nkšãiy kjyh« m©l - chief educational officer · y m pv wlx ikj ªx ¯ji jy q ¯jg*ym y/y-...

nkšãiy Kjyh« M©L

ä‹ ÏaªÂu§fS« rhjd§fS«

neu« : 2½ kâ : 90

- m 15 x 1 = 15

I.

Ï

fhªj

------------

d

H2O M) H2So4 Ï) So4 <) Pb

?

2 4 1

š

---------

----------

ÏU«

- M 10 x 3 = 30

- Ï 5 x 5 = 25

- < 2 x 10 = 20

% HP

---------

1

nnkšãiy Kjyh« M©L

mmwÏaš

fhy«: 2 ½ kâ kÂ¥bg© : 90

gFÂ – I

: (20 x 1 = 20)

1. Ethos

(<)

2.

(m)

(<)

3.

(m) rka« (M) nahfh

(<) M‹Ûf«

4.

(<)

5.

(M)

(Ï) (<)

6. xU khzt‹ nkšãiy¥

(M)

(<)

7.

aš aš

( aš (<) aš

8.

(m)

(Ï) (<)

2

9. ‘ ’ ehLf F

(m) (M) -

(<)

10.

(m) muR (M) FL«g«

(Ï) rKjha« (<) ehL

11.

(M) rçahdit

(<)

12.

(m) 1945-« M©L (M) 1955-« M©L

(Ï) 1975-« M©L (<) 1965-« M©L

13.

(m) (M)

(Ï) (<) thšÛ»

14. ?

(m) fšé (M) c©ik

(Ï) ÚÂ (<) f

15.

(m) c©ik ngRjš (M)

( (<) ãZ

16. m

m) ehL (M) r_f«

17.

(m) kfçî gjŠrè (M) ïu©a f

(Ï) thšÛ»

18.

(m) nahfhrd«

(<) Ïka«

3

19.

(m) jhuiz (M) Ïka«

(Ï) ãak« (<) fêKf«

20.

ggFÂ – II

(7 x 2 = 14)

f©o¥ghf

21. ?

22. ?

23. ?

24. ?

25. rKjha ey‹ v‹whš v‹d?

26. ?

27. -

28. ?

29. d

30. Mrd« v‹whš v‹d?

gFÂ – III

VnjD« 7

(339 édh f©o¥ghf )

(7 x 3 =21)

31. ?

32. ?

33.

34.

35. mf

36. ?

37. ?

38. ?

39. ?40.

4

ggFÂ -- IV

(7 x 5 = 35)

41.

42. a

43. j‹d ?

f

44.

?

45.

?

46. ?

–

47.

-------

nnkšãiy Kjyh« M©L

czÎ nkyh©ikÍ« FHªij eyD«

kÂ¥bg© 900

neu« : 2 1/2 kâ 15 X 1 = 15

gFÂ - m

15 X 1 = 15

1.

2.

m) <

3.

m) WHO M) ICMR Ï) UNICEF <) UNESCO

4.

5.

B1 B2

B6 B12

6.

<) btšy«

7. ?

M) iunghÃn

M) e

8.

9.

m)

Ï)

M)

10.

-

11.

m) 2 % M) 3 % Ï) 4 % <) 5 %

12. d«

13. “ ”

Ï) 2 –

<) 12 –

14. IQ

m) 110 - 115 M) 116-132

Ï) 117 – 133

<) 118 - 134

15.

m) ïšyhç

<) eȫ

ggFÂ -- MM

10 X 3 = 30

16.

17.

18.

19.

20. L

21.

22.

23. D

24.

25. .

26.

27.

28. ABC

gFÂ – ÏÏ

X 5 = 25

29.

30.

31.

32.

33.

34.

35.

ggFÂ -- <<

2 X 10 = 20

36.

étç.

37.

