Education Telugu 21-01-2018

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 21,  2019 - 

Lenticels are mainly involved in..

BIOLOGY 1. A major characteristic of monocot root is the presence of 1) vasculature without cambium 2) cambium sandwiched between phloem and xylem along the radius 3) open vascular bundles 4) scattered vascular bundles 2. Vascular bundles in monocotyledons are considered closed because 1) there no vessels with perforations 2) xylem is surrounded all around by phloem 3) a bundle sheath surrounds each bundle 4) cambium is absent 3. Read the different components from (i) to (iv) in the list given below and tell the correct order of the components with reference to their arrangement from outer side to inner side in a woody dicot stem. i) Secondary cortex ii) Wood iii) Secondary phloem iv) Phellem The correct order is 1) iv, i, iii, ii 2) iv, iii, i, ii 3) iii, iv, ii, i 4) i, ii, iv, iii 4. Tracheids differ from other tracheary elements in 1) having casparian strips 2) being imperforate 3) lacking nucleus 4) being liquified 5. Lenticels are mainly involved in 1) food transport 2) photosynthesis 3) transpiration 4) gaseous exchange 6. Interfascicular cambium develops from the cells of 1) endodermis 2) pericycle 3) transpiration 4) xylem parenchyma 7. Companion cells are closely associated with 1) sieve elements 2) vessel elements 3) trichomes 4) guard cells 8. Water containing cavities in vascular bundles are found in 1) sunflower 2) maize 3) cycas 4) pinus 9. As compared to a dicot root, a monocot root has 1) more abundant secondary xylem 2) many xylem bundles 3) inconspicuous annual rings 4) relatively thicker periderm 10. Ground tissue includes 1) all tissues external to endodermis 2) all tissues except epidermis and vascular bundles 3) epidermis and cortex 4) all tissues internal to endodermis 11. The cork cambium, cork and secondary cortex are collectively called 1) phelloderm 2) phellogen 3) periderm 4) phellem 12. The function of companion cells is to 1) provide energy to sieve elements for active transport 2) provide water to phloem 3) load sucrose into sieve elements by passive transport 4) load sucrose into sieve elements by active transport 13. Some vascular bundles are described as open because these 1) are surrounded by pericycle but no endodermis 2) are capable of producing secondary xylem and phloem 3) possess conjunctive tissue between xylem and phloem 4) are not surrounded by pericycle

14. Palisade parenchyma is absent in leaves of 1) mustard 2) soya bean 3) gram 4) sorghum 15. In barley stem, vascular bundles are 1) closed and scattered 2) open and in a ring 3) closed and radial 4) open and scattered 16. Passage cells are thin – walled cells found in 1) phloem elements that serve as entry points for substance for transport to other 2) testa of seeds to enable emergence of growing embryonic axis during seed germination 3) central region of style through which the pollen tube grows towards the ovary 4) endodermis of roots NEET facilitating rapid Special transport of water from cortex to pericycle 17. (A): No secondary growth takes place in monocots (R): Secondary growth is not related with cambium 1) both(A) and (R) are true, and (R) is the correct explanation of (A).

2) both (A) and (R) are true, and (R) is not the correct explanation of (A).

3) (A) is true (R) is false 4) both (A) and (R) are false 18. Sclerenchyma usually _ _ _ _ and _ _ _ _ protoplasts.

1) live, without 2) dead, with 3) live, with 4) dead, without 19. Which of the following statements is/are true? a) Uneven thickening of cell wall is characteristic of sclerenchyma. b) Periblem forms cortex of the stem and the root c) Tracheids are the chief water transporting elements in gymnosperms. d) Companion cell is devoid of nucleus at maturity e) The commercial cork is obtained from Quercus suber.

1) a and d only 2) b and e only 3) c and d only 4) b, c and e only 20. (A) : Vessels are more efficient for water conduction as compared to tracheids (R): Vessels are dead lignified.

1) both(A) and (R) are true, and (R) is the correct explanation of (A).

2) both (A) and (R) are true, and (R) is not the correct explanation of (A).

3) (A) is true (R) is false 4) both (A) and (R) are false 21. Study the following lists ...............

LIST – I LIST – II 1) Primary meristem I. Interfascicular cambium 2) Secondary meristem II. Intercalary meristem 3) Apical meristem III. Shoot apex 4) Lateral meristem IV. Intra fascicular cambium V. Phellogen The correct match is A B C D 1) V II IV I 2) IV III V II 3) IV V III I 4) I IV III V 22. Study the following lists

LIST – I LIST – II 1) Bean shaped guard cell I. Adaxial tissue 2) Trichomes II. Dicot leaf 3) Bulliform cells III. Abaxial tissue 4) Palisade parenchyma IV. Monocot leaf V. Stem epidermis The correct match is A B C D 1) II IV I V 2) II I IV V 3) II III IV I 4) II V IV I 23. Study the following lists LIST – I LIST – II 1) Bast I. Periderm + bast 2) Phelloderm II. Dead impervious tissue 3) Bark III. Secondary phloem 4) Cork IV. Lignified tissue V. Secondary cortex The correct match is A B C D 1) III I V II 2) III V I II 3) II I IV III 4) IV II III I 24. Study the following lists LIST – I LIST – II 1) Heart wood I. Tannins 2) Spring wood II. Conduction 3) Sap wood III. Large xylem vessels 4) Autumn wood IV. Cork cambium V. Narrow xylem vessels The correct match is A B C D 1) I II III V 2) II III I IV 3) I III II V 4) I V IV II 25. Study the following lists LIST – I LIST – II 1) Epidermis I. Lateral roots 2) Endodermis II. Secondary cambium 3) Pericycle III. Stomata 4) Conjugative tissue IV. Cuticle V. Suberized walls The correct match is A B C D 1) I II III IV 2) II III IV I 3) IV V I II 4) IV I V II 26. Study the following lists LIST – I LIST – II 1) Dicot stem I. Exarch xylem 2) Monocot leaf II. Ground tissue 3) Monocot stem III. Secondary growth 4) Dicot root IV. Collenchymatous hypodermis V. Bundle sheath The correct match is A B C D 1) IV I V III 2) IV II I V 3) IV I III V 4) IV V II III 27. Study the following lists LIST – I LIST – II 1) Autumn wood I. Hard and highly durable 2) Spring wood II. Main role in conduction 3) Heart wood III.Constitutes one annual ring 4) Spawood IV. Lighter in appearance V. Narrow xylem vessels

