. 1

Q. 6. Define dielectric constant of a medium. Briefly explain why the capacitance of a parallel plate capacitorincreases, oii introducing a dielectric medium between the plates. 2

Q. 7. Why does a paramagnetic substance display greater magnetisation for the same magnetising field whencooled? How does a diamagnetic substance respond to similar temperature changes? 2

Q. 8. Explain how electron mobility changes for a good conductor when (i) the temperature of the conductor isdecreased at constant potential difference and (ii) applied potential difference is doubled at constant temperature.2

Q. 9. A capacitor and a resistor are connected in series with an a.c. source. If the potential difference across C, Rare 120 V, 90 V rspectively and if the r.m.s. current of the circuit is 3 A, calculate the (i) impedance, (ii) powerfactor of the circuit. 2

Or

An inductor 200 mH, a capacitor C and a resistor 10 ohm are connected in series with a 100 V, 50 s -1 a.c. source.If the current and voltage arc in phase with each other, calculate the capacitance of the capacitor.

Q. 10. Draw the curve showing variation of binding energy/nucleon with mass number of different nuclei. Brieflystate, how nuclear fusion and nuclear fission can be explained on the basis of this graph. 2

Q. 11. Give r for the following:

(a) Rainbow is never observed on the surface of the Moon.(b) The Sun looks reddish at sunrise and sunset as viewed from Earth.

Q. 12 . The following figure shows the input waveforms (A, B) and the output waveform (Y) of a gate. Identify thegate and write its truth table. 2

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Q. 13 . What are eddy currents? How are these minimised? Mention two applications of eddy currents. 3

Q. 14. Draw the graphs showing the variation of photoelectric current with an ode potential of a photocell for (i)the same frequencies but different intensities I 1 > I2 > I3, of incident radiation, (ii) the same intensity but differentfrequencies V 1 > V2 > V3 of incident radiation.

Explain why the saturation current is independent of the anode potential. 3

Q. 15. State Faradays laws of electrolysis. Deduce the relation connecting Faraday constant, chemicalequivalent and electrochemical equivalent. 3

Q. 16. 4 cells of identical emf E, internal resistance r, are connected in series to a variable resistor. The followinggraph shows the variation of terminal voltage of the combination with the current output:

(i) What is the emf of each cell used?(ii) For what current from the cells, does maximum power dissipation occur in the circuit?(iii) Calculate the internal resistance of each cell. 3

Q. 17 . What is pulse modulation? Distinguish between pulse amplitude modulation and pulse duration modulationby drawing suitable modulated signals. 3

Q. 18. Write any two criteria required for a detector of an optical communication system.A photo-detector is made from a semiconductor having E g = 0.73 eV. What is the maximum wavelength which itcan detect? 3

Q. 19. Using Gauss theorem, deduce an expression for the electric field intensity at any point due to a thin,

infinitely long wire of charge/length 3

Or

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Using Gauss theorem, derive an expression for the electric field intensity at any point outside a charged

spherical shell of radius R and of charge density

Q. 20. A metallic square loop ABCD of size 15 cm and resistance is moved at a uniform velocity of v m/s,

in a uniform magnetic field of 2 Tesla, the field lines being normal to the plane of the paper. The loop isconnected to an electrical network of resistors, each of resistance Calculate the speed of the loop, forwhich 2 m A current flows in the loop.

Q. 21. Sketch a graph showing the variation of potential energy of a pair of nucleons as a function of theirseparation.Write three characteristic properties of nuclear force which distinguish it from the electrostatic force. 3

Q. 22. Explain, using Huygen principle, how diffraction is produced by a narrow slit which is illuminated by amonochromatic light.Show that central maximum is twice as wide as the other maxima and the pattern becomes narrower as the widthof the slit is increased. 3

Q. 23. Draw a labelled diagram o the experimental set-up used by Hertz to produce electromagnetic waves.

Explain how the electromagnetic waves are detected. 3

Q. 24. Define the term electric potential due to a point charge.

Calculate the electric potential at the centre of a square of side having charges

at the four corners of the square. 3

Q. 25. Derive an expression for the magnetic field along the axis of an air- cored solenoid, using Amperescircuital law.Sketch the magnetic field lines for a finite solenoid. Explain why the field at the exterior mid-point is weak while atthe interior it is uniform and strong. 5

Or

Explain with the help of a labelled diagram the working principle of a cyclotron.Show that the cyclotron frequency does not depend on the speed of the particle. Write one of the uses and pointout one of the drawbacks of a cyclotron.

