CBSE sample papers 2015

1SAMPLE PAPER 2014-15ENGLISH CORE CLASS- XII

Time allowed: 3hours Maximum marks:100

SECTION A READING (30 Marks )Read the following passage carefully. (12 Marks)1.

actions and choices do not have much impact on our lives. We think that it isonly the big things, the big actions and the big decisions that really count. Butwhen you look at the lives of all great people, you will see that they built theircharacter through small decisions, small choices and small actions that theyperformed every day. They transformed their lives through a step-by-step or day-by-day approach. They nurtured and nourished their good habits and chippedaway at their bad habits, one step at a time. It was their small day-to-daydecisions that added up to make tremendous difference in the long run. Indeed, inmatters of personal growth and character building, there is no such thing as an

overnight success.

2. Growth always occurs through a sequential series of stages. There is an organic

process to growth. When we look at children growing up, we can see this processat work: the child first learns to crawl, then to stand and walk, and finally to run.The same is true in the natural world. The soil must first be tilled, and then theseed must be sowed. Next, it must be nurtured with enough water and sunlight,

and only then will it grow, bear fruit and finally ripen and be ready to eat.

3. Gandhi understood this organic process and used this universal law of nature tohis benefit. Gandhi grew in small ways, in his day-to-day affairs. He did not

nothing much in his early life that showed signs of greatness. But from his mid-twenties onwards, he deliberately and consistently attempted to change himself,reform himself and grow in some small way every day. Day by day, hour by

Page No. 1

2hour, he risked failure, experimented and learnt from mistakes. In small and large

situations alike, he took up rather than avoid responsibility.

4. People have always marvelled at the effortless way in which Gandhi couldaccomplish the most difficult tasks. He displayed great deal of self-mastery anddiscipline that was amazing. These things did not come easily to him. Years ofpractice and disciplined training went into making his successes possible. Veryfew saw his struggles, fears, doubts and anxieties, or his inner efforts to

overcome them. They saw the victory, but not the struggle.

5. This is a common factor in the lives of all great people: they exercised theirfreedoms and choices in small ways that made great impact on their lives andtheir environment. Each of their small decisions and actions, added up to have aprofound impact in the long run. By understanding this principle, we can move

, disheartened andpessimistic. However, when we choose to grow in small ways, taking small steps

one at a time, performing it becomes easy.

(I) On the basis of your understanding of the passage, answer the followingquestions by choosing the most appropriate option. (14 = 4 Marks)

1. The main idea in the first paragraph is that

a. Big things, big actions and big decisions make a person great

b.

c. Overnight success is possible for all of us

d. Personal changes are not important

2.

a. Steadily gave up bad habits

b. Slowly produced bad habits

c. Gradually criticized bad habits

d. Did not like bad habits

Page No. 2

33. Which of the following statements is true in the context of the thirdparagraph?

a. Gandhi became great overnight

b. Gandhi showed signs of greatness in childhood itself

c. Every day Gandhi made efforts to change himself in some small way

d. Gandhi never made mistakes

4. What is done by great people to transform their lives?

a. They approach life on a day-by-day basis

b. They build character in small ways

c. They believe in performing everyday

d. All of these

(II) Answer the following questions as briefly as possible. (16 = 6 Marks)5. How do small actions and choices impact our lives?

6. Describe organic process of growth through an example from the text.

7. What according to the author is the universal law of nature ?

8. How did Gandhi accomplish the most difficult tasks effortlessly?

9. W

10. How can we achieve our ideal goals ?

(III) Pick out words from the passage which are similar in meaning to thefollowing: (2 Marks)

a. intentionally / purposely (Paragraph 3)b. of deep significance; far-reaching (Paragraph 5)

Page No. 3

4Q2. Read the following passage carefully. (10 Marks)1. South India is known for its music and for its arts and rich literature. Madras or

Chennai can be called the cultural capital and the soul of Mother India. The cityis built low in pleasant contrast to the ghoulish tall structures of Mumbai andKolkata. It has vast open spaces and ample greenery. The majestic spaciousMount Road looks like a river, wide and deep. A stroll on the Marina beach inthe evening with the sea glistening in your face is refreshing. The breeze soothes

the body, it refreshes the mind, sharpens the tongue and brightens the intellect.

2. One can never feel dull in Chennai. The intellectual and cultural life of the city issomething of a marvel. Every street corner of Chennai has a literary forum, a

debating society and music, dance and dramatic club. The intelligent arguments,the sparkling wit and dashing irony enliven both the political and the literary

and equally brilliant listeners to its meetings. It is a treat to watch the speakersuse their oratorical weapons. Chennai speakers are by and large sweet andurbane, though the cantankerous, fire-eating variety is quite often witnessed inpolitical campaigning. The more urbane speakers weave their arguments slowly

like the unfolding of a leisurely Karnataka raga.

3. Music concerts and dance performances draw packed houses. There is hardly anycultural family in Chennai that does not learn and patronize music and dance inits pristine purity. Rukmani Devi Arundinternational centre. It has turned out hundreds of celebrated maestros anddancers who have brought name and glory to our country. Karnataka music has apeculiar charm of its own.

Thousands of people flock to the temple maidans to get drunk with themellifluous melodies of their favorite singers. They sit out all night in the

and rollicking with the

nightingale of the South.

Page No. 4

54. The Gods might descend from heaven to see a South Indian damsel dancing.There are several varieties of South Indian dance Bharat Natyam, MohiniAttam, Odissi, Kathakali etc. age cannot wither nor custom stale its beautifulvariety. Bharat Natyam is the most graceful and enchanting dance form whereasKathakali is most masculine and virile. South Indian dances combinevoluptuousness with purity. Here every muscle and fibre of the body vibratesinto life, and as the tempo increases, a divine flame-like passion bodies forth as if

making an assault on heaven.

5. South Indian dress, particularly of the males, is puritanically simple. There youby their dress. South Indian ladies too

look charming and graceful in their colourful Kanjeevaram and Mysore silksaris.

6.now we can enjoy them almost everywhere in India as well as in some foreign

(I) On the basis of your understanding of the passage, answer the followingquestions by choosing the most appropriate option. (2 Marks)

1. South India is known mainly for its

(a) tasty food(b) traditional music, art, literature(c) scenic beauty(d) delicate and precise ways

2. South Indian dances are special because

(a) Gods come from heaven to see them(b) t eties of dance(c) they are pure as well as sensuous(d) they make an assault on heaven

Page No. 5

6(II) Answer the following questions as briefly as possible. (16 = 6 Marks)3. How does the breeze on Marina Beach affect the author?

4. How do we know that music is very important for the people of South India?

5. What is the common connection between language, music and dance of SouthIndia?

6. What makes Karnataka music charming?

7. Enumerate the features of Bharat Natyam and Kathakali form of dance.

8. What is Kalakshetra renowned for?

(III) Find words from the passage which are similar in meaning to the following.(2 Marks)

(a) ill-tempered and quarrelsome (Paragraph 2)(b) smooth and sweet (Paragraph 3)

Q3. Read the following passage carefully. (8 Marks)Whether work should be placed among the causes of happiness or among the causes

of unhappiness may perhaps be regarded as a doubtful question. There is certainlymuch work which is exceedingly irksome, and an excess of work is always verypainful. However, work is not, to most people, more painful than idleness. There are,in work, all grades; from more relief of tedium up to the profoundest delights,according to the nature of the work and the abilities of the worker. Most of the workthat most people have to do is not interesting in itself, but even that work has certaingreat advantages. To begin with, it fills a good many hours of the day without the needof deciding what one shall do. Most people, when they are left free to fill their owntime according to their own choice, are at a loss to think of anything sufficientlypleasant to be worth doing. And whatever they decide on, they are troubled by thefeeling that something else would have been more pleasant here. To be able to fillleisure intelligently is the last product of civilization and at present very few peoplehave reached this level. Moreover the exercise of choice is tiresome in itself. Except,

Page No. 6

7to people with unusual initiative, it is positively agreeable to be told what to do at eachhour of the day, provided the orders are not too unpleasant. Most of the idle rich sufferunspeakable boredom. At times they may find relief by hunting big game in Africa orby flying around the world, but the number of such sensations is limited, especiallyafter youth is past. Accordingly, the more intelligent rich men work nearly as hard as

if they were poor.

Work, therefore is desirable, first and foremost as a preventive of boredom, althoughuninteresting work is as boring as having nothing to do. With this advantage of work,another associated advantage is that it makes holidays much more delicious when theycome. Provided that a man does not have to work so hard as to impair his vigour, he is

likely to find far more zest than an idle man would possibly find.