–

--------

1

nnkšãiy Kjyh« M©L

bghJ ÏaªÂuéaš(gâkid¥ bgh¿æaš)

fhy« : 2 1/2 kâ : 90

gFÂ - I 15 x 1 = 115

1. bbjhê‰rhiyæš bghU£fis

m) M)

Ï) Kjyhë <)

2. KKjš cjé v‹gJ

m)

Kiw

M)

Ï)

V‰gL«nghJ bfhL¡f¥gL«

<)

3.

m) u~¥igš M) brf©L f£ igš

Ï) <)

4.

m) msÎ nfhš M)

Ï) £u«kš <)

5.

m) msÎnfhš M)

Ï) <)

6.

m) M)

Ï) <)

7. MM¡Á#nd‰w« v‹gJ

m) M)

Ï) <)

8.

m) M)

Ï) <)

9.

m) M)

Ï) <)

10. I.S.I. m) V‰f¥gL« msÎ M)

Ï) <)

2

11.

m) M)

Ï) <)

12.

m) 100 br.Û. M) 25 br.Û.

Ï) 40 br.Û. <) 50 br.Û.

13.

m) Û ² M) ² Ï) Û ³ <)

14.

m) 50 c/s M)

Ï) <)

15.

m) bA‹¿~ngaš M)

Ï) F.W. <)

ggFÂ – II

«« 110 x 33 = 30

( )

16.

17. fUéfë‹

18.

19. cnyhf§fë‹ K¡»a

20.

21. .

22.

23. R.P.M.

24.

25. ohms, 8 ohms 12 ohms v

26.

27.

3 28.

ggFÂ – III

: 55 x 5 = 25

29.

30.

31. Engineering Materials Properties

32.

33.

34.

35.

gFÂ -- IV : 2 x 10 = 20

36.

(mšyJ)

è¥gç‹ (Vernier Caliper

37.

(mšyJ)

**********

HIGHER SECONDARY IST YEAR

GEOGRAPHY

MODEL QUESTION PAPER Time : 2.30 hrs Maximum Marks : 70

PART – I

I Choose the Correct answers :- 15 x 1 = 15

Answer all the questions:-1. The Broadest Earth Eco-system

a) Lithosphere b) Stratosphere c) Biosphere d) Mesosphere

2. The Earth shape is

a) Spherical b) Round c) Circular d) Cylinderical

3. The crust and upper layer of the mantle together make up a zone called

a) Hydrosphere b) Lithosphere c) Biosphere d) Plate

4. Evergreen forest are found around the

a) Polar region b) Temperate region

c) Subtropical region d) Equatorial region

5. This energy is the primary source of energy for all surface phenomena and life on eartha) Sun’s energy b) Wind energy

c) Electrical energy d) Tidel energy

6. This is a warm current

a) Canary Current b) Peru Current

c) Gulf stream Current d) Labrador Current

7. Eucalyptus tree is the native of

a) Australia b) Africa c) Asia d) Europe

8. The second population increase corresponds to

a) discovery of fire b) domestication of plants

c) scientific and industrial revolutions d) period of computers

9. The planet which is called a snow ball is

a) Jupiter b) Earth c) Mercury d) Pluto

10. Rio Grande rift is in

a) Kenya b) Ethiopia c) New Mexico d) Indonesia

11. The discovery of this made a significant change in the attitude of humans.

a) Agriculture b) Fire c) Wheel d) Iron

12. The largest ocean on the Earth is

a) Atlantic Ocean b) Indian Ocean c) Arctic Ocean d) Pacific Ocean

13. Weather phenomena such as clouds, thunder storm, lightning and rain take place is this layer of atmosphere.

a) Troposphere b) Mesosphere c) Thermosphere d) Stratosphere

14. This is an important constituent of Cell membrane.

a) oxygen b) carbon c) phosphorous d) nitrogen

15. Desert cover about ---------- of the Earth’s surface.

a) 1/4th b) 1/5th c) 1/3rd d) 2/3rd

PART – II

II Answer any six (6) questions, Which Question No.20 is compulsory.

6 x 2 = 12

16. Write a short note on Deforestation?

17. What are earth movements?

18. Define – weathering.

19. What is continental shelf?

20. Write a short note on chemical composition of the atmosphere.

21. Eco-system - define.

22. Give an account of Taiga Forest?

23. What are concept maps?

24. Write short notes on Igneous rocks.

PART – III

Answer any six question, in which Question No.25 is compulsory.

6 x 3 = 18

25. The fire became one of the important ecological tools – explain?

26. Explain the planetary system.

27. Describe the lithosphere.

28. Draw a diagram on Ocean floor topography.

29. Differentiate Troposphere and Stratosphere.

30. Describe carbon cycle.

31. Name the cultural energy inputs in an agricultural biomes.

32. Population growth – explain.

33. The sun’s energy is the primary source of energy – Explain.

PART – IV

Answer all the questions. 5 x 5 = 25

34. Illustrate human environment relationship.

(OR)

Explain the universe and its sub system with diagram.