Q. 26. Draw a labelled circuit diagram of a transistor oscillator. Briefly explain its principle and state how theoscillations are sustained. 5

Or

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Q. 10. Differentiate between conformation and configuration in open chain molecules by giving one exampleeach. (2)

Q. 11. Give reasons for the following:

a. Ortho-nitrophenol is more acidic than ortho-methoxyphenol. (1) b. Glycerol is used in cosmetics. (1)

Q. 12. Write the structures of monomoers used and one use of each of the following polymers: (1)

a. Teflonb. Buna-N

Or

What are biodegradale polymers? Give two examples.

Q. 13. What is meant by dual nature of electrons? Calculate the energy and wavelength of the photon emitted byhydrogen atom when the electron makes a transition from n =2 to n = 1. Given that the ionization potential is 13.6eV.[1 eV =1.6 x 10 19 J]

Q. 14. Calculate the distance between Na + and Cl ions in NaCl crystal if its density is 2.165 g cm -3. [ Molar massof NaCl= 58.5 g mole -1; NA = 6.02 x 10 23 moI -1] (3)

Q. 15.

a. Urea forms an ideal solution in water. Determine the vapour pressure of an aqueous solution containing10% by mass of urea at 40C.(Vapour pressure of water at 40C = 55.3 mm of Hg) (2)

b. Why is freezing point depression of 0.1 M sodium chloride solution nearly twice that of 0.1 M glucosesolution? (1)

Q. 16. How is the concept of coupling reactions useful in explaining the occurrence of non-spontaneousthermochemical reactions? Explain giving an example. (3)

Q. 17. A certain reaction is 50% complete in 20 minutes at 300 K and the same reaction is again 50% completein 5 minutes at 350 K. Calculate the activation energy. if it is a first order reaction. [R = 8.314 JK -1 mol -1; log 4 =0.602] (3)

Q. 18.

a. In which of the following does adsorption take place and why? (1) i. Silica gel placed in the atmosphere saturated with water.ii. Anhydrous CaCl 2 placed in the atmosphere saturated with water.

b. How does BF 3 act as a catalyst in industrial process? (1) c. Give an example of shape-selective catalysis. (1)

Or

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a. What are micelles? How do they differ from ordinary colloidal particles? Give two examples of micellesforming substances. (2)

b. State Hardy-Schulze rule. (1)

Q. 19.

a. Write the electronic configuration of the element with atomic number 102. (1) b. What is lanthanoid contraction? What is its effect on the chemistry of the elements which follow the

lanthanoids? (2)

Q. 20.

a. Using valence bond theory, predict the shape and magnetic character of [Ni (CO) 4]. [Ni = 28] (2) b. Give one example of application of coordination compounds in medicine. (1)

Q. 21.

a. State Group Displacement Law. Calculate the numb er of - particles and -- particles emitted when

(2) b. What is meant by K-capture in nuclear chemistry? (1)

Q. 22.

a. Write the steps and conditions involved in the following conversions:i. Acetophenone to 2-phenyl-2butanol (1) ii. Propene to acetone. (1)

b. Give a chemical test to distinguish between Methyl acetate and Ethyl acetate.