The second advantage of most paid work and some of unpaid work is that it giveschances of success and opportunities for ambition. In most work, success is measuredby income and while our capitalistic society continues, this is inevitable. However dullwork too, becomes bearable, if it is a means of building up a reputation. Continuity ofpurpose is one of the most essential ingredients of happiness and that comes chieflythrough work.

A. On the basis of your reading of the above passage make notes on it, usingheadings and sub headings. Use recognizable abbreviations (wherevernecessary minimum 4) and a format you consider suitable. Also supply anappropriate title to it. (5 Marks)

B. Write a summary of the passage in about 80 words. (3 Marks)

SECTION B ADVANCE WRITING SKILLS (30 Marks)Q4. Your school is organizing a Public Awareness Exhibition. In connection with it,

prepare a poster to bring home the importance of conservation of electricity.Your school is A.K. Public School, Green Park, Delhi. (4 Marks)

Or

Page No. 7

8Namita/ Namit has come out successful in the XII class examination. She/he has

decided to have a party for her/his friends. Draft an invitation in about 50 wordsgiving details of venue, time and date.

Q5. You are Amit/Amita staying at Sunrise Apartments, Gymkhana Road, Pune. Themain road leading to this colony has three open manholes causing frequentaccidents at night. The streetlight is also not available. Write a letter to the Editor

the

authorities towards this situation. Also suggest ways to mobilize city dwellers,

with the help of school children, for the cause for safe roads. (6 Marks)

Or

You are Shreya/Shreyas. Write an application in response to the followingadvertisement in a national daily. You consider yourself suitable and eligible for

this post.

Applications are invited for the post of a Nursery teacher/PRT in Y.K. InternationalSchool, Ghaziabad, UP. The candidate must have a minimum experience of 3 years ofteaching at the primary and pre-primary level. The applicant must have a pleasant and

energetic personality. She/he should be creative and adaptable. Attractive salary.Interested candidates should apply to the Principal with a detailed resume.

Q6. You are an active member of the Animals Lovers Club of your school whichworks for preventing cruelty to animals. Write an article in 150 -200 words foryour school magazine emphasising the need to co-exist peacefully with animals.You are Zaheeda/Zahir of P. K. Senior Secondary School, Hyderabad.

Or

Over the past few years there has been a constant rise in coaching institutes andprivate tuition centers all over India. Write an article in about 150-200 wordshighlighting the exploitation of young minds that seek sincere counselling andproper direction. You are Gurpreet, a student of class XII of Indira Public

School, Jamshedpur. (10 Marks)

Page No. 8

9Q7. You are Suraj/Sandhya of Gargi Senior Secondary School Delhi. Games andSports should be made compulsory in schools. Write a speech for morningassembly on the Importance of Games and Sports in PersonalityDevelopment in about 150 -200 words. (10 Marks)

Or

You have been asked to participate in a debate competition on the topic

ed in all schools and should be

Write the speech in about 200 words either for or against the motion.

SECTION C (TEXT BOOKS {FLAMINGO AND VISTAS}and LONG READING TEXT {NOVEL}) (40 Marks)

Q8. Read the lines given below and answer the questions that follow. (4 Marks)I looked again at her, wan pale

but all I said was, see you soon, Amma

and

a) Who looked pale and wan and why? (1 Mark)b) (1 Mark)c) (1 Mark)d) Name the poem and the poet. (1 Mark)

Or

Surely, Shakespeare is wicked, the map a bad example,

With ships and sun and love tempting them to steal

For lives that slyly turn in their cramped holes

From fog to endless night.

Page No. 9

10

a) Why is Shakespeare wicked? (1 Mark)b) Why is the map a bad example? (1 Mark)c) What is the condition of these children as described in these lines? (1 Mark)d) . (1 Mark)

Q9. Answer any FOUR of the following questions in about 30-40 words each:(43=12 Marks)

a) How does M. Hamel prove to be an ideal teacher?

b) Why did Edla still entertain the peddler even after she knew the truth about him?

c) Mention the hazards of working in a bangle factory.

d) Why does Dr. Sadaoprisoner of war? What is ironical about his words?

e) What did Jo want Roger Skunk s mother to be punished for?

f) Why did Zitala-Sa not want her hair to be cut short?

Q.10. Answer the following in about 120 150 words (6 marks)Though Rajkumar Shukla was an illiterate peasant; he was resolute and was able tobring a change in the lives of the people of Champaran. Taking hints from the text,

Or

A big boy pushed Douglas into the deep end of the swimming pool which could haveled to his death. Concerns regarding bullying and ragging persists in many teenagegroups. Quoting examples from the text, discuss the problem of bullying and itseffects on the victims. Also suggest ways to deal with this problem.

Q11. Answer the following in about 120 150 words (6 marks)

Page No. 10

11

Do you think Sophie is overambitious and Jansie is more practical? Discuss.

Or

How behavior and attitude different towards people

because of their physical impairment?

Q12. Answer the following in about 120 150 words (6 marks)

Or

Illustrate is the ending of the novel happy and just? What is yourreaction when Griffen gets killed and Marvel gets to keep all the stolen money? Are

you glad that the invisibility formula is hidden from Kemp , who could use it?

Q13. Answer the following in about 120 150 words (6 marks)Eppie is a character who remains highly predictable in her reactions. Prove this with

reference to her character traits.

Or

Why did Kemp turn out differently than Griffen? After all they are both scientists. Is

Kemp less isolated than Griffen? Is it simply because Kemp has more money?

Page No. 11

1English Core

MARKING SCHEME

1. Reading Passage 1 12 marks

1. 1mark

2 Gave up bad habits 1 mark

3. Every day Gandhi made efforts to change himself in some small way1mark

4. In small ways 1 mark

5. built character 1 mark

6. sequential series - Ex of child 1 mark

7ay.. to make oneself grow in a small way - every 1mark

8..tried to change himself reform grow in small ways 1 mark

9. practice- discipline self mastery used freedom in right way worked on small thingslearned from mistakes. 1 mark

10. small step one at a time remain optimistic 1 mark

11 nurtured, impact 2 marks

2. Passage 2 10 marks

1. b) traditional music, art, literature 1 mark

2. d) saree 1 mark

3.soothing effect refreshing brightens intellect 1 mark

4. Thousands flock to hear sit all night in adverse conditions 1 mark

5. Very pure enchanting divine 1 mark

6. soft beauty soft pace 1 mark

7. South Indian graceful, enchanting - voluptuous pure - full of life divine

North Indian monotonous, mechanical 1 mark

8. 1 mark

9. pleasant, urbane 1 mark

3. Passage 3 Note Making and Summary 8 marks

Page No. 12

2Title - Work: Desirable or Boring 1 mark

Abbreviations : work wrk. hour hr., advantage adv., opportunities opp.

Positively - +ly., exercise ex. 1 mark

Notes 3 mark

1. Doing wrk leads to

a)Happiness b) unhappiness

2. Adv. Of wrk

brings relief, delight, compulsive worthwhile input daily, occupied, fills time usefully, feelpleasant, prevents boredom, makes holidays more important & zestful, provides chances ofsuccess ,good opportunities, fulfillment of ambition, sound income, continuity of purpose

3. Disadv of wrk

Unspeakable boredom, waste of tme, something out of compulsion

4. Wrk desirable for complete happiness

Summary 3 marks

Coherence, spellings, grammar, sequence, correct understanding of the content, punctuation

4.Poster

Layout- Eye catching and visually attractive 1 mark

Content Highlights of the main topic- Need of saving electricity 2 marks

Expression Grammatical accuracy, spellings 1 mark

Or

Invitation

Format 1 mark

Content- what, where, when 2 marks

Expression Coherence, relevance, spellings, grammatical accuracy 1 mark

5. Letter

1 mark

Content Uncovered manholes, frequent accidents

Page No. 13

3- Can be lethal for all persons, especially small children.- Causes bad smell, pollution, breeding area for mosquitoes- Lack of street light adds to the woes and difficulties.- Authorities should take action. 3 marks

Expression Coherence and relevance, grammar and spellings 2 marks

Or

1 mark

Content Introduction reference to the advertisement

Complete Bio data 3 marks

Expression Coherence and relevance, grammar and spellings 2 marks

6.

Format 1 mark

Content- 4 marks

Report animal abuse if you see it

Understand the link between animal cruelty and abuse

Teach children to respect animals

Volunteer to help animals

Support law that promotes kindness to animals

Expression Coherence, relevance, 2.5 marks

Spellings, grammatical accuracy 2.5 marks

Or

Format 1 mark

Content- 4 marks.