35. Soil is an important natural resource – Elucidate?

(OR) How are gyres formed? Describe North Atlantic gyre.

36. Write about the importance of ozone layer.

(OR)

Explain different layers of the atmosphere?

37. What are the basic components of an eco system? Describe them.

(OR)

Write in detail about the grassland biomes.

38. Explain – desert biomes.

(OR)

What are concept maps? Illustrate with an example.

--------

1

HIGHER SECONDARY IST YEAR

HISTORY

MODEL QUESTION PAPER

TIME : 2 ½ Hours MARKS : 90

PART - I

Answer all the questions.Choose the correct answer

20 X 1 = 20

1. The region between two rivers is calleda) Plateaub) Peninsulac) Islandd) Doab

2. The highest Peak in the Southern Peninsula isa) Mt.Everestb) Anaimudic) Doddabettad) Mt.Abu

3. The Port City of the Harappan Culturea) Kalibanganb) Lothalc) Banawalid) Rupar

4. The Arctic home for the Aryans was suggested bya) Gokhaleb) Bala Gangadhara Tilakc) D.P.Agarwald) Fairservis

5. Vardhamana Mahavira was born ata) Kapilavastub) Pataliputrac) Kundagramad) Kusumapura

6. The capital of Magadha wasa) Rajagrihab) Ujjainc) Kosalad) Kausambi

2

7. The details of Asoka’s war with Kalinga is given in thea) Kalinga Edictb) XIII Rock Edictc) Saranath Pillard) Arthasastra

8. Nasik inscription describes the achievements ofa) Pushyamitra Sungab) Gautamiputra Satakarnic) Kanishkad) Menander

9. List the correct order of places held Buddhist Council1. Vaisali 2. Kashmir 3. Rajagriha 4. Pataliputraa) 1,2,3,4b) 2,4,1,3c) 2,4,3,1d) 2,1,3,4

10. The earliest Tamil grammar work of the sangam perioda) Nannoolb) Tolkappiyamc) Sathuragarathid) Tirukkural

11. The Gupta era starts from the yeara) 310 A.D.b) 320 A.D.c) 330 A.D.d) 300 A.D.

12. The founder of Nalanda Universitya) Samudraguptab) Chandragupta IIc) Kumaraguptad) Skandagupta

13. The Banskhera inscriptions contains the signature ofa) Hiuen Tsangb) Banac) Harshad) Pulakesin II

14. The Pallava ruler who destroyed the Kalabhrasa) Vishnugopab) Simhavishnuc) Mahendravarman Id) Rajasimha

3

15. The author of Kitab-i-Hind a) Firdausib) Baranic) Mahmudd) Alberuni

16. Sequential order of Delhi Sultans1) Khalji2) Slave3) Sayyids4) TughIaq

a) 1, 2, 3, 4 b) 2,1,4,3 c) 1,2,4,3 d) 3, 4, 2, 1

17. The Kotla fort at Delhi was the creation ofa) Firoz Tughlaqb) Iltutmishc) Alauddin Khaljid) Sikkandar Lodi

18. The most famous disciple of Ramanandaa) Kabirb) Ramadasc) Namadevad) Chaitanya

19. Krishna Deva Raya belonged to dynasty ofa) Sangamab) Saluvac) Tuluvad) Aravidu

20. St.George Fort is located at a) Kolkattab) Chennaic) Delhid) Mumbai

PART - II

Explain any seven Questions briefly. In which

Question No.30 is compulsory

7 X 2 = 14

21. Deccan Plateau

22. The Great Bath

23. Tripitakas

24. Kadai Yelu Vallalhal

4

25. Kautilya’s Arthasastra

26. Aryabatta

27. Qutab Minar

28. Din Illahi

29. Faterpur sikri

30. Comments on Raziya’s bravery

PART - III

Answer any 7 Questions. Out of which Question No.40 is compulsory

7 X 3 = 21

31. Briefly Describe the Geography of South India

32. Write a note on the old stone Age

33. Account for the decline of Buddhism in India

34. Trace the causes for the rise of Marathas

35. Write a note on the Internal and foreign trade under the

Mughals

36. Write the development of Tamil literature under the Cholas

37. Explain: Nalanda University

38. Examine the market reforms of Alauddin Khalji

39. Write a short note on Indo-Java Art

40. Explain the reasons of the British Victory over the French

PART - IV

Answer all the Questions 7 X 5 = 35

41. India is a land of unity in diversity - Elucidate

(or)