Nakrekanti Seenaiah Senior Faculty NEET expert Hyderabad 8008969621

The correct match is A B C D 1) V IV I II 2) II III IV I 3) V II I IV 4) III IV V I 28. Study the following lists LIST – I LIST – II 1) Complimentary cells I. Thin walled parenchyma 2) Secondary cortex II. Meristematic layer 3) Cork cambium III. Bast 4) Primary cortex IV. Lenticel V. Thick walled parenchyma The correct match is A B C D 1) IV III II I 2) I II IV V 3) IV V II I 4) II III V IV 29. Study the following lists LIST – I LIST – II 1) Discontinuous cambium rong I. Produces secondary vascular tissues 2) Complete cambium ring II. Dicot root 3) Lenticel III. Monocot root 4) Wavy cambium ring IV. Primary dicot stem V. Lens shaped The correct match is A B C D 1) IV I V II 2) IV V I II 3) III IV II V 4) V II IV III 30. Study the following lists LIST – I LIST – II 1) Tracheids I. Irregular shaped cells 2) Spongy parenchyma II. Rectangular cells 3) Sieve tubes III. Cylindrical tube like cells 4) Phloem parenchyma IV. Elongated cells with tapering ends V. Oval cells The correct match is A B C D 1) I IV III V 2) IV I III II 3) III I II V 4) III II I V

ANSWERS 1-1, 7-1, 13-2, 19-4, 25-3,

2-4, 8-2, 14-4, 20-2, 26-4,

3-1, 9-2, 15-1, 21-3, 27-1,

4-4, 10-2, 16-4, 22-4, 28-3,

5-4, 11-3, 17-3, 23-2, 29-1,

6-3, 12-4, 18-2, 24-3, 30-2.

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 21,  2019 - 

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Why does she hate classical music?

CORRECTION OF SENTENCES I). Nouns: 1) Your informations are wrong.

2) He has bought expensive furnitures.

3) Children should learn the alphabets with joy.

4) He has deep knowledges of various fields.

5) The sceneries of Darjeeling are very beautiful.

6) keep your surrounding clean.

7) The police has caught the smugglers.

8) This good is imported.

9) He bought a new pant.

10) We must express thank to those who help us.

11) Economics are an interesting subject.

12) Athletics are an interesting sport.

13) The news of the earthquake have spread like wildfire.

14) Measles are an infectious disease.

15) Ocean sands are not used for construction.

16) C.V.Raman’s Knowledges of all branches of physics are amazing.

17) Both my brother-in-laws are working in the U.S.A. 18) There is a scarcity of man-servants now-a-days.

19) Many passer-bys observed the accident.

20) Mouses have spoiled the crop.

21) There are five womans in the team.

22) My cousin brother is a doctor.

23) We should wash our foots before coming into the house.

24) He has many sheeps.

25) Some cattles are grazing in the field.

II) Pronouns: 26) One of my classmates are a doctor.

27) Neither of the girls are absent.

28) One should look after her parents.

29) Every men are responsible for this situation.

30) Neither Parimala nor Nethaji are interested in politics.

31) His both hands are paralyzed.

32) The principal and the chairman has attended the programme.

33) Each of them were given a gift.

34) Students must avail the opportunities.

35) The two players blamed one another for their defeat.

36) His all family members are employed.

37) All Indians must respect each other.

38) Yourself are responsible for your future.

39) There are no less than ten employed persons in their village.

40) He and me are brothers.

III) Adjectives: 41) She is more shorter than her brother.

42) As there are only few students, I can interact with them easily.

43) Everest is the most highest of all the mountains in the world.

44) My all friends are very active.

45) Gandhi is more truthful than any political leader.

46) This is taller than many buildings in Hyderabad.

47) Raghu is my older brother.

48) The streets of Hyderabad are wider than warangal.

49) We are honest than they are.

IV) Articles: 50) You must eat an fruit daily.

51) Suma is an popular anchor.

52) I waited for a hour.

53) Bring five dozens oranges and distribute them among the students.

54) Sun rises in east.

55) Many people take roties for the lunch.

56)Do you like to play violin?

57) Onions cost Rs.20 kilogram.

V) Verbs: 58) When he was trying to explain the problem, his friend disturbs him.

59) They are staying in the same flat for the last many years.

60) How long are you waiting here?

61) He is interested to do a job.

62) They have moved to the new house last week.

63) He is having many imported clothes.

64) As soon as I opened the doors the birds fly away.

65) If I will stand on my own legs, my parents will feel happy.

66) If you consult me I would have advised you.

67) He is visiting the library daily.

INTERMEDIATE s p e c i a l J U N I O R

VI) Adverbs: 68) I am too happy to meet you.

69) The tiffin is very hot to eat.

70) He walks very fastly.

71) we don’t hardly believe it.

72) They don’t do anything careful.