One can find coaching centers in every nook and corner - Teachers and parents have equallypromoted their growth - coaching institutes boast of guaranteed success rate - publish inflatednumbers every year in leading newspapers and magazines - Education is a natural process oflearning that should not be forced upon the students.- institutes provide professional teachers- necessary material required for preparation - provide a competitive environment - examsare conducted by them to help the students evaluate themselves on a regular - charge highamount of fees and sometimes provide sub-standard teachers to the students -to choose theright institute is of prime importance - decision should note b hasty .

Page No. 14

4Expression Coherence, relevance, 2.5 marks

Spellings, grammatical accuracy 2.5 marks

7. Format Title 1 mark

Introduction

- Outdoor games make us active, agile and alert- Exchange of ideas and thoughts- Social circle is broadened- More joyful than sitting alone on computers and chatting 4 marks

Expression Relevance and coherence 2.5 marks

Grammar and Spellings 2.5 marks

Or

8. a) s mother looked pale and wan. She was very old 1 mark

b) The fear of ageing and ultimate death / separation 1 mark

. c) She has lost her shining skin and strength and was like the hazy, obscure winter moon.1 mark

d) My Mother at Sixty-Six, Kamla Das 1 mark

Or

a) Shakespeare and his work are of no use to slum children 1 mark

b) The map does not depict their own world of narrow lanes. 1 mark

c) They lived like rats in their cramped holes. 1 mark

d) Their future is foggy and uncertain. Their birth, life and death all are enveloped bydarkness. 1 mark

9 ( 4X3= 12)

9 a) selfless dedication- helped in the inception of school- 40 years of meritorious service-made people conscious of imp. of their lang and national identity.

b) Basically kind trusting and compassionate wanted peddler to enjoy be at peace didnot want to turn away a guest on Christmas eve kind gesture to reform the peddler.

c) Ill lit, ill-ventilated, unhygienic,dingy hovels high temp. bends back of young childrenloss of vision become old before time.

Page No. 15

5d) Dr. Sadao trained to talk to patients to comfort them elicit response.

Ironical as the soldier/sailor is an enemy - Sadao saves his life.

e) Jo finds mum stupid mum should not have spanked wizard - wants Skunk to get backsmell of roses mum to be punished as insensitive , cruel, unfair

f) Hair cut by enemies of unskilled captured warriors short hair worn by mournersshingled hair by cowards - indecent, undignified

10. Value points

An illiterate did not give tenacity of resolution bore fruit able to bring Gandhiji goodexample of grit and determination key to success high achievement optimismpersistence always yields positive result leads to incouragement, enlightment andinspiration grit and determination dynamic and action oriented.

OR

Effect author unable to forget terrifying memories of childhood robbed him ofconfidence develop life long complex leads to major health and mental problemsconstant feeling of fear

Suggestions deliberate planned effort understanding of self and people setting up ofschool committee for monitoring support of parents and community awareness amongchildren to understand and report bullying

11. Value points

Both belong to poor families Jansie practical and realistic ready to work in a biscuitfactory advices Sophie not to day dream father will not allow

Sophie not practical dreamer dreams of wonderful shop wants to become an actress orfashion designer looking for something sophisticated and fancy full over ambitious andwavering mind

OR

avoids seeing and meeting people as people afraid/avoid to look at himugly call him poor boy hates to talk to people people unsympathetic and cruel

loves to meet and talk to people garden house open to all childrenchildren tease him make fun of him Mr. Lamb not troubled not afraid and shy of hisphysical imapirment

12. Value points

Marner compared to a spider weaving a web.When he loses gold feels helpless likened to an ant

Page No. 16

6Silas tries to rehabilitate a new emerging plantHis relationship with Eppie flower in bloom

OR

Ending happy just in away Griffen dies Marvel becomes rich with stolen money Sadand not just because Griffen dies Marvel should not have become rich with the stolenmoney Griffen misuses his powers creates terror harms steals Kemp could alsomisuse the research happy ending if Griffen had realized his mistake

13. Value points

Eppie comes as a touch of cheer

Has golden curls which Silas fantasized as return of his lost goldLoveable accepts Silas as her fatherFond of outdoors persuades Silas to grow a garden affectionate to animalsHer sense of responsibility and gratitude to Silas remain constant and wavering.OR

Both scientists different approach Griffen does not think about humanitypreoccupied with himself and his research disconnects himself with everyoneoverambitious selfish isolated from others.

Kemp caring attitude reflected in his actions he asks the housemaids to keepthemselves locked irrespective of anything apprise ,warns, and advises all about theinvisible man money is not a valueisolation or evil acts

Page No. 17

1SAMPLE PAPER: MATHEMATICSCLASSXII: 201415

TYPOLOGY

VSA (1 M) LAI (4 M) LAII (6 M) 100

Remembering 2, 5 11, 15, 19 24 20

Understanding 1, 4 8, 12 23 16

Applications 6 14, 18, 13 21, 26 25

HOTS 3 10, 17 20, 22 21

Evaluation & MD 7, 9, 16 25 18

Page No. 18

2SECTIONAQuestion number 1 to 6 carry 1 mark each.

1. The position vectors of points A and B are and respectively.P divides AB in the ratio 3 : 1 and Q is mid-point of AP. Find the positionvector of Q. 1

2. Find the area of the parallelogram, whose diagonals are =5 and =2 13. If P(2, 3, 4) is the foot of perpendicular from origin to a plane, then write the vector

equation of this plane. 1

4. If =

, Write the cofactor of a32 (the element of third row and 2nd

column). 15. If m and n are the order and degree, respectively of the differential equation

y + x3 -xy = sin x, then write the value of m+n. 16. Write the differential equation representing the curve y2 = 4ax, where a is an

arbitrary constant. 1

SECTION-BQuestion numbers 7 to 19 carry 4 marks each.7. To raise money for an orphanage, students of three schools A, B and C organized

an exhibition in their locality, where they sold paper bags, scrap-books and pastelsheets made by them using recycled paper, at the rate of Rs. 20, Rs.15 and Rs. 5 perunit respectively. School A sold 25 paper-bags 12 scrap-books and 34 pastel sheets.School B sold 22 paper-bags, 15 scrapbooks and 28 pastel-sheets while school Csold 26 paper-bags, 18 scrap-books and 36 pastel sheets. Using matrices, find thetotal amount raised by each school.By such exhibition, which values are inculcated in the students? 4

8. Let A = , then show that A2 4A + 7I = O.

Page No. 19

3Using this result calculate A3 also.OR

If A =

, find A-1 , using elementary row operations. 4

9. If x, y, z are in GP, then using properties of determinants, show that

= o, where x y z and p is any real number. 4

10. Evaluate : dx. 4

11. Evaluate : . e2x dx. 4

OR

Evaluate : dx

12. Consider the experiment of tossing a coin. If the coin shows tail, toss it again but ifit shows head, then throw a die. Find the conditional probability of the event thatthe die shows a number greater than 3 given that there is at least one head. 4

OR

How many times must a man toss a fair coin so that the probability of having atleast one head is more than 90%?

13. For three vectors , and if = and , then prove that andare mutually perpendicular vectors, | |= | |and| | = 1 4

14. Find the equation of the line through the point (1,-1,1) and perpendicular to thelines joining the points (4,3,2), (1,-1,0) and (1,2,-1), (2,1,1) 4

OR

Page No. 20

4Find the position vector of the foot of perpendicular drawn from the point P(1,8,4)to the line joining A(O,-1,3) and B(5,4,4). Also find the length of this perpendicular.

15. Solve for x: sin-1 6x + sin-1 6 =

OR

Prove that: 2 sin-1 - tan-1 = 4

16. If x = sin t, y = sin kt, show that(1-x2) - x + k2y = 0 4

17. If yx + xy + xx = ab, find 418. It is given that for the function f(x) = x3 + bx2 + ax + 5 on [1, 3], Rolles theorem

holds with c = 2 + Find values of a and b. 4

19. Evaluate : dx 4

SECTION-CQuestion numbers 20 to 26 carry 6 marks each.20. Let A = and R be the relation in A x A defined by (a, b) R (c, d) if a+d

= b+c for a, b, c, d A.Prove that R is an equivalence relation. Also obtain the equivalence class [(2, 5)]. 6

ORLet f : N R be a function defined as f(x) = 4x2 + 12x + 15.Show that f : N S is invertible, where S is the range of f. Hence find inverse of f.

21. Compute, using integration, the area bounded by the lines

x+2y = 2, y-x=1 and 2x+y= 7 6

Page No. 21

522. Find the particular solution of the differential equation 6

given that

y = 0, when x = 1

OR

Obtain the differential equation of all circles of radius r.