Give a brief account of the life and teachings of Buddha

42. Give an account of Alexander’s invasion of India

(or)

Give an account of Ashoka’s achievements and his policy of

Damma

5

43. Give an account of Achievements of Samudragupta

(or)

Mention the salient features of the Pallava Art

44. Examine the Achievements of Rajaraja I

(or)

Give an account of the spread of Indian Culture in South-East

Asia.

45. Estimate the achievements of Krishna Devaraya

(or)

Assess the achievements of Akbar

46. Examine the salient features of the Mughal Art and Architecture

(or)

Give an account of the Life and Achievements of Shivaji

47. Mark the extent of the Gupta’s empire and mark the following

place on India Map.

Pataliputra, Vaisali, Prayag, Malwa, Magadha

(or)

Draw the time line chart Marking any five incidents from 1600

A.D. to 1700 A.D.

-------

1

nnkšãiy Kjyh« M©L

tuyhW

neu«: 2 ½ kâ : 90

gFÂ - m

20 X 1 = 20

2

-

â

3

gh‹

-Ï-

<

4

ggFÂ – II

-

7 X 2 = 14

21

gFÂ - III

éédh

-

7 X 3 = 21

31

tiuf

f

:

5

-

ggFÂ - IV

7 X 3 = 21

41

6

VnjD«

-------

Home Science

Standard XI Maximum Mark : 70

Time 02.30 Hours PART - A

I. Answer all the questions

Choose the Correct Answer 15 X 1 = 15

1. _________ Million people in India are homeless

A) 35 B) 53 C) 21 E) 25

2. The role played by _________ mission helped to attain full literacy

A) IMY B) NLM C) BSY D) CSWB

3. ______ mineral is essential for blood clotting

A) Iron B) Sodium C) Calcium D) Iodine

4. _____ is required to bind bones together

A) Joints B) Suture C) Collagen D) Bone marrow

5. ______ rich food is required for growth and repair of body tissues

A) Carbohydrate B) Vitamin C) Protein D) Fat

6. Braising is a combined method of ________

A) Roasting and stewing B) Pan boiling and frying C) Poaching and simmering D) Steaming and grilling

7. In a _________ birth the foetus is positioned crosswise in the mothers uterus.

A) Transverse B) Breech C) Natural D) Instrument

8. Tuberculosis is the childhood disease spreads through ______

A) food B) air C) water D) soil

9. _______ shape is good for Kitchen

A) “U” B) “L” C) “g” D) “V”

10. When yellow and blue colour is mixed in equal proportions we get _______ colour

A) Orange B) Violet C) Green D) Yellow Green

11. ______ fabrics is popularly used during special occassionsss.

A) Cotton B) Silk C) Wool D) Nylon

12. This is a simplest form of weaving A) Novelty B) Rib C) Plain D) Basket

13. Suggest a dye that long last on Protein fibers. A) Vat B) Basic C) Acid D) Direct

14. In _______ model of communication, the source encodes a message and sends it to the receiver through one or more of the sensory channels.

A) Transactional B) Interaction C) Linear D) Multi directional

15. _______ is an art, serving feast for the eyes, ears and mind simultaneously.

A) Puppet show B) Folk dance

C) Folk song D) Drama

PART - B 6 X 2 = 12

II. Answer any Six questions out of which Question No.17 isCompulsory .

16. Why Home Science education is called as an interdisciplinary course?

17. Define Osteoporosis.

18. Give any two sources of Vitamin – C.

19. Mention the two periods in infancy.

20. Give few examples for warm and cool colours and its applications.

21. Give any two physical properties of wool fibre.

22. Classify teaching methods.

23. Give the diagram for Transactional Model.

24. Why is infancy a plateau in development?

PART – C

III. Answer any Six questions out of which question No.24 iscompulsory.

6 X 3 = 18

25. Write the mechanism of blood clotting. 26. Who are the beneficiaries of the programs implemented by the

Department of social defense. ?