73) They speak English very good.

74) She scarce attends classes.

75) He works very hardly.

76) He is walking very slow.

VII) Prepositions: 77) Unity is important between people.

78) The property was divided between the four brothers.

79) I prefer fruits than sweets.

80) He is afraid with darkness.

81) We should not feel superior than others.

82) We entered into the hall to watch the play.

83) Can you prevent them to enter the swimming pool?

84) Beside being a poet, Tagore is also a short story writer.

85) The shops will be opened between 10 am to 8 pm.

86) Every one congratulated her for her wonderful performance.

VIII) 87) Either/you must take up a job or start a business.

88) Neither she drinks tea nor coffee.

89) Sheela is as proud like a peacock.

90) They asked me that where SBI was.

IX) 91) They asked me what was my name.

92) Unless you don’t concentrate, you won’t understand anything.

93) I am forty years.

94) This article is made with cotton.

95) The doctor advised him that not to eat oily food.

96) We look forward to meet the minister.

97) I know them for the last many years.

98) The collector discussed about the problems of the villagers.

99) He is not remembering numbers.

100) You have to agree for my proposals.

101) Why is she hating classical music?

102) Students should to ask questions if they have doubts.

103) My friends made me to stay there.

104) It is raining since yesterday.

105) I am good in English.

106) Some students come lately to college everyday.

107) I reached there before two hours.

108) If cleanliness will be maintained,we will be healthy.

109) We had seen them two weeks ago.

110) The river has overflown its banks in many places.

111) He has hanged his coat on a nail.

112) All banks are open from 10.30 am and 4 pm.

113) If she is felicitated, she would have felt happy.

114) He is not an expert in grammar, isn’t it?

115) We saw him to do the work.

116) Children are fond for chocolates.

X) Learning from mistakes: 1).Very good morning!

2).What is your good name?

3).Why you are late today.

4).The staff meeting has been preponed.

5).I will report it to the concerned teacher.

6). We go home by walk.

7). Q: Where you come from? A:I am coming from khammam.

8). I do not know what is your name.

9) He went to the back-side of the house.

10). She is not on talking terms with me.

11). They find it very difficult to make both their ends meet.

12). We have to take care of the females in our family.

13). What you are going to do during your leave?

14). I hope you enjoyed the beautiful sceneries at ooty.

15). I have worked here since one year.

KEY i). Nouns 1) Information 2) Furniture 3) Alphabet 4) Knowledge 5) Scenery, is 6) Surroundings 7) Have 8) Goods 9) pants 10) thanks 11) is 12) is 13) has 14) is 15) Ocean sand is 16) C.V. Raman’s knowledge 17) brothers-in-law 18) men-servants 19) Passers-by 20) mice 21) women 22) cousin 23) our feet 24) sheep 25) cattle ii). Pronouns 26) classmates is 27) is 28) one’s 29) man, is 30) is 31) Both his hands 32) have 33) was 34) avail themselves of the pportunities 35) each other 36) All his family 37) one other 38) you 39) no fewer than 40) I iii). Adjectives 41) Shorter 42) a few 43) highest 44) All my friends 45) Any other political leader 46) many other buildings

VIVEKANANDA .B Narayana group of Institutions, Hyderabad

9912343401

47) elder 48) wider than those of 49) more honest iv) . Articles 50) a 51) a 52) an hour 53) dozen 54) the sun, the east 55) lunch 56) the violin 57) Rs. 20 a kilogram v) Verbs 58) disturbed 59) have been staying 60) have you been waiting 61) in doing 62) moved 63) has 64) flew away 65) stand 66) you had consulted 67) visits vi). Adverbs 68) very 69) too hot to 70) fast 71) hardly/ don’t believe it hard 72) carefully 73) well 74) scarcely 75) hard 76) slowly vii) Prepositions 77) among 78) among 79) to 80) of 81) to 82) Remove,’into’ 83) from entering 84) Besides 85) between 10 and 8 p.m viii) 86) on 87) you must either take up 88) she drinks neither 89) as proud as 90) where SBI was, remove ‘that’ ix) 91) what my name was 92) Remove ‘don’t’ 93) Remove ’years’/ (years old) 94) of95) remove ‘that’ 96) to meeting 97) have known.

98) remove ‘about’ 99) doesn’t remember 100) to 101) does she hate 102) remove’to’ 103) remove’to’ 104) has been raining 105) at 106) late 107) in two hours / two hours before 108) is 109) saw 110) has overflowed 111) hung 112) to 113) had been felicitated 114) is he?

115) do/doing 116) of x) Learning from mistakes 1) Remove ’very’ 2) name 3) Are you 4) advanced 5) Remove ‘it’ 6) On foot 7) Are you coming 8) Your name was 9) Back 10) Not on speaking terms 11) to make their both ends meet 12) women1 13) what are you going, on your leave / during vacation 14) enjoyed yourself, scenery 15) for

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Jr.Inter - English Grammar CORRECTION OF ERRORS IN SENTENCES I) 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) II) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38)

VIVEKANANDA.B Academic Prog.Head Narayana Group Of Educational Institutions

Nouns: Your informations are wrong.

He has bought expensive furnitures.

Children should learn the alphabets with joy.

He has deep knowledges of various fields.

The sceneries of Darjeeling are very beautiful.

Keep your surrounding clean.

The police has caught the smugglers.

This good is imported.

He bought a new pant.

We must express thank to those who help us.

Economics are an interesting subject.

Athletics are an interesting sport.

The news of the earthquake have spread like wildfire.

Measles are an infectious disease.

Ocean sands are not used for construction.

C.V.Raman's Knowledges of all branches of physics are amazing.