Q. 23.

a. Explain the following giving suitable examples: (2) i. Sandmeyers reactionii. Coupling reaction of a diazonium salt

b. Explain the observed K b order:Et2NH > ET 3N > EtNH 2 in aqueous solution (1)

Q. 24. Define the following and give one example of each: (3)

a. Antipyreticsb. Vat dyesc. Antibiotics

Q. 25.

a. State two advantages of H 2 O2 fuel cell over ordinary cell. (2) b. Silver is electrodeposited on a metallic vessel of total surface area 900 cm 2 by passing a current of 0.5

amp for two hours. Calculate the thickness of silver deposited.[Given: Density of silver = 10.5 g cm -3,

Atomic mass of silver = 108 amu, F= 96,500 C mol1

] (3)

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Q. 2. What makes the crystal of KCI appear sometimes violet? (1)

Q. 3. Define activation energy of a reaction. (1)

Q. 4. Give the IUPAC name of the following compound: (1)

CH3CH (NO 2) CH 2CH 3

Q. 5. Complete the reaction equation

.

Q. 6. On what basis can you say that in an atom an s-orbital is spherical and the p-orbitals are dumb-bellshaped? (2)

Q. 7. Prove that in a process heat change at constant pressure is a measure of the change in enthalpy. (2)

Q. 8. What happens when

i. Tin dissolves in a hot alkali solution?ii. Xe0 3 reacts with an aqueous alkali solution?

Write the complete chemical equation in each case. (2)

Or

Write balanced chemical equations for the following processes

i. SiO 2 is treated with an excess of KOH.ii. Bi2O3 is treated with conc. HNO 3.

Q. 9. How is the variability in oxidation states of the tansition elements different from that of the non-transitionelements? Illustrate with examples. (2)

Q. 10. Convert the following wedge-and-dash formula to Fischer projection formula. (2)

Q.11. How are the following conversions carried out (2)

i. Propene to porpan-2-olii. Phenol to salicylaldehyde

Q. 12. Differentiate between a homopolymer and a copolymer. Give one example of each. (2)

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Q. 13. Compare the relative stability of the following species and indicate their magnetic (diamagnetic orparamagnetic) characters O 2 +, O 2 and O 2 2

Is only bond order a quantitative measure of the bond strength in a species? (3)

Or

Draw the molecular orbital diagrams for the species N 2+ and N 2-- .Comment on the magnetic property and bondstrength of each.

Q. 14. What is a semiconductor? Describe two main types of semiconductors, giving examples and theirdistinctive features (3).

Q. 15. A 0.2 per cent aqueous solution of a non-volatile solute exerts a vapour pressure of 1.004 bar at 1000 C.What is the molar mass of the solute?(Given: Vapour pressure of pure water at 100C is 1.013 bar and molar mass of water is 18 g mol 1 ) (3)

Q. 16. Calculate r Gand the equilibrium constant for the following reaction at 298 K and 1 atmospherepressure:CO (g) + 3 H 2 (g) CH 4 (g) + H 2 O (l) (Given that at 298 K r Hfor the reaction is 250.3 kJ mol --1 and f Sfor the reaction is 333.3 JK --1 and R= 8.314 J K 1 mol --1 (3)

Q. 17. At 300C the thermal dissociation of HI is 20%. What will be the equilibrium concentrations of H 2 and l 2 inthe system H 2 + l2 2Hl at this temperature if the equilibrium concentration of HI is found to be 0.96 mol L 1 ?(3)

Q.18. State what you will observe when

i. an electrolyte is added to a colloidal solution,ii. an electric current is passed through a colloidal solution,iii. a beam of light is passed across pure water and then across a colloidal solution of sulphur when you are

not in the path of light. (3)

Q.19. How would you account for the following observations: (3)

i. The enthalpies of atomisation of the transition metals are high.ii. Of the lanthanoids only Cerium (Z = 58) is known to exhibit quite stable + 4 state in solutions.iii. Sodium thiosulphate solution is us ed in the fixing step of photography.

Q. 20. Draw the structures of the following: (3)

i. Cis-dichlorotetracyanochromate (III)ii. Pentaamminenitrito-N-cobalt (III)iii. Hexamethyldialuminium

Q. 21. Write the product nucleides for the following radiaction decays: (3)

i.

ii.

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iii.(Note: You can put X for the symbol if it is not known to you).