27. Name the facial bones.

28. How do you classify foods according to their functions?

29. What are the foods to be included in a pregnant women’s diet? Give reason.

30. What type of discipline is adopted by your parent in your home? Why do you think so? Give reason.

31. What are the factors to be considered while selecting a site?

32. How is Batik done on fabrics?

33. What are the three factors that control communicable diseases?

PART – D

IV. Answer all the questions 5 X 5 = 25

34. What are the differences between formal and extension education ? (Or) Write a short note on the Vertebral Column.

35. Write a short note on Cancer. (Or) How will you plan a menu for a Pre-School Child? Give reason.

36. List some of the childhood diseases and write on the measures taken to overcome.

(Or) Explain the different emotions expressed by children.

37. Draw the floor plan and explain how would you make provisions for various activities in a one room apartment.

(Or) How would you select and preserve flowers while making flower arrangement?

38. Discuss weaving mechanism and its operation. (Or) Explain the functions of communication.

kkidæaš

11--« tF¥ò kÂ¥bg© 70

neu« 2.30 kâ gFÂ -- mm 15 X 1 = 15

I.

1.

m) 35 M) 53 Ï) 21 <) 25

2.

m) IMY M) NLM Ï) BSY <) CSWB

3.

m) ÏU«ò M) Ï) <)

4.

5.

m) M)

Ï) <)

6.

M)

<)

7.

°

8.

<) k©

9.

m) “U” M) “L” Ï) “g” <) “V”

10.

m) MuŠR Ï)

11.

12.

M) ç¥ Ï) <)

13.

M) Ï) <)

14.

15.

<)

ggFÂ -- MM 6 X 2 = 12

II. ..

16. kid

17.

18. -C

19.

20.

21.

22.

23. ia tiu .

24.

ggFÂ – ÏÏ 6 X 3 = 18

III.

25.

26.

27.

28.

29.

30.

31.

32.

33.

ggFÂ -- <<

5 X 5 = 25

IV.

34.

35.

TW.

36.

37.

38.

nnkšãiy Kjyh« M©L

: 90

: 2 ½ kâ neu«

gFÂ - m

ééilaë

15 X 1 = 15

1.

M. gâia

2. ............................................. eÅd nkyh©ikæ‹ jªij.

M.F.W.

Ï. bA‹¿ ~ngahš

3. ............................................. braš.

4.

<.

5. .

6. .

<. v‹.Á.Á.

7. .

m. nkšãiy

M. eLãiy

8.

¡ .

<.

9.

10.

m. _‹W

M. Ïu©L

11.

Ï. jiy

12. ...............................

13. Y

Ï. eLãiy

14.

M. W.G.

<. kh°nyh

15

.

gFÂ - M

ééilaë

(édh v©. 27

10 X 3 = 30

16. .

17.

18.

19.

20.

21. .

22.

23.

24.

25.

26.

27.

28.

ggFÂ - Ï

éilaë

5 X 5 = 25

29.

30. nkyh©ik

31.

32.

33.

34.

35.

gFÂ - <

ééilaë 2 X 10 = 20

36. .

.

37.

.

-------

HIGHER SECONDARY IST YEAR

MATHEMATICS

MODEL QUESTION PAPERTIME:2 ½ HOURS Max.Marks:90

PART-I

All questions are compulsory.Choose the correct answer.

1. Number of elements in a matrix of order 2x3 is (a) 5 (b) 2 (c) 3 (d) 6

2. If A is a square matrix of order 4 then | |is (a) | | (b)K2| |P

(c)K3 | | (d)K4| |3. If “G” is centroid of the triagle ABC and ‘O’ is any other point then