Both my brother-in-laws are working in the U.S.A. There is a scarcity of man-servants nowa-days.

Many passer-bys observed the accident.

Mouses have spoiled the crop.

There are five womans in the team.

My cousin brother is a doctor.

We should wash our foots before coming into the house.

He has many sheeps.

Some cattles are grazing in the field.

Pronouns: One of my classmates are a doctor.

Neither of the girls are absent.

One should look after her parents.

Every men are responsible for this situation.

Neither Parimala nor Nethaji are interested in politics.

His both hands are paralyzed.

The principal and the chairman has attended the programme.

Each of them were given a gift.

Students must avail the opportunities.

The two players blamed one another for their defeat.

His all family members are employed.

All Indians must respect each other.

Yourself are responsible for your future.

39) There are no less than ten employed persons in their village.

40) He and me are brothers.

59)

III) Adjectives:

60) 61) 62)

41) She is more shorter than her brother.

42) As there are only few students, I can interact with them easily.

43) Everest is the most highest of all the mountains in the world.

44) My all friends are very active.

45) Gandhi is more truthful than any political leader.

46) This is taller than many buildings in Hyderabad.

47) Raghu is my older brother.

48) The streets of Hyderabad are wider than warangal.

49) We are honest than they are.

IV) 50) 51) 52) 53) 54) 55) 56) 57) V)

Articles: You must eat an fruit daily.

Suma is an popular anchor.

I waited for a hour.

Bring five dozens oranges and distribute them among the students.

Sun rises in east.

Many people take roties for the lunch.

Do you like to play violin?

Onions cost Rs. 20 kilogram.

Verbs:

58) When he was trying to explain the prob-

Key 31) Both his hands i) Nouns: 32) have 33) was 1) Information 2) Furniture 34) avail themselves of the 3) Alphabet 4) Knowledge opportunities 35) each other 5) Scenery, is 6) Surroundings 36) All his family 7) Have 8) Goods 37) One other 38) you 9) pants 10) thanks 39) no fewer than 40) I 11) is 12) is 13) has 14) is 15) Ocean sand is iii) Adjectives: 16) C.V.Raman's knowledge 41) Shorter 42) a few 17) Brothers-in-law 43) highest 44) All my friends 18) men-servants 19) Passers-by 45) Any other political leader 20) mice 21) women 46) many other buildings 22) cousin 23) our feet 47) elder 48) wider than those of 24) sheep 25) cattle 49) more honest ii) Pronouns: iv) Articles: 26) classmates is 27) is 28) one's 50) a 51) a 52) an hour 29) man, is 30) is

63) 64) 65) 66) 67) VI) 68) 69) 70) 71) 72) 73) 74) 75) 76)

lem, his friend disturbs him.

They are staying in the same flat for the last many years.

How long are you waiting here?

He is interested to do a job.

They have moved to the new house last week.

He is having many imported clothes.

As soon as I opened the doors the birds fly away.

If I will stand on my own legs, my parents will feel happy.

If you consult me I would haveadvised you.

He is visiting the library daily.

Adverbs: I am too happy to meet you.

The tiffin is very hot to eat.

He walks very fastly.

Wedon't hardly believe it.

They don't do anything careful.

They speak English very good.

She scarce attends classes.

He works very hardly.

He is walking very slow.

VII) Prepositions: 77) Unity is important between people.

78) The property was divided between the four brothers.

79) I prefer fruits than sweets.

80) He is afraid with darkness.

81) We should not feel superior than others.

53) dozen 54) the sun, the east 55) lunch 56) the violin 57) Rs. 20 a kilogram v) Verbs: 58) disturbed 59) have been staying 60) have you been waiting 61) in doing 62) moved 63) has 64) flew away 65) stand 66) you had consulted 67) visits vi) Adverbs: 68) very 69) too hot to 70) fast 71) hardly/ don't believe it hard 72) carefully 73) well

82) We entered into the hall to watch the play.

83) Can you prevent them to enter the swimming pool?

84) Beside being a poet, Tagore is also a short story writer.

85) The shops will be opened between 10 am to 8 pm.

86) Every one congratulated her for her wonderful performance.

VIII) 87) Either/you must take up a job or start a business.

88) Neither she drinks tea nor coffee.

89) Sheela is as proud like a peacock.

90) They asked me that where SBI was.

IX) 91) They asked me what was my name.

92) Unless you don't concentrate, you won't understand anything.

93) I am forty years.

94) This article is made with cotton.

95) The doctor advised him that not to eat oily food.

96) We look forward to meet the minister.

97) I know them for the last many years.

98) The collector discussed about the problems of the villagers.

99) He is not remembering numbers.

100) You have to agree for my proposals.

101) Why is she hating classical music?

102) Students should to ask questions if they have doubts.

103) My friends made me to stay there.

104) It is raining since yesterday.

105) I am good in English.

106)Some students come lately to college everyday.

107) I reached there before two hours.

108) If cleanliness will be maintained,we will be healthy.

109) We had seen them two weeks ago.

110) The river has overflown its banks in many places.

111) He has hanged his coat on a nail.

112) All banks are open from 10.30 am and 4 pm.

113)If she is felicitated, she would have felt happy.

114) He is not an expert in grammar, isn't it?

115) We saw him to do the work.

116) Children are fond for chocolates.

74) scarcely 75) hard 76) slowly vii) Prepositions: 77) among 78) among 79) to 80) of 81) to 82) Remove,'into' 83) from entering 84) Besides 85) between 10 and 8 p.m 86) on 87) you must either take up 88) she drinks neither 89) as proud as 90) where SBI was, remove 'that' 91) what my name was 92) Remove 'don't' 93) Remove 'years'/ (years old) 94) of 95) remove 'that'

96) to meeting 97) have known.