23. Show that the lines = + (-3 + + 5 ) and = + are coplanar. Also, find the equation of the plane containing these

lines. 6

24. 40% students of a college reside in hostel and the remaining reside outside. At theend of year, 50% of the hosteliers got A grade while from outside students, only30% got A grade in the examination. At the end of year, a student of the collegewas chosen at random and was found to get A grade. What is the probability thatthe selected student was a hostelier? 6

25. A man rides his motorcycle at the speed of 50km/h. He has to spend Rs. 2 per kmon petrol. If he rides it at a faster speed of 80km/h, the petrol cost increases to Rs. 3per km. He has atmost Rs. 120 to spend on petrol and one hours time. Using LPPfind the maximum distance he can travel. 6

26. A jet of enemy is flying along the curve y = x2+2 and a soldier is placed at the point(3, 2). Find the minimum distance between the soldier and the jet. 6

Page No. 22

6MARKING SCHEMESAMPLE PAPERSECTION-A

1. 12. 5 sq. units 13. = 29 14. 14 15. m + n = 4 16. 2x y = 0 1

SECTION-B

7. Sale matrix for A, B and is

Price matrix is

=

Amount raised by =

School A = Rs 850, school B = Rs 805, school C = Rs 970Values

Helping the orphans 1Use of recycled paper 1

8. A2 = =

1

Page No. 23

7A2 4A + 7I = + +

=

2

A2 = 4A-7I A3 = 4A2 7A = 4(4A-7I) -7A

= 9A 28I = +

= 1

OR

Write A = IA we get

=

.A

R2 R2-2R1

=

A 1

R2 R2-3R3

=

A 1

=

A 1

A-1

9. =

C1 C1- pC2 C3, =

1

Expanding by R3

= (-p2x-2py-z) (xz-y2) 1

Page No. 24

8Since x, y, z are in GP, y2 = xz or y2 xz = 0 1

= 0

10. dx=2 1

= 2 dx+2 dx 1

= 2 2 1

= 2 2 = 1

11. I = e2xdx = et dt (where 2x=t)

= +

et dt 1

= etdt 1

tan = f(t) then f(t) = sec2 Using et dt = f(t) et + C, we get

I = tan . et + C = tan x. e2x + C 1

OR

We have

= +

= + .. (1) 1

Now express = +

.. (2)

Page No. 25

9So,

1 = ( )+ ( ) (

= +

Equating coefficients, A + B = 0, C B = 0 and A C = 1,

Which give A = B = C = - . Substituting values of A, B, and C in (2), we get

=

-

-

.. (3) 1

Again, substituting (3) in (1), we have

= + - - Therefore

= + 1+1

12. Let E : Die shows a number > 3

E : {H4, H5, H6]

and F : there is atleast one head.

F : {HT, H1, H2, H3, H4, H5, H6}

P(F) = 1 = 1

P(E F) = = 1

P(E/F) = = = 1

Page No. 26

10

OR

p = , q = , let the coin be tossed n times

P(r 1) >

or 1-P(r=0) >

P(r=0) < 1- =

nC0 < < 1

2n > 10, n = 4 1

13.

1

and 1

sin = and sin =

= = = 1 1

1. = =

14. DRs of line (L1) joining (4, 3, 2) and (1, -1, 0) are

DRs of line (L2) joining (1, 2, -1) and (2, 1, 1) are

A vector to L1 and L2 is

= 10 -4 -7 1

Equation of the line passing through (1, -1, 1) and to L1 and L2 is

= ( - + ) + (10 -4 -7 ) 1

Page No. 27

11

OR

Equation of line AB is

= (- +3 ) + (5 +5 + ) 1

Point Q is (5 , -1+5 , 3+ )

= (5 -1) +(5 -9) + ( -1)

PQ AB 5(5 -1) + 5 (5 -9) + 1 ( -1) = 0

51 = 51 =1

foot of perpendicular (Q) is (5, 4, 4)

Length of perpendicular PQ = = units 1

15. sin-1 6x + sin-1 x =

sin-1 6x =

6x = sin = - sin

= - cos [sin-1 6 ] = - 1

36x2 = 1-108 x2 144 x2 = 1

x =

since x = does not satisfy the given equation

x = 1

OR

LHS = 2 sin-1 - tan-1

Page No. 28

12

= 2 tan-1 - tan-1 1

= tan-1 - tan-1 1

= tan-1 - tan-1 1

= tan-1

= tan-1 (1) = 1

16. x = sin t and y = sin kt= cost and = k cost kt

= k 1

or cost. = k. coskt

cos2t = k2 cos2 kt

cos2t = k2 cos2 kt

(1-x2) = k2 (1-y2) 1

Differentiating w.r.t.x

(1-x2) + = -2k2y 1

(1-x2) - x + k2y = 0

17. let u = yx, v = xy, w = xx

(i) logu = x logy = yx 1

(ii) log v = y log x = xy

Page No. 29

13

(iii) log w = x logx = xx , (1+logx)

+ xy + xx (1+logx) = 0 1

=

1

18. f(x) = x3 + bx2 + ax + 5 on [1, 3]f(x) = 3x2 + 2bx+a

f(c) = 0 3 + 2b + a = 0 - - - - - - (i) 1

f(1) = f(3) b+a+6 = 32 + 9b +3aor a + 4b = -13 - - - - - - - - - - (ii) 1Solving (i) and (ii) to get a=11, b= -6 1

19. Let 3x + 1 = A (2x 2) + B A = -3/2, B = 2 1

I =

1+1

1

SECTIONC

20. (i) for all a, b A, (a, b) R (a, b), as a + b = b + aR is reflexive 1

(ii) for a, b, c, d A, let (a, b) R (c, d)a + d = b + c c + b = d + a (c, d) R (a, b)R is symmetric 1

(iii) for a, b, c, d, e, f, A, (a, b) R (c, d) and (c, d) R (e, f)

Page No. 30

14

a + d = b + c and c + f = d + e

a + d + c + f = b + c + d + e or a + f = b + e

(a, b) R (e, f) R is Transitive 2

Hence R is an equivalence relation and equivalence class [(2, 5)] is

{(1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)} 1

OR

Let y S, then y=4x2+12x+15, for some x Ny = (2x + 3)2 + 6 x = , as y > 6 1

Let g : S N is defined by g(y) = 1

gof (x) = g (4x2+12x+15) = g ((2x+3)2+6) = = x 1

and fog (y) = f = +6 = y 1Hence fog (y) = IS and gof(x) = IN

f is invertible and f-1 = g 121. Let the lines be, AB: x+2y = 2, BC: 2x+y = 7, AC = y-x = 1 1

Points of intersection are

A(0,1), B(4,-1) and C(2, 3) 1

A = dy - dy dy 1

= 1

= 12 4 2 = 6sq.Unit.

22. Given differential equation is homogenous.

Page No. 31

15

Putting y = vx to get = v + x

= 1

- - - - - - - - (i) 1

I1 = sinv.e-v +

= -sinv.e-v

I1 = (sin v + cosv) 1

Putting (i), (sinv + cosv) = logx +C2

1

x = 1, y = 0 c = 1 1

Hence, Solution is

OR

(xa)2 + (yb)2 = r2 ..........(i)

2(xa) + 2(yb) = 0 .........(ii)

1+(yb) .........(iii)

(yb) = 1

From (ii), (xa) = 1

Page No. 32

16

Putting these values in (i)

1

or 1

23. Here

1

= 10 + 10 = 0lines are coplaner.

Perpendicular vector to the plane =

2

or 2Eqn. of plane is 1

or x 2y + z = 0

24. Let E1: Student resides in the hostel

E2: Student resides outside the hostel

+

A: Getting A grade in the examination

1+1

Page No. 33

17

1

1+1

25. Let the distance travelled @ 50 km/h be x km.and that @ 80 km/h be y km.

LPP isMaximize D = x + y

St. 2x + 3y 120 2

x 0 , y 02

Vertices are.

(0, 40), (50,0)

Page No. 34

18

Max. D is at

Max. D = km. 1

26. Let P(x, y) be the position of the jet and the soldier is placed at A(3, 2)

.......(i)

As y = x2 + 2 y 2 = x2 .......(ii) AP2 = (x3)2 + x4 = z (say)

2(x3) + 4x3 and 12x2 + 2 2

0 x = 1 and (at x = 1) > 0 1+1

z is minimum when x = 1, when x = 1, y = 1+2 = 3

minimum distance = 1

Page No. 35

Sample Question Paper

Class XII Physics

(Applicable for March 2015 Examination)Time Allowed: 3 Hours Maximum Marks: 70

General Instructions1. All questions are compulsory. There are 26 questions in all.