+ + = is equal to

(a) (b) (c) 3 (d)4

4. If =2 and = - then the magnitude of - is

(a) 1 (b)9 (c)3 (d) 3

5. A polygon has 44 diagonals, then the number of its sides is (a) 11 (b)7 (c)8 (d)12

6. ( )( ) = _ then A is

(a)13 (b)-13 (c)-10 (d) 10

7. The A.M., G.M., H.M., between two positive numbers a and b are equal then

(a) a=b (b)ab=1 (c)a > b (d) a < b

8. If an = n2 3 –n then the third term is

(a) (b) 1 (c) (d) 3

9. If the pair of straight lines given by ax2+2hxy+by2=0 are perpendicular,then

(a) ab=0 (b) a+b=0 (c) a-b=0 (d) a=0

10. The radius of the circle x2+y2-2x+4y-4=0 is (a) 1 (b) 2 (c) 3 (d) 4

11. If cos =0 then is (a)n (b) (2n+1) (c) (d) -n

12. If the terminal side is collinear with the initial side in the opposite direction, then the angle included is (a) 0 ° (b) 90° (c)180° (d)270°

13. The range of the function logex is

(a) (0, ) (b) (- , ) (c) (- (d) [0, )

14. The value of 3.5 is (a) 2 (b) 3 (c) 4 (d) 5

15. ( ) is

(a) (b) (c) (d)

16. lim 1 + is

(a) e (b) ex (c) e3 (d)

17. log = is

(a) +c (b) ( )

+C (c ) x log + + (d) x log +18. sin 3 ( ) is

(a) e2x (2sin 3x - 3 cos 3x)+c (b) e2x (3sin 2x - 2 cos 2x)+c 13 13

(c) e2x (2sin 3x + 3 cos 3x)+c (d) e2x (3cos 3x + 2 sin 3x)+c 13 13

19. If two events A and B are independent then P(A/B)= ------------(a) P(A) (b) P(A B) (c) P(A)=P(B) (d) P(A)

P(B)20. X speaks truth in 95 percent of cases and Y in 80 percent of cases.

The percentage of cases they likely to contradict each other in stating same fact is

(a) 14% (b) 86% (c) 23% (d) 85.5%PART - II

Answer any SEVEN questions. 7 x 2 = 14Question 30 is compulsory.

21. 2

a1 b1 = a12+a2

2 a1 b1+ a2 b2

Prove that a2 b2 a1 b1+ a2 b2 b12 + b2

2

22. If ABC and A B C are two triangles and G, G be their corresponding

centroids, prove that + + =3

23. If 10Pr = 5040, find the value of r.

24. A point moves so that it is always at a distance of 6 units from the point (1, -4). Find its locus.

25. Simplify : Cos (-870°)

26. If f,g : R R, defined by f(x)=x+1 and g(x)=x2 then find (fog) (3)

27. Find d2y if y=x3-6x2+7x+6dx2

28. Evaluate : 29. Three coins are tossed once. Find the probability of getting atleast two

heads.30.

show that = ………………………. PART III

Answer any SEVEN questions. 7x3=21Question 40 is compulsory.

31. Prove that the sum of the vectors directed from the vertices to the mid-point opposite sides of a triangle is zero.

32. Find the co – efficient of x5 in the expansion of + P2

33. Find 5 geometric means between 576 and 9.

34. The slope of one of the straight lines ax2+2hxy+by2=0 is twice that of the other, show that 8h2=9ab.

35. Show that : Sin20o Sin40° Sin 80° = 36. Let f: R R be defined by f (x) = 3x+2 find P and show that

fo P = P of=I.

37. Evaluate : Lim 1 + – 1x 0 Sin-1 x

38. Integrate : (3 + 4) 3 + 7 dx

39. Two cards are drawn from a pack of 52 cards in succession. Find the probability that both are kings when,(i) The first drawn card is replaced (ii) The card is not replaced.

40. Find k so that A2 = KA – 2I where A = 3 24 2

PART -IV

Answer all the question : 7x5=3541. Using factor theorem prove that

(b+c)2 a2 a2

b2 (c+a)2 b2 = 2abc (a+b+c)3 c2 c2 (a+b)2

(Or)

Examine whether the vectors +3 + , 2 – - and 7 +5 are coplanar.

42. If A + B = 45°, show that (1 + tanA) (1 + tanB) = 2 and hence deduce the value of tan 22 °

(Or)

State and prove Napier’s formulae.