98) remove 'about' 99) doesn't remember 100) to 101) does she hate 102) remove'to' 103) remove'to' 104) has been raining 105) at 106) late 107) in two hours / two hours before 108) is 109) saw 110) has overflowed 111) hung 112) to 113) had been felicitated 114) is he?

115) do/doing 116) of

12 k˛eTyês¡+ 21.1.2019 ôV’≤<äsêu≤<é

Explain the procedure to find Median of...

Statistics

Introduction: - Statistics is a branch of Mathematics which consists of collection, computation and Analysis of data - Father of Statistics “Sir Ronald A Fisher” - Frequency :- The number of items in each class of a frequency distribution is called class Frequency - Class External :- difference betw een upper boundary and lower boun dary is called class Interval Ex :Class 0 – 10 10 – 20 20 – 30 Frequency 4 10 6 Here class Interval = 10 – 0 = 10 (or) 20 – 10 = 10 (or) 30 – 20 = 10 L.C.F :- In a frequency distribution the sum of all frequency from the beginning to the upper boundary of a particular class is called less than cumulative frequency us to that class G.C.F :- In a frequency distribution the sum of all frequency from the end of the lower boundary of a particular class is called the greater than cumulative frequency upto that class Cumulative frequency curve :- Taking classes on X – axis and corresponding cumulative frequencies on Y – axis the points are plotted and the resulting curve is called “Cumula tive frequency curve” (or) an ogive Median can be obtained from cumulative frequency curve: - From n/2 frequency draw a line parallel to X–axies cutting the curve at point from this point draw a perpendicular to the axis the point at which the perpendicular meets the X–axis determines the median sum of obernations → Arithmetic Mean:- x Total no of obernations

Types of Methods :- AM by direct ε fx method, x= ε fi

ε fidi ε fi Here a → assumed mean, di → deviat -ion = xi-a

→ A.M by deviation method, x=a+

→ AM by step - deviation method: - x =  ε fiui   ε fi  × h,  

Prepared by

Mr. K. Kumar Senior Faculty Hyderabad ph:9492956214

Find the value of ∈ firi for the above dat a, where ÷; is the mid value of each class Sol : Class

l – lower boundary of the modal class h – size of the modal class Interval f1 - Frequency of modal class f0 - Frequency of the class preceding the modal class f2 - Frequency of the class succeeding the modal class Median :- Any given data first write ascending order (or) descending order in a middle most value is called Median.

Eg: - 5, 4, 6, 10, 12, 9, 11 then final Median Sol:- A.O: 4,5,6 9 10,11,12 Median=9

 n2 − cf Median = l +   f

Median for a grouped data: Here l –lower boundary of median class, N – number of observation Cf – cumulative frequency of class preceding the median Class F – frequency of median class, h – site of the median class - Relation between mean, median, mode :Mode=3×Median-2×mean -

1) Explain the procedure to find Medi an of ungrouped data Sol:- For finding the Median of ungro uped data we first arrange the observations in ascending order.

Let ‘n’ be the total number of observations. Then If n is add. The th

Median is the  n + 1  observation    2 

class xi-a h

Mode:- Mode is the size of variable which occurs most frequently Eg :- 3, 6, 5, 3, 9, 4, 3 then find mode Mode = 3 Mode of  af1grouped -f 0  data : - Mode = l +  ×h 2f -f -f  1 0 2 where

Range = Maximum value – Minim um value Central Tendency: - Mean, Median, Mode is called central tendency.

1 Marks :-

Here a-assumed mean, h-height of the ui =

 × h 

-

3) Write the first 10 prime numbers and find the Median Sol :- First 10 prime numbers are 2, 3, 5, 7, 11, 13 17, 19, 23, 29 Median =

4) “The Median of observations -2, 5, 3, -1, 4, 6 is 3.5” is it correct?

Sol:- Given observations -2,5, 3, -1, 4, 6 A.O: -2, -1, 3.4 5, 6

Median=

th

th

2) What are the Measures of Central Tendency? Which Measure can be determined graphically?

Sol :- Mean, Median, Mode are the measures central tendency Median can be determined graphically

3+4 7 = =3.5 Yes, correct 2 2

10th Class Special MATHS

5) Find the mode of the scores 13, 15, 17, 13, 15, 14, 19, 13,11, 15, 13, 17 Sol :- Mode=13 ( repeated data) 6) Find the mean of scores 6,7,8,12,9,2 sol : − x = x=

Sum of observation Total no.of observation

6 + 7 + 8 + 12 + 9 + 2 44 = = 7.733 6 6

2 Marks :-

1) The height of 12 members of a family are given below in the table Height (in ft) 5 5.2 5.4 5.6 No.of family 3 4 3 2 members Height of the family members: sol:Height No.of family members(f) f × χ 5 3 15.0 5.2 4 20.8 16.2 5.4 3 5.6 2 11.2 ∈ f1 = 12 ∈ f x = 63.2 Mean x =

If n is even, then the Median will be n n the Average of the  and  + 1 2 2  observations

11+13 24 = =12 2 2

∈ fixi 63.2 = 5.25 ,x = sfi 12

2) Write the formula of mode for grouped data, and explain each term in it.

3) Write the formula of median for grouped data, and explain each term?