2. This question paper has five sections: Section A, Section B, Section C, Section D andSection E.

3. Section A contains five questions of one mark each, Section B contains five questions oftwo marks each, Section C contains twelve questions of three marks each, Section Dcontains one value based question of four marks and Section E contains three questionsof five marks each.

4. There is no overall choice. However, an internal choice has been provided in onequestion of two marks, one question of three marks and all the three questions of fivemarks weightage. You have to attempt only one of the choices in such questions.

5. You may use the following values of physical constants wherever necessary.

c = 3 X 108 m/s

h = 6.63 X 10-34 Js

e = 1.6 X 10-19 C

o = 4 X 10-7 T m A-1

= 9 X 109 N m2 C-2

me = 9.1 X 10-31 kg

Page No. 36

mass of neutron = 1.675 X 10-27 kg

mass of proton = 1.673 X 10-27 kg

Avogadro 23 per gram mole

Boltzmann constant = 1.38 X 10-23 JK-1

Section A

1. What is the value of the angle between the vectors and for which the potential

energy of an electric dipole of dipole moment , kept in an external electric field ,

has maximum value. 1

2. Name the colours corresponding to the digits 4 and 7 in the colour code scheme forcarbon resistors. 1

3. State which of the two, the capacitor or an inductor, tends to become a SHORT when

the frequency of the applied alternating voltage has a very high value. 14. Redraw the diagram given below and mark the position of the centre of curvature of

the spherical mirror used in the given set up. 1

5. In the given diagram C(t) stands for the carrier wave and m(t) for the signal to betransmitted. What name do we give to the wave labeled as Cm(t) in the diagram? 1

Page No. 37

Section B

6. Calculate the value of the unknown potential V for the given potentiometer circuit.The total length (400 cm) of the potentiometer wire has a resistancebalance point is obtained at a length of 240 cm. 2

7. Name the phenomenon which proves transverse wave nature of light. Give two uses

of the devices whose functioning is based on this phenomenon. 2OR

Name the phenomenon which is responsible for bending of light around sharp corners ofan obstacle. Under what conditions does this phenomenon take place? Give oneapplication of this phenomenon in everyday life.

Page No. 38

8. The equivalent wavelength of a moving electron has the same value as that of a

photon having an energy of 6 X 10-17 J. 2

Calculate the momentum of the electron.

9. The short wavelength limit for the Lyman series of the hydrogen spectrum is 913.4 .Calculate the short wavelength limit for Balmer series of hydrogen spectrum. 2

10. (a) Arrange the following networks in increasing order of the number of computersthat may be present in the network:

Internet ; LAN ; WAN

(b) What is the minimum number of satellites that enables a Global Positioning System(GPS)fix. 1+1=2

Section C

11. Eight identical spherical drops, each carrying a charge 1 nC are at a potential of 900V each. All these drops combine together to form a single large drop. Calculate thepotential of this large drop. 3

(Assume no wastage of any kind and take the capacitance of a sphere of radius r asproportional to r).

12 . The current flowing in the galvanometer G when the key k2 is kept open is I. On

closing the key k2 , the current in the galvanometer becomes I/n, where n is an integer.

Obtain an expression for resistance Rg of the galvanometer in terms of R, S and n. Towhat form does this expression reduce when the value of R is very large as compared to

S? 3

Page No. 39

13. The magnitude F of the force between two straight parallel current carryingconductors kept at a distance d apart in air is given by 3

Where I1 and I2 are the currents flowing through the two wires

Use this expression, and the sign convention that the:

Force of attraction is assigned a negative sign and Force of repulsion is assigned.

Draw graphs showing dependence of F on

(i) when d is kept constant

(ii) d when the product is maintained at a constant positive value.

(iii) d when the product is maintained at a constant negative value.

OR

The given graphs show the variation of intensity of magnetization I with strength

of applied magnetic field H for two magnetic materials P and Q.

Page No. 40

(i) Identify the materials P and Q.(ii) For material P, plot the variation of Intensity of Magnetisation with

temperature. Justify your answer.

14. Find the value of the phase lag/lead between the current and voltage in the

given series LCR circuit. Without making any other change, find the value of theadditional capacitor, such to the capacitor ( C= 2F)as shown, would make the power factor of this circuit unity. 3

15. Explain howapplied to the process of charging a capacitor.

moved by introducing the concept of an3

16. A point object O is kept at a distance of 30 cm from a convex lens of power+4D towards its left. It is observed that when a convex mirror is kept on the rightside at a distance of 50 cm from the convex lens, the image of the object Oformed by the lens-mirror combination coincides with the object itself.Calculate the focal length of the convex mirror. 3

Page No. 41

17. The arrangement used by Thomas Young to produce an interference pattern isshown in the given diagram.

illuminated slit (S) is shifted to the position as shown. 3

18. A given number of atoms No of a radioactive element with a half life T isuniformly distributed in the blood stream of a 3

(i) normal person A having total volume V of blood in the body(ii) person B in need of blood transfusion having a volume of blood inthe body.

The number of radioactive atoms per unit volume in the blood streams of the twopersons after a time nT are found to be N1 and N2.Prove mathematically that the additional volume of blood that needs to be

transfused in the body of person B equals ) V19. A student has to use an appropriate number of 3

(i) NAND gates (only) to get the output Y1(ii) NOR gates (only) to get the output Y2

From two given inputs A and B as shown in the diagram.

Page No. 42

appropriate number of (i) NAND (ii) NOR gates respectively in the two cases to

20. The data given below gives the photon energy (in eV) for a number of waveswhose wavelength values (in nm) are also given. 3

Wavelength

(in nm) 200 400 600 800 1000 1200Photon

Energy (ineV)

6.216 3.108 2.072 1.554 1.243 1.036

(Without doing any calculation/taking any reading), explain how one can use thisdata to draw an appropriate graph to infer(i) photon energy corresponding to a wavelength of 100 nm.(ii) the wavelength value (in nm) corresponding to a photon energy of 1 eV.(iii) v

21. A (sinusoidal) carrier wave 3

C(t) = AC c t

Page No. 43

is amplitude modulated by a (sinusoidal) message signal

m(t) = Am m t

Write the equation of the (amplitude) modulated signal.Use this equation to obtain the values of the frequencies of all the sinusoidalwaves present in the modulated signal.

22. Give reasons for the following: 3(i) The Zener diode is fabricated by heavily doping both the p and n sides of thejunction(ii) A photodiode, when used as a detector of optical signals is operated underreverse bias.(iii) Tmust at least be 1.8 eV.

Section D

23.straight conductor. She noticed that the force on the straight current carrying conductorbecomes zero when it is oriented parallel to the magnetic field and this force becomesmaximum when it is perpendicular to the field. She shared this interesting informationwith her grandfather in the evening. The grandfather could immediately relate it tosomething similar in real life situations. He explained it to Dimpi that similar thingshappen in real life too. When we align and orient our thinking and actions in anadaptive and accommodating way, our lives become more peaceful and happy.However, when we adopt an unaccommodating and stubborn attitude, life becomestroubled and miserable. We should therefore always be careful in our response todifferent situations in life and avoid unnecessary conflicts.

Answer the following question based on above information:a) Express the force acting on a straight current carrying conductor kept in a magnetic

field in vector form. State the rule used to find the direction of this force.b) Which one value is displayed and conveyed by grandfather as well as Dimpi?

c) Mention one specific situation from your own life which reflects similar valuesshown by you towards your elders. 2+1+1=4

Page No. 44

Section E

24 a) State the theorem which relates total charge enclosed within a closed surface 5

and the electric flux passing through it. Prove it for a single point charge.

point nucleus of charge +Ze at its centre. This nucleus was believed to be surrounded bya uniform density of negative charge that made the atom neutral as a whole.

Use this theorem to find the electric field at a distance r (r a) from thecentre of the atom.

OR

A Dipole is made up of two charges + q and q separated by a distance 2a.

Derive an expression for the electric field due to this dipole at a point distant r from

the centre of the dipole on the equatorial plane.

Draw the shape of the graph, between and r when r

If this dipole were to be put in a uniform external electric field obtain an expression

for the torque acting on the dipole.

25. State the law which relates to generation of induced emf in a conductor being movedin a magnetic field. 5

Apply this law to

rectangular conductor is free to move in a uniform,magnetic field.

Apply the concept of the Lorentz (magnetic) force acting on a moving charge to justifythe expression obtained above.

OR

Page No. 45

An a.c. voltage = m sin t is applied across an inductor of inductance L.