Q. 22. How would you bring about the following conversions: (3)

i. Propanal to butanoneii. Benzaldehyde to benzophenoneiii. Benzoyl chloride to benzonitrile

Give the complete chemical equation and reaction conditions in each case.

Q. 23.

a. Explain the following observations:i. Primary amines are higher boiling than comparable tertiary amines.ii. Aromatic amines are less basic than aliphatic amines.

b. Mention two important uses of N, N-Dimethyl aniline (DMA). (3)

Q. 24. Describe the following with examples:

i. Tranquilizersii. Preservativesiii. Biliquid propellants

Q. 25.

a. State the products of electrolysis obtained on the cathode and the anode in the following casesi. A dilute solution of H

2S0

4with platinum electrodes

ii. An aqueous solution of AgNO 3 with silver electrodesb. Write the cell formulation and calculate the standard cell potential of the galvanic celL in which the

following reaction takes place:Fe 2+ (aq) + Ag + (aq) Fe 3+ (aq) + Ag (s)Calcuate f Gfor the above reaction.[Given: E Ag+ / Ag = + 0.80 V and E Fe 3+ / Fe 2+ = + 0.77 V; F = 96500 C mol 1] (2, 3)

Or

a. What are fuel cells? Write the electrode reactions of a fuel cell which uses the reaction of hydrogen with

oxygen.b. Write the cell formulation and calculate the standard cell potential of the galvanic cell which uses thefollowing reaction in its operation:2 Cr (s) + 3 Cd 2+ (aq) 2 Cr 3+ (aq) + 3 Cd (s)Calculate r G0 for the above reaction.[Given: E 0Cr3+ / Cr = 0.74 V and E 0 cd2+ / Cd = 0.40 V; F = 96500 C mol 1]

Q. 26.

a. How would you account for the following:i. Tin (II) is a stronger reducing agent than lead (II).

ii. Enthalpy of dissociation for F 2 is much less than that for Cl 2.iii. Sulphur in vapour state exhibits paramagnetism.

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b. Draw the structures of the following molecules:i. H3P0 2 ii. XeOF 4

Or

a. Explain the following observations:i. Anhydrous aluminium chloride has a lower melting point than aluminium fluorideii. Bismuth oxide is not acidic in any of its reactionsiii. HF is weaker acid than HI in aqueous solutions

b. Draw the structures of the following moleculesi. XeF 4 ii. SF 4

Q. 27.

a. Enumerate the structural differences between DNA and RNA. Write down the structure of a nucleosidewhich is present only in RNA.

b. What are reducing sugars ? Give an example each of a reducing sugar and a non-reducing sugar. (3, 2)

Or

a. Name the three classes of lipids and give one example of each class.b. Explain the term mutarotation giving an example.

Mathematics 2006 (Set I Compartment Outside Delhi)

SECTION - A

Q. 1.

Q. 2. Using properties of determinants, prove the following:

Q. 3. In a group of 9 students, there are 5 boys and 4 girls. A team of 4 students is to be selected for a quizcompetition. Find the probability that there will be 2 boys and 2 girls in that team.

Q. 4. A and B throw two dice simultaneously turn by turn. A will win if he throws a total of 5, B will win if he throwsa doublet. Find the probability that B will win the game, though A started it.

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Q. 5.

Q. 6.

Or

Q. 7. The volume of a cube is increasing at the rate of 7 cubic centimeters per second. How fast is the surfacearea of the cube increasing when the length of an edge is 12 centimeters?

Q. 8.

Or

.

Q. 9. Examine the validity of the following argument:

Or

Using Boolean algebra simplify the circuit:

Q. 10.

Or

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If (x) is continuous at x = 0, find the value of a.

Q. 11. Differentiate

Q. 12. Differentiate x sin x w.r.t. x from the first principle.

Q. 13. Find the equations of the tangent and the normal to the curvey y = x 3at the point P (1, 1).

Q. 14.

Q. 15.

Q. 16.

find AB and use this result in solving the following system of equations:

Or

Using matrices, solve the following system of linear equations:

Q. 17. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of thevolume of the sphere.

Q. 18. Using integration, find the area of the triangle ABC, the coordinates of whose vertices are A (2, 0), B (4, 5)and C (6, 3).