4)

Class

10 - 20 20 - 30 30 - 40 40 - 50 50 - 60

Frequency

5

8

10

5

2

Mid value (i) frequency Fi xi

10-20

15

5

75

20-30

25

8

200

30-40

35

10

350

40-50

45

5

225

50-60

55

2

110 ∈ fi=960

5) Find the mode Class 1-3 3-5 5-7 7-9 Frequency 6 7 9 2 Sol :Class . I Frequency 1-3 6 3-5 7(fo) (l) 5 = 7 9(f1) 7-9 2(f2) 9-11 1

9-11 1

 f1 − f 0  Mode = l +  ×h  2 f1 − f 0 − f 2  l=5, f1=9, f0=7,f2=2, h=2  9−7  Mode = 5 +  ×2  18 − 7 − 2    2  2 = 5+  × 2 = 5 + ×2    18 − 9  9  4 = 5 + = 5 + 0.44 = 5.44 9 6) The mean of 10 observations is 16.3 by an error, one observation is registered as 32 instead of 23. Find the correct mean.

Sol :- Mean of 10 observations =

ε xi = 16.3 ⇒ ε xi = 16.3 ×10 = 163... 1 10 Current value Wrong value Result 23 32 ε xi − 9 correct sum of the items ε xi 9 = 163 − 9 = 154 154 correct mean of the data = = 15.4 10

→

to be continued

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Unit-III The Musculo Skeletal System 2 Marks Questions

Q. What is triad system?

A: In a skeletal muscle each transverse tubule (T-tubule) on either have serval cisternae of the sarcoplasmic reticulum. T-tubule and two terminal cisternae at it sides form the triad system.

Q. Name two cranial sutures and their locations.

A: 1. Coronal suture - present between frontal and parietal bones.

2. Lambdoid suture - Present between frontal and occipital bones.

Q. Name the keystone bone of cranium.

Where it is located?

A: 1. Sphenoid bone is the key stone bone of cranium.

2. It is located at the middle part of the

base of the skull.

Q. Human skull is described as dicondylic skull. Give the reason.

A: Human skull have two occipital condyles on both sides of foramen magnum. Hence, it is called dicondylic skull.

Q. Name the ear ossicles and their evolutionary origin in human beings.

Writer P. Murali Krishna Subject Expert

Myosin

1. The thin filament in the myofibril is called action.

2. Action is made up of action, troponin and tropomyosin proteins.

1. The thick filament in the myofibril is called myosin.

2. Myosin is made up of only myosin protein.

Q. Distinguish between red muscle fibres and white muscle fibres.

Red muscle fibres

1. Myoglobin is high 2. Plenty of mitochondria 3. Red in colour

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What is corpus callosum?

Action

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Q. Write the difference between action and myosin.

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White muscle fibres 1. Myoglobin is less 2. Few mitochondria 3. White in colour

A: 1. Malleus - modification of articular.

2. Incus - modification of quadrate.

3. Stapes - modification of hyomandibula.

4 Marks Questions Q. What is Cori Cycle? Explain the process.

A: Muscle contraction requires energy. This energy is supplied by the oxidation of glucose. During the rapid contraction of skeletal muscle under low availability of oxygen, the glucose undergo anaerobic respiration and produce lactic acid.

This lactic acid is carried to the liver by the blood where it is converted into pyruvate and then to glucose. This process is called gluconeogenesis. If needed this glucose reaches to the skeletal muscle for further release of energy. If muscle stopped contraction the glucose in the liver is converted into reserve glycogen through glycogenesis. This two way traffic of glucose between skeletal muscle and liver is called Cori Cycle.

B. Neural Control and Co-ordination 2 Marks Questions Q. Name the cranial menings covering the brain of man.

A: Brain is covered by three membranes called menings. They are 1. Dura mater

Zoology 2.Arachnoid mater, 3. Pia mater.

Q. What is corpus callosum?

A: The two cerebral hemispheres are internally connected by a transverse, wide and flat bundle of myelinated fibres beneath the cortex is called corpus callosum.

Q. What is all - or - none principle?

A: In a nerve the action potential occurs in response to a threshold stimulus or supra threshold stimulus. But it dose not occur at sub threshold stimus. This is called all - or - none principle.

Q. How does rods and cones of human eye differ from each other chemically and functionally?

A: Rods: 1) Rads contain a purplish red protein called rhodopsin. 2) They are important in vision under low light conditions.

Cones: 1) Cones contain a visual pigment called iodopsin. 2) They are important in daylight and colour vision.

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AƇ¬™ól B C§ýlªÇ Ð]lÅMýS$¢Ë ¿êV>ÌZÏ ™ólyé G…™èl?

RMýS$

E¯]l² §ýl*Æý‡… G…™èl(MìS.Ò$.ËÌZ)?

1) 43 2) 45 íÜ. fĶæ${ç³M>ÔŒæ Æð‡yìlz 1) 20 2) 21 3) 50 4) 60 & & 3) 23 4) 24 9. JMýS §é°MìS 4% ^öç³#µ¯]l, Ð]l$Æø §é°MìS çÜ»ñæjMýS$t °ç³#×æ$Ë$ 7. JMýS ©Æý‡ƒ ^èl™èl$Æý‡{çÜç³# M>W™é°² Æð‡…yýl$ çÜÆý‡Ó 4½% ^öç³#µ¯]l Æð‡…yýl$ çÜÐ]l*¯]l Ððl¬™é¢Ë¯]l$ çÜÐ]l*¯]l ¿êV>Ë$V> JMýS f™èl ¿¶æ$gêË OÐðlç³# ò³r$tºyìl ò³sêtÆý‡$. 7 çÜ…Ð]l™èlÞÆ>Ë ™èlÆ>Ó™èl Ð]l$yìl_¯]lç³#µyýl$ JMöPMýSP ¿êVýSç³# ^èl$r$tMöËÆð‡…yø Ððl¬™èl¢…Oò³ Ð]l_a¯]l Ý뫧éÆý‡×æ Ð]lyîlz, ™èl 34 òÜ….Ò$.E…sôæ, Ð]l$Æø f™èl ¿¶æ$gêË Ððl¬§ýlsìæ §é°Oò³ Ð]l_a¯]l §é° MýS…sôæ Æý‡*. Ð]l*¨Ç {ç³Ô¶æ²Ë$ OÐðlç³# Ð]l$yìl_¯]lç³#µyýl$ A§ól ^èl$r$tMöË™èl 38 94.50 GMýS$POÐðl™ól, JMöPMýSP Ððl¬™èl¢…

1 òÜ….Ò$.V> E…¨. AƇ¬™ól B M>W™èl… (Æý‡*.ËÌZ) G…™èl?