(i) the current flowing in the circuit(ii) the inductive reactance L

Hence find the instantaneous power Pi supplied to the inductor.

Show graphically the variation of Pi with t.

26. (a) Explain, with the help of a diagram, how is the phenomenon of total internal reflectionused in

(i) an optical fibre(ii) a prism that inverts an image without changing its size

(b) A right angled prism made from a material of refractive index is kept in air. A rayPQ is incident normally on the side AB of the prism as shown.

Find (in terms of ) the maximum value of upto which this incident ray necessarily undergoestotal internal reflection at the face AC of the prism. 2+3=5

ORin wave-optics. How did Huygen the absence of the

backwave?

Page No. 46

Use this principle to draw the refracted wave front for a plane wave incident from a denser to ararer medium. Hence

Page No. 47

Class XII Physics

Sample Question Paper(Marking Scheme)

Time Allowed: 3 Hours Maximum Marks: 70

01. P.E. = = p E Cos ()P.E. is maximum when Cos = -1, i.e. = (1800) ()

02. 4 yellow ()7 Violet ()

03. The capacitor (1)

04.

(1)

05. Cm (t) is the frequency modulated wave. (1)

06. The current through the potentiometer wire = = 10-2 A ()

Potential drop per unit length of the

potentiometer wire = = = X (1)Balancing length (l) = 240 cm (given)

Page No. 48

V= l = X

(= 60 mV) ()

07. Polarization (1)Two Uses:Polaroids can be used in sunglasses, window panes, photographic cameras, 3D moviecameras (Any Two) (+)

OR

Diffraction; Condition: Size of the obstacle sharpness should be comparable tothe wavelength of the light falling. (1+1/2)Any application (1/2)

08. E = Energy of the photon = h = ()

=

Wave length of the moving electron = = ()Momentum of the electron = p

= ()

= kg = 2 X kg ()

09. Rydberg formula for the wavelengths of spectral lines in hydrogen spectrum is

= R ( - ) ()

The short wavelength limit for the Lyman series would be

= R ( ) = R

R = ()

Page No. 49

The short wavelength limit for the Balmer series, would be

= R ( - ) = ()

= = 4 X 913.4

= 3653.6 ()

10. a) LAN, WAN, Internet (1)

b) Three (1)

11. Let the radius of each drop be r. The capacitance C of each drop is kr, where k is aconstant.Also q = CV, V = 900 volt ()

charge on each drop = q = (kr X 900) C ()Total charge on all the eight drops = Q = 8 q

=7200 kr ()

Let R be the radius of the large drop. Then

R3 = 8 X r3

R = (8) r = 2r ()Capacitance of the large drop = kR = 2kr ()Potential of the large drop = = volt

= 3600V ()

12. With key K2 open, the current I in the galvanometer is given by

I =

When K2 is closed, the equivalent resistance, , of the parallel combination of Sand is given by

= ()

The total current, say drawn from the battery would now be

Page No. 50

=This current gets subdivided in the inverse ratio of S and ; Hence the current throughG, would now be given by

= = ()

=

= ()

But = =

= ()

Or n RS + n S = RS + R + S

or (n-1) RS = R - (n-1) S

or (n-1) RS +

()

This is the required expression

When R S , we have

= (n-1) S ()

13. We know that F is an attractive (-ve) force when the currents I1 and I2currents i.e. when the product I1I2 is positive.

Similarly F is a repulsive (+ve) force when the currents I1 and I2 , i.e.when the product I1I2 is negative. (1/2)

Now F (I1 I2 ), when d is kept constant and F when I1I2 is kept constant. (1/2)

The required graphs, therefore, have the forms shown below.

Page No. 51

(1+1/2+1/2)

OR

(i) P- Paramagnetic (

Q-Ferromagnetic materials (

(ii) (1)

14.The current, I, leads the voltage, V, by an angle where

tan =

Here = = 500 (1/2)and L = 100

tan = 1 ()= 450

Page No. 52

The power factor becomes unity when = 00. (1/2)

= ()

Thus, phase angle is 450 with the current LEADING the voltage.To make power factor as unity we need to have Xc also equal to 100 ohms. For this C needsto have a value of 10 F. (1/2)We, therefore need to put an additional capacitor of (10-2), i.e, 8 F in parallelwith the given capacitor (1/2)

inconsistency

current, called the displacement current . (1 +1)

(Pages 270 and 271 of NCERT Book, Part I)

16. Focal length of the convex lens = m (1/2)Let v be the position of the image, I, of the object formed by the convex lens alone.We then have

= = 150cm (1/2)

Hence the distance of the image (formed by the convex lens alone ) from the convexmirror would be (150-50) cm ,i.e.,100 cm. This distance equals the radius of curvature of theconvex mirror. (1/2)

Hence focal length of the convex mirror equals100/2, i.e., 50 cm. ( )

Radius of curvature of the convex mirrorR = LI LM

()

Page No. 53

(1/2)

17. Calculation , the normal set up (1)Calculation of fringe width, in the changed set up (1)Observing that ( )

(Reference : NCERT Book, Part II, pages 363, 364)

18. Initial number of radioactive atoms, per unit volume, in the blood streams ofpersons A and B are ( /V) and ( ( )After a time nT (T = Half life), these numberswould get reduced by a factor 2n. ( )

Hence N1= ( ) .And N2 = ( ) . ( )

= ( )

or = V ( )Additional volume of blood needed by person B is

V - = V V = ( ) V ( )

19. The equivalent gates in the two cases are the OR gate and the AND gate respectively.

(1/2 + )(i) A combination of three NAND gates, connected in the manner shown, would beequivalent to an OR gate.

(Fig 14.46 (b) Page 511) (1)

Page No. 54

(i) A combination of three NOR gates connected in the manner shown would beequivalent to an AND gate.

(Fig 14.48 (b) page 512) (1)

20. One can calculate the values of and plot a graph between E (photon energy in eV)

and (in nm-1). (1)

The resulting straight line graph can be used to

(i) read the value of , corresponding to = nm-1 (1/2)

(ii) read the value of ( in nm-1) corresponding to E = 1eV (1/2)

(iii) We have E =

The slope of the graph (after appropriate adjustment of the units) would equal hc.Since h is known, one can calculate c. (1)

21. The equation of the (amplitude) modulated signal is

(1)

This can be rewritten as

Where = = modulation index (1/2)

These are the three sinusoidal waves present in the amplitude modulated signal.

The frequencies of these three waves are

Page No. 55

(1/2)

and

22. (i) Heavy doping makes the depletion region very thin. This makes the electric field ofthe junction very high, even for a small reverse bias voltage. This in turn helps the Zener

(1)

(ii) When operated under reverse bias, the photodiode can detect changes in current withchanges in light intensity more easily. (1)

(iii). The photon energy, of visible light photons varies from about 1.8 eV to 3 eV. Hence forvisible LED , the semiconductor must have a band gap of 1.8 eV. (1)

23. (i) Expression for the force in vector form (1)

- (1)

(ii) Adaptation to different situations and flexible and adjustable attitude (1)- Sharing excitement in classroom learning with family members

(iii) Avoiding unnecessary arguments in conflicting situations in everyday life(1)

24. (1)

(2)

(Pages 33 and 34 of NCERT Book I)

(b) Set of negative charge. We then have

Taking a sphere of radius r (centred at the nucleus) as the Gaussian surface, we have

Page No. 56

Where Q is the net charge enclosed by the Gaussian surface. Now

Q = (+Ze) + ( - )

= Ze Ze ( ) = Ze ( 1- )

Substituting this value of Q, we get

E(r) = (1- )

= ( - )

OR

Derivation of the expression for

(page 28 NCERT Book I)

For r >> a, = (3)

Thus, the graph has the form shown. (1)

Derivation of the expression for torque (Page 31, NCERT Book I) (1)

-m induction (1)

Page No. 57

Derivation of the expression for induced emf (2)

(2)

(Page 212 + page 213 NCERT Part I)

OR

Applying

(i) Current flowing in the circuit ((ii) Inductive reactance of L (1/2)

Finding expression for instantaneous power, Pi, the graph has the form shown. (1)

(1)

26. (a) Explaining the use of the phenomenon of total internal reflection in

(i) an optical fibre (NCERT Page 322 fig 9.16 + Explanation) (1/2 +1)

(ii) a prism that inverts an image without changing its size. (NCERT Page 322 fig9.15 9(c) + Explanation) (1/2 +1)

Page No. 58

(b)

(1/2)

The angle of incidence at the face AC = i

But i = A

(Angle between two lines is the same as the angle between their perpendiculars)