43. Prove by Mathematical Induction

12+22+32+.........................................+n2 = n(n+1) (2n+1) ,for all n N6

(Or)

If a,b,c are in H.P. Prove that + = 2

44. Find the equation of the circle passing through the points (1,1), (2,-1) and (3,2).

(Or) Find the co-ordinates of orthocentre of the triangle formed by the

straight lines x – y – 5 = 0, 2x – y – 8 = 0 and 3x – y – 9 = 0

45. If y = cos (sinx), Prove that + + = 0(OR)

For

< 1 and for any rational index n, prove that

lim =na n-1 (a 0)

46. Evaluate the definite integral as limit of sum (2 + 5)

(OR)

Evaluate

47. If x is real, prove that the range of f(x) = x2-2x+4 is between [ , 3]

x2+2x+4(OR)

In a bolt factory machines A1, A2, A3 manufacture respectively 25%, 35% and 40% of the total output of these 5, 4, 2 percent are defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine A2?

------

nnkšãiy Kjyh« M©L

fâjéaš

nneu« :2.30 kkâ kÂ¥bg©:90

gFÂ--I

2x

(m) 5 (M) 2 (Ï) 3 (<) 6

A | |

(m)K| | (M)K2 | | (Ï)K3 | | (<)K4| | ABC G O D

+ + =

(m) (M) (Ï) 3

=2 = - - -

(m) 1 (M)9 (Ï)3 (<) 3

(m) 11 (M)7 (Ï)8 (<)12

( )( ) = _ A-

(m)13 (M)-13 (Ï)-10 (<) 10

a,b A.M., G.M., H.M., M»ait

(m) a=b (M)ab=1 (Ï)a > b (<) a < b

an = n2 3 –n - 3

(m) (M) 1 (Ï) (<) 3

ax2+2hxy+by2=0

(m) ab=0 (M) a+b=0 (Ï) a-b=0 (<) a=0

x2+y2-2x+4y-4=0

cos =0 -

(m) n (M) (2n+1) (Ï) (<)-n

(m) 0 ° (M) 90° (Ï)180° (<)270°

logex -

(m) (0, ) (M) (- , ) (Ï) (- (<) [ )

3.5 -

(m) 2 (M) 3 (<) 5

( ) =

(m) (M) ) Ï) (<)

lim 1 + =

(m) e (M) ex (Ï)e3 (<)

log =(m) +c (M)

( ) +C (Ï ) x log + + (<)x log +

sin 3 ( ) =

(m) e2x (2sin 3x - 3 cos 3x)+c (M) e2x (3sin 2x - 2 cos 2x)+c 13 13

(Ï) e2x (2sin 3x + 3 cos 3x)+c (<) e2x (3cos 3x + 2 sin 3x)+c 13 13

A B P(A/B)= ------------(m) P(A) (M) P(A B) (Ï) P(A)=P(B) (<) P(A)

P(B)

X, Y

% (M)86% (Ï) 23% (< %

ggFÂ--II x 2 =14

2

a1 b1 = a12 a2

2 a1 b1+ a2 b2

a2 b2 a1 b1+ a2 b2 b12 + b2

2

ABC A B C

G G + + =3

10Pr = 5040 r-

(1, -4)

: Cos (-870°)

f,g : R R f(x)=x+1, g(x)=x2

fog) (3)-

y=x3-6x2+7x+6 d2y -

dx2

-

= ……………………….

ggFÂ-III 7x3=21

xU K

+ - x5-

ax2+2hxy+by2=0 8h2=9ab

: Sin20o Sin40° Sin 80° =

f: R R f (x) = 3x+2 P -fo P = P of=I

: Lim 1 + – 1x 0 Sin-1 x

(3 + 4) 3 + 7 dx

A = 3 24 2 A = KA 2I K fh©f

ggFÂ--IV 7x5=35

(b+c)2 a2 a2

b2 (c+a)2 b2 = 2abc (a+b+c)3

c2 c2 (a+b)2

(

+3 + , 2 – - , 7 +5

+ = 45° (1 + tan A) (1 + tan B)= 2 tan 22 °

12+22+32 n2 = n(n+1) (2n+1) ,for all n N 6

a,b,c M»ait H.P- +

(1,1), (2,-1)

x – y – 5 = 0, 2x – y – 8 = 0 3x – y – 9 = 0

y = cos (sinx) + + = 0

n < 1 lim =na n-1 (a 0)

(2 + 5)

:

x f(x) = = x2-2x+4 f« [ , 3]

x2+2x+4

A1, A2, A3 %, 35%, %

%, 4%, 2%

A2- ?-------