2 1 1. x, ( x ≠ 0) Ë Ü ç Vý S r$ M AƇ¬™ól x , 2 x x OÐðlÔ>ËÅ… (^èl.òÜ….Ò$.ËÌZ) G…™èl?

1) 2600 2) 2700 1) 140 2) 240 3) 2700.50 4) 2685 Ë çÜVýSr$ G…™èl?

3) 560 4) 360 ç³° ç³NÆý‡¢Æ‡¬…§ýl° ™ðlË$çÜ$MýS$¯é²yýl$. °Æó‡ªÕ™èl 1) 1−M2 2) 1−2M 10. JMýS Ð]lÅMìS¢ OòÜMìSÌŒæOò³ {ç³Ä¶æ*×ìæ…_, JMýS {糧ól3) 2M2−1 çÜÐ]l$Ķæ*°MìS ç³° ç³NÇ¢ ^ólĶæ$yé°MìS 4) 2M2+1 8. 200 Ò$. 180 Ò$. ´÷yýlÐ]l#¯]l² Æð‡…yýl$ OÆð‡â¶æ$Ï Ô>°² 6 VýS…rÌZÏ ^ólÆý‡™éyýl$. B Ð]lÅMìS¢ A™èlyìl 2. Æð‡…yýl$ çÜ…QÅË MýS.Ýë.VýS$. 495, Ðésìæ G…™èlÐ]l$…¨ ç³°ÐéÇ° ™èlWY…^éÍ? Æð‡…yýl$ çÜÐ]l*…™èlÆý‡ ç³sêtËOò³ {ç³Ä¶æ*×ìæÐólV>°² I§ø Ð]l…™èl$ ™èlWY…^èl$MýS$…sôæ, A§ól G…™èl?

1) 24 2) 56 çÜ$¢¯é²Æ‡¬. AÑ JMóS ¨Ô¶æÌZ Ððlâ¶æ$¢¯]l²ç³#µyýl$ çÜÐ]l$Ķæ$…ÌZ A™èlyýl$ 5 MìS.Ò$. ™èlMýS$PÐ]l {ç³Ä¶æVýS.Ýë.¿ê. 5. B Æð‡…yýl$ çÜ…QÅË Ððl¬™èl¢…

1) 30 2) 33 3) 64 4) 80 ÐésìæÌZ GMýS$PÐ]l ÐólVýS…™ø ÐðlâôæÏ OÆð‡Ë$ ™èlMýS$PÐ]l ×ìæÝë¢yýl$.AƇ¬™ól A™èlyìl ÐólVýS…? (MìS.Ò$/VýS….)

100 AƇ¬™ól Ðésìæ Ð]l$«§lý Å ¿ôæ§ýl… G…™èl?

3) 36 4) 44 ÐólVýS…™ø ÐðlâôæÏ OƇð Ë$¯]l$ 38 òÜMýS¯]lÌÏ Z §ér$1) 10 2) 46 5. Ô¶æ…MýS$Ð]l# BM>Æý‡…ÌZ E¯]l² JMýS VýS$yéÆý‡ç³# G™èl$¢ 6. P, QË Ð]l$«§lý Å §ýl*Æý‡… 27 MìS.Ò$. A, BA¯ól 1 4 2) 6 1) 5 ™èl$…¨. AÐól ÐólV>Ë™ø G§ýl$Æð‡§ýl$Æý‡$ ¨Ô¶æÌZÏ 3) 70 4) 90 C§ýlªÆý‡$ Ð]lÅMýS$¢Ë$ P ¯]l$…_ QMìS VýS…rMýS$ 14 Ayýl$VýS$Ë$, §é° ¿¶æ* ÐéÅÝëÆý‡®… 6 Ayýl$Ððlâôæ¢, AÑ JMýS§é°MöMýSsìæ ç³NÇ¢V> 5 òÜMýS¯]lÏÌZ 3. C§ýlªÆý‡$ Ð]lÅMýS$¢Ë$ JMýS ç³°° Æý‡*. 1200ËMýS$ VýS$Ë$. B VýS$yéÆý‡…ÌZ 12 Ð]l$…¨ Ð]lÅMýS$¢Ë$ Ð]lÆý‡$çÜV> 4, 5 MìS.Ò$.Ë ^öç³#µ¯]l ¯]lyìl^éÆý‡$.