Also i (1/2)

The minimum value of I, so that there is total internal reflection at the face AC, equals icwhere ic = (1/2)

The maximum value of corresponding to the minimum value of i (= ic) is therefore,

max ic (1/2)

OR

(1)

Absence of (1)

Drawing the refracted wave front (

(

Page No. 59

Page 1 of 10

SAMPLE QUESTION PAPER

CHEMISTRY (043)

CLASS XII (2014-2015)

QUESTION PAPER DESIGNCLASS XII CBSE

Types of Questions

S.No Type of Question Marks foreachQuestion

No. ofQuestions

Total Marks

1. Long Answers (LA) 5 03 152. Value based question 4 01 043. Short Answers-II(SA II) 3 12 364. Short Answers-I(SA I) 2 05 105. Very Short Answer (VSA) 1 05 05 Total 26 70

Type of questions VSA(1) SA1(2) SA2(3) VB(4) LA(5) Total(%)Knowledge 2 1 1 - - 07 (10%)Understanding - 2 4 - 1 21 (30%)Application - 2 4 - 1 21 (30%)HOTS (Higher order thinking skills) 2 - 1 - 1 10(14%)Evaluation and Multi-disciplinary 1 - 2 1 - 11(16%)

Page No. 60

Page 2 of 10

SAMPLE QUESTION PAPER

CHEMISTRY

CLASS XII (2014 2015)

Time Allowed: 3 hr Maximum marks: 70

General Instructions: (a) All questions are compulsory. (b) Q.no. 1 to 5 are very short answer questions and carry 1 mark each. (c) Q.no. 6 to 10 are short answer questions and carry 2 marks each. (d) Q.no. 11 to 22 are also short answer questions and carry 3 marks each (e) Q.no. 23 is a value based question and carry 4 marks. (f) Q.no. 24 to 26 are long answer questions and carry 5 marks each (g) Use log tables if necessary, use of calculators is not allowed.

1. The following figure shows the variation of adsorption of N2 on charcoal with pressure atdifferent constant temperatures:

Page No. 61

Page 3 of 10

Arrange the temperatures T1, T2 and T3 in the increasing order.

2. Give the formula of a noble gas species which is isostructural with IBr2-.3. What is the effect of synergic bonding interactions in a metal carbonyl complex?4. PCl5 acts as an oxidizing agent. Justify.5. Write the name of the product formed when benzenediazonium chloride solution is treated with

potassium iodide.6. Name the crystal defect which reduces the density of an ionic solid? What type of ionic

substances show this defect?7. The molar conductivity (

m) of KCl solutions at different concentrations at 298 K is plotted as

shown in the figure given below:

Determine the value of 0m and A for KCl.8. Aluminum crystallizes in anfcc structure. Atomic radius of the metal is 125 pm. What is the

length of the side of the unit cell of the metal?9. Draw the structure of the following compounds:

(i) H2S2O7(ii) XeOF4

OR

Write balanced chemical equations for the following: (i) Reaction of chlorine with hot and concentrated NaOH.

Page No. 62

Page 4 of 10

(ii) Sulphur dioxide is passed through an aqueous solution of Fe (III) salt.10. 0.5 g of KCl was dissolved in 100 g of water and the solution originally at 200C, froze at

-0.240C. Calculate the percentage dissociation of the salt. (Given :Kf for water = 1.86 K kg /mol, Atomic mass: K = 39 u, Cl= 35.5 u)

11. State briefly the principles involved in the following operations in metallurgy. Give anexample.(i) Hydraulic washing.(ii) Zone refining.

12. i) What type of deviation from Raoults law is observed, when two volatile liquids A andB on mixing produce a warm solution? Explain with the help of a well labeled vapourpressure graph.ii) Consider separate solutions of 0.5 M CH3OH, 0.250 M KCl (aq) and 0.125 M Na3PO4(aq). Arrange the above solutions in the increasing order of their Vant Hoff factor.

13. Write the Nernst equationand calculate the emffor the following cell at 298 K:Mg(s) / Mg2+ (0.001 M) // Cu2+ (0.0001 M) / Cu(s)How does Ecellvary with the concentration of both Mg2+ and Cu2+ ions? (GivenEocell= 2.71 V)

14. Explain the following observations giving appropriate reasons:(i) Ozone is thermodynamically unstable with respect to oxygen. .(ii) The HEH bond angle of the hydrides of group 15 elements decrease as we move down

the group.(iii) Bleaching effect of chlorine is permanent.

15.(i) Predict the number of unpaired electrons in the tetrahedral [MnBr4]2- ion.(ii) Draw structures of geometrical isomers of [Co(NH3)4Cl2]+.(iii) Write the formula for the following coordinate compound:

Amminebromidochloridonitrito-N-platinate(II)16. Explain what is observed when

(i) Silver nitrate solution is added to potassium iodide solution.(ii) The size of the finest gold sol particles increases in the gold sol.(iii) Two oppositely charged sols are mixed in almost equal proportions.

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17.(i) In the following pairs of halogen compounds, which would undergo SN1 reaction

faster? Explain.

and

ClCl

(ii) Amongst the isomeric dihalobenzenes which isomer has the highest melting point andwhy?

(iii) Arrange the following haloalkanes in the increasing order of density. Justify youranswer.CCl4, CH2Cl2 and CHCl3.

18. An organic compound ( A ) has characteristic odour. On treatment with NaOH, it formscompounds ( B ) and ( C ). Compound ( B ) has molecular formula C7H 8Owhich on oxidationgives back ( A ). The compound ( C ) is a sodium salt of an acid. When ( C ) is treated withsoda-lime, it yields an aromatic compound ( D ). Deduce the structures of ( A ), ( B ), ( C ) and( D ). Write the sequence of reactions involved.

19. (a) Give one chemical test to distinguish between the following pairs of compounds:(i) Methylamine and dimethylamine.(ii) Aniline and benzylamine

(b) Write the structures of different isomers corresponding to the molecular formula C3H9N,which will liberate nitrogen gas on treatment with nitrous acid.

20. (a) Exemplify the following reactions:(i) Rosenmund reduction reaction.(ii) Kolbe electrolysis reaction.

(b) Arrange the following compounds in increasing order of their reactivity towards HCN: Acetaldehyde, Acetone, Di-tert-butyl ketone.

OR

(a) Predict the products of the following reactions:

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(i)(i) Cl2 / Red phosphorous

(ii) H2OCH3-CH2-COOH

(ii)CH3

+ CrO2Cl2(i) CS2(ii) H3O+

(b) Arrange the following compounds in increasing order of acid strength: Benzoic acid, 4-Nitrobenzoic acid, 4-Methoxybenzoic acid.

21.(i) Identify the monomer in the following polymeric structure:

[ CH2-CH=CH-CH2-CH2-CH ]n

CN

(ii) On the basis of forces between their molecules in a polymer to which class doesneoprene belong?

(iii) Can both addition and condensation polymerization result in the formation of a co-polymer?

22.(i) Which of the following biomolecule is insoluble in water? Justify. Insulin, Haemoglobin, Keratin.(ii) Draw the Haworth structure for -D-Glucopyranose.(iii) Write chemical reaction to show that glucose contains aldehyde as carbonyl group.

23. John had gone with his mother to the doctor as he was down with fever. He then went to thechemist shop with his mother to purchase medicines prescribed by the doctor. There heobserved a young man pleading with the chemist to give him medicines as he had nasalcongestion. The chemist gave him cimetidine. John advised and also explained to the youngman that he should only take the medicines prescribed by the doctor.

Answer the following questions:a) Did the chemist give an appropriate medicine? Justify your answer.

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b) Johns action was appreciated by his mother. List any two reasons.24. (a) Write the mechanism of hydration of ethene to form ethanol.

(b) How are the following conversions carried out? (i) Propanol to propan-2-ol. (ii) Propanol to 1-propoxypropane.(c) Give the structure and the IUPAC name of the major product obtained in the following

reaction:OH

conc. HNO3

OR(a) Write the mechanism of the reaction of HI with methoxymethane.(b) Identify A and B in the following reactions:

(i)OH

NaOHA

(i) CO2(ii) H+

B

(ii)

A BC2H5OHCu, 573 K CH3MgBr

H2O / H+

(c) Give the structure and the IUPAC name of the major product obtained in the followingreaction:

OC2H5 conc. HNO3conc. H2SO4

25. (a) A blackish brown coloured solid (A) which is an oxide of manganese, when fused withalkali metal hydroxide and an oxidizing agent like KNO3, produces a dark green coloured

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compound (B). Compound (B) on disproportionation in neutral and acidic solution gives apurple coloured compound (C). Identify A, B and C and write the reaction involved whencompound (C) is heated to 513 K.(b)

(i) E0 M3+ / M2+values for the first series of transitionelements are given below.Answer the question that follows:

E0 (V) Ti V Cr Mn Fe CoM3+ / M2+ -0.37 -0.26 -0.41 +1.57 +0.77 +1.97

Identify the two strongest oxidizing agents in the aqueous solution from theabove data.

ii) Copper (I) ion is not known in aqueous solutioniii) The highest oxidation state of a metal is exhibited in its oxide.