Or

Find the area of the region bounded by the curve y 2 = 4x, x = 1, x = 4 and the x-axis in the first quadrant.

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SECTION - B

Q. 19. If are mutually perpendicular vectors of equal magnitude, show that they are equally inclined

to the vector

Q. 20. Show that the four points A, B, C and D with position vectors

respectively are coplanar.

Q. 21. A bullet fires into a target loses half of its velocity after penetrating 3 cm. Find how much further it willpenetrate.

Q. 22. The resultant of two velocities u and v is and is v/2 at right angles to u. Prove that the ratio between u and

v is ,and the angle between a and v is 150.

Or

A bullet is fired with velocity 98 rn/sec at an angle 30to the horizontal. Find (i) the time of flight, (ii) the greatestheight attained, and (iii) the horizontal range. (Use g = 9.8 rn/sec 2)

Q. 23. A plane passes through a fixed point A (a, b, c). Show that the locus of the foot of the perpendicular from

the origin on the plane is the sphere .

Q. 24. The resultant of two forces is the same when their directions are inclined at an angle as when they are

inclined at an angle Find the value of tan .

Q. 25. In a triangle ABC, three forces acting along OA, OB, OC respectively are in equilibrium. If

O is the circumcentre of the

prove that

Or

The resultant of two like parallel forces P and Q acting at A and B, 8 cm apart, is 40 N. If the resultantpasses through C, where AC = 3 cm, find the magnitude of the forces. Also show that if the forces wereinterchanged, the resultant shifts through a distance of 2 cm.

Q. 26. 26. A sphere of radius a cm passes through the origin and meets the axes at the points A, B and C. Prove

that the locus of the centroid of the

SECTION - C

Q. 19. A bill of Rs. 15,000 due on July 13,2005 and another of Rs. 40,000 due on September 24, 2005 are both

discounted on May 1,2005. If the difference between the two discounts be Rs. 520, find the rate of discount.

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Show that the average cost and marginal cost are the same at the minimum average cost.

Physical Education 2007 (Set I Delhi)

Part - A

Qs. 1. Briefly explain the importance of wellness. (2)

Qs. 2. Write short notes on any two means of fitness development. (2)

Qs. 3. Discuss about any two principles of physical fitness development. (2)

Qs. 4. Write about the concept of interval training method. (2)

Qs. 5. Briefly explain about the importance of sociology in sports. (2)

Qs. 6. Explain the meaning and concept of training in sports. (4)

Qs. 7. Highlight the sociological aspect of physical education. (4)

Qs. 8. Describe the factors affecting physical fitness and wellness. (6)

Qs. 9. Explain the meaning of warming up and highlight its importance for good Performance in competition. (6)

Part - B

Qs. 10. What do you know about Rajiv Gandhi Khel Ratna Award? (2)

Qs. 11. Answer the following questions on the basis of any one game/sport of your choice

i. Briefly explain the historical development of the game/sport. (2) ii. Name any four famous award winning personalities of the game/sport. (2) iii. Give brief explanation of any four terminologies related with game/sport. (2) iv. Explain in detail any three skills of the game/sport. (3) v. Discuss any three skills of the game/sport. (3) vi. Explain the dimension and draw the diagram of the play field/court/table of game/sports. (6)

Part - C

Qs. 12. What do you understand by disaster preparedness? (2)

Qs. 13. Briefly explain essential elements of healthful environment. (2)

Qs. 14. Elaborate the concept of environment. (2)

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Qs. 15. Briefly explain role of parents in child care. (2)

Qs. 16. Write short notes on joint injuries and its f irst aid. (3)

Qs. 17. Discuss the needs and problems of adolescents. (3)

Qs. 18. Define the term sports injury. Explain types of soft tissue injuries and its preventive measures. (6)