5 §ér$™éƇ¬. AƇ¬™ól GMýS$PÐ]l ÐólVýS…™ø ^ólĶæ$yé°MìS Jç³#µMýS$¯é²Æý‡$. ÐéÇÌZ JMýSPyól °{§ýl´ù™èl$…sôæ JMöPMýSPÇMìS A…§ól çÜVýSr$ Q§ýlVýSYÇMìS ^ólǯ]l B Ððl…r¯ól †ÇW 3) 4½ 4) 3 6 ¯]lyìl^ól OÆð‡Ë$ ÐólVýS… G…™èl ? (Ò$/òÜMýS¯]lÏÌZ) ÑyìlV> §é°° 6 ÆøkÌZÏ ^ólõÜ¢, Ð]l$ÆöMýSÆý‡$ V>Í çœ$¯]lç³ÇÐ]l*×æ… (çœ$¯]l Ayýl$VýS$ÌZÏ) ºÄ¶æ$Ë$§ólÇ A° RÐ]l§ýlª MýSÍÔ>yýl$. P ¯]l$…_ ÑyìlV> 8 ÆøkÌZÏ ^ólÝë¢yýl$. JMýS MýS${Æý‡Ðéyìl Üç àĶæ$…™ø ÐéÆý‡$ B ³ç °° 3 ÆøkÌZÏ ç³NÇ¢ ^ólÔ>Æý‡$. AƇ¬™ól B C§ýlªÆý‡$ Ð]lÅMýS$¢Ë ¿êV>ÌZÏ ™ólyé G…™èl(Æý‡*´ëĶæ$ÌZÏ)?

1) 150 2) 200 3) 250 4) 300 4. JMýS VýS$™ól¢§éÆý‡$ JMýS ³ ç °° 124 ÆøkÌZÏ ³ç NÇ¢ ^ólĶæ$yé°MìS A…XMýSÇ…^éyýl$. A…§ýl$MøçÜ…

120 Ð]l$…¨ Ð]lÅMýS$¢Ë¯]l$ ç³°ÌZMìS 2 ¡çÜ$Mö¯é²yýl$. 64 ÆøkË ™èlÆ>Ó™èl 3 Ð]l…™èl$

=

çÜÐ]l*«§é¯éË$ 1.

x,

1 x

x+ 2 x+

=

{ç³™ólÅMýS…

çœ$¯]lç³ÇÐ]l*×æ…

528 = = 44 çœ$¯]lç³# Ayýl$VýS$Ë$ 12

1 1 1 : : = 4 : 3 :1 6 8 24

P

Ððl¬§ýlsìæ Ð]lÅMìS¢ ´÷…§ól ¿êVýS… =

4 4 × 1200 = ×1200 4 + 3 +1 8

= Æý‡*. 600

2

1  2 + x   = (2M) x  1 x 2 + 2 + 2 = 4M 2 x 1 x 2 + 2 = 4M 2 − 2 x 1 x 2 + 2 = 2(2M 2 − 1) x

x

R

27-x

f:4 Q

PQË Ð]l$«§lý Å §ýl*Æý‡… = 27 MìS.Ò$.

RQË Ð]l$«§lý Å §ýl*Æý‡… = x PRË Ð]l$«§lý Å §ýl*Æý‡… = 27−x MìS.Ò$.

A {ç³Ä¶æ*×ìæ…_¯]l §ýl*Æý‡… = 27 − x MìS.Ò$.

B {ç³Ä¶æ*×ìæ…_¯]l §ýl*Æý‡… = 27 + x

= 4 : 3 :1

CÆý‡$OÐðlç³#Ìê Ð]lÆý‡Y… ^ólõÜ¢

27km

6.

Æý‡*.1200 Ð]l¬VýS$YÆý‡$ ç³…^èl$MýS$¯ól °çÙµ†¢

1 x =M 1 = 2M x

AÆý‡¦Ððl$sìæMŠæ

1 1 1 1 7 1 − +  = − = 3  6 8  3 24 24

Ð]l¬VýS$YÆý‡$ Ð]lÅMýS$¢Ë 糯]l$Ë °çÙµ†¢

Ë Üç VýSr$

GOòÜÞ M>°õÜtº$ÌŒæ

©.^èl. ^èl$r$t MöË™èl

b = 2(l ) + 2   = 38  2

2l + b = 38 ––––(2) (1), (2) Ë ¯]l$…_ 2l + 4b = 68 2l + b = 38 3b =30 b = 10 òÜ….Ò$. l = 34 - 2 (10) = 14 òÜ….Ò$. ©.^èl. OÐðlÔ>ËÅ… = l × b = 14 ×10 = 140 ^èl.òÜ….Ò$.

9.

x = 43 Ò$/òÜ.

JMöPMýSP Ððl¬™èl¢… = x Ððl¬§ýlsìæ ¿êVýS…Oò³ Ð]lyîlz Æó‡r$ = 4% M>Ë… = 7 çÜ…Ð]l™èlÞÆ>Ë$ Æð‡…yø Ððl¬™èl¢…Oò³ Ð]lyîlz Æó‡r$

f:1

1 9 =4 %= % 2 2

Ð]lyîlzË Ð]l$«§lý Å ™ólyé = 94.50 Oò³.

x × 4½ × 7 x × 4 × 7 − = 94.50 100 100 x× 4×7 9 7 x× × − = 94.50 2 100 100 63 x 28 x − = 94.50 200 100 63 x 56 x − = 94.50 200 200

MìS.Ò$.

3 3 f:1 = × 1200 = × 1200 M>Ë… = §lý*Æý‡…

4 + 3 +1 8 Ðó Vý … = Æý‡*. 450 A, BË ÐólV>Ë$ 4 MìS.Ò$., 5 MìS.Ò$.

8. GMýS$PÐ]l ÐólVýS…™ø ¯]lyìl^ól OÆð‡Ë$ ÐólVýS… MýS${Æ>yýl$ ´÷…§ól ¿êVýS… A {ç³Ä¶æ*×ìæ…_¯]l M>Ë… = B = x Ò$/òÜ.

1 {ç³Ä¶æ*×ìæ…_¯]l M>Ë… ™èlMýS$PÐ]l ÐólVýS…™ø ¯]lyìl^