OR(a) Write balanced equations to represent what happens when

(i) Cu2+ is treated with KI.(ii) Acidified potassium dichromate solution is reacted with iron (II) solution. (ionic equation)

(b)i) The figure given below illustrates the first ionization enthalpies of first, second

and third series of transition elements. Answer the question that follows

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Which series amongst the first, second and third series of transition elements havethe highest first ionization enthalpy and why?

ii) Separation of lanthanide elements is difficult. Explain.iii) Sm2+, Eu2+ and Yb2+ ions in solutions are good reducing agents but anaqueous solution of Ce4+ is a good oxidizing agent. Why?

26.i) Graphically explain the effect of temperature on the rate constant of reaction? How can

this temperature effect on rate constant be represented quantitatively?ii) The decomposition of a hydrocarbon follows the equation

Calculate EaOR

i) In the reactionQ + R ProductsThe time taken for 99% reaction of Q is twice the time taken for 90% reaction of Q.The concentration of R varies with time as shown in the figure below:

What is the overall order of the reaction? Give the units of the rate constant for thesame. Write the rate expression for the above reaction.

ii) Rate constant for a first order reaction has been found to be 2.54 x 10-3s-1. Calculate its three-fourth life.

TK

esxk 28000111 )105.4(

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(i) All questions are compulsory.

(ii) Programming Language: Section A C+ +.(iii) Programming Language : Section B Python.(iv) Answer either Section A or B, and Section C is

compulsory.

Section A (C++)

Q1. a. Differentiate between ordinary function and member functions in C++.Explain with an example. [2]

b. Write the related library function name based upon the given information inC++.

(i) Get single character using keyboard. This function is available in stdio.h file.(ii) To check whether given character is alpha numeric character or not. This

function is available in ctype.h file. [1]

c. Rewrite the following C++ program after removing all the syntactical errors (ifany), underlining each correction. : [2]

include#define PI=3.14void main( ){ float r;a;

cin>>r;a=PI*pow(r,2);

}

d. Write the output from the following C++ program code: [2]

#include#include

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void strcon(char s[]){

for(int i=0,l=0;s[i]!='\0';i++,l++);for(int j=0; j

}} ;void main(){Class C1(5),C2;C1.addmission(25);C1.ClassShow();C2.addmission();C1.addmission(30);C2.ClassShow();C1.ClassShow();

}

f. Study the following C++ program and select the possible output(s) from it :Find the maximum and minimum value of L. [2]

#include#include#includevoid main(){randomize();char P[]="C++PROGRAM";long L;for(int I=0;P[I]!='R';I++){L=random (sizeof(L)) +5;cout

char Model[10];char Date_of_purchase[10];char Company[20];

public( );AC( );

void entercardetail( );void showcardetail( );

};class Accessories : protected AC{protected:

char Stabilizer[30];char AC_cover[20];

public:float Price;Accessories( );void enteraccessoriesdetails( );void showaccessoriesdetails( );

};class Dealer : public Accessories{

int No_of_dealers;char dealers_name[20];int No_of_products;

public:Dealer( );void enterdetails( );void showdetails( );

};

(i) How many bytes will be required by an object of class Dealer and classAccessories?

(ii) Which type of inheritance is illustrated in the above c++ code? Write the baseclass and derived class name of class Accessories.

(ii) Write names of all the members which are accessible from the objects ofclass Dealer.

(iv) Write names of all the members accessible from member functions of classDealer.

Q3a) An array T[-1..35][-2..15] is stored in the memory along the row with eachelement occupying 4 bytes. Find out the base address and address of elementT[20][5], if an element T[2][2] is stored at the memory location 3000. Find thetotal number of elements stored in T and number of bytes allocated to T

[3]

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b. Write a function SORTSCORE() in C++ to sort an array of structure IPL indescending order of score using selection sort .

[3]Note : Assume the following definition of structure IPL.struct IPL{int Score;char Teamname[20];};

c. Write member functions to perform POP and PUSH operations in adynamically allocated stack containing the objects of the following structure:

[4]

struct Game{ char Gamename[30];

int numofplayer;Game *next; };

d. Write a function in C++ to print the sum of all the non-negative elementspresent on both the diagonal of a two dimensional array passed as the argumentto the function. [2]

e. Evaluate the following postfix expression. Show the status of stack afterexecution of each operation separately:

2,13, + , 5, -,6,3,/,5,*,< [2]

Q4. a. Write the command to place the file pointer at the 10th and 4th recordstarting position using seekp() or seekg() command. File

[1]

b. Write a function in C++ to count and display the no of three letter words in[2]

Example:

If the file contains:A boy is playing there. I love to eat pizza. A plane is in the sky.Then the output should be: 4

c. Given the binary file CAR.Dat, containing records of the following class CARtype: [3]

class CAR{

int C_No;char C_Name[20];float Milage;

public:void enter( )

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{cin>> C_No ; gets(C_Name) ; cin >> Milage;}

void display( ){cout

COMPANYCID NAME CITY PRODUCTNAME

111 SONY DELHI TV

222 NOKIA MUMBAI MOBILE

333 ONIDA DELHI TV

444 SONY MUMBAI MOBILE

555 BLACKBERRY MADRAS MOBILE

666 DELL DELHI LAPTOP

CUSTOMERCUSTID NAME PRICE QTY CID

101 Rohan Sharma 70000 20 222

102 Deepak Kumar 50000 10 666

103 Mohan Kumar 30000 5 111

104 Sahil Bansal 35000 3 333

(i) To display those company name which are having prize less than 30000.(ii) To display the name of the companies in reverse alphabetical order.(iii) To increase the prize(iv) To add one more column totalprice with decimal(10,2) to the table customer(v) SELECT COUNT(*) ,CITY FROM COMPANY GROUP BY CITY;(vi) SELECT MIN(PRICE), MAX(PRICE) FROM CUSTOMER WHERE QTY>10 ;

(viii) SELECT PRODUCTNAME,CITY, PRICE FROM COMPANY,CUSTOMER

Q6. a) State and define principle of Duality. Why is it so important in BooleanAlgebra? [2]

b) Write the equivalent boolean expression for the following logic circuit [2]

105 Neha Soni 25000 7 444

106 Sonal Aggarwal 20000 5 333

107 Arjun Singh 50000 15 666

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c) Write Product Of Sum expression of the function F (a,b,c,d) from the giventruth table [1]

a b c d F

00000000111

00001111000

00110011001

01010101010

00110110001

d) Obtain the minimal SOP form for the following boolean expression using K-Map.F(w,x,y,z) = (0,2,3,5,7,8,10,11,13,15) [3]

Q7.a.Give any two advantage of using Optical Fibres. [1]

b. Indian School, in Mumbai is starting up the network between its differentwings. There are Four Buildings named as SENIOR, JUNIOR, ADMIN andHOSTEL as shown below.: [4]

11111

01111

10011

10101

10001

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SENIOR

JUNIOR

ADMIN

HOSTEL

The distance between various buildings is as follows:ADMIN TO SENIOR 200mADMIN TO JUNIOR 150mADMIN TO HOSTEL 50mSENIOR TO JUNIOR 250mSENIOR TO HOSTEL 350mJUNIOR TO HOSTEL 350m

Number of Computers in Each BuildingSENIOR 130JUNIOR 80ADMIN 160HOSTEL 50

(b1) Suggest the cable layout of connections between the buildings.(b2) Suggest the most suitable place (i.e. building) to house the server of thisSchool, provide a suitable reason.(b3) Suggest the placement of the following devices with justification. Repeater Hub / Switch(b4) The organization also has Inquiry office in another city about 50-60 Kmaway in Hilly Region. Suggest the suitable transmission media to interconnect toschool and Inquiry office out of the following .

Fiber Optic Cable Microwave Radio Wave

c. Identify the Domain name and URL from the following. [1]

http://www.income.in/home.aboutus.hmld. What is Web Hosting? [1]e. What is the difference between packet & message switching? [1]f. Define firewall. [1]g. Which protocol is used to creating a connection with a remote machine? [1]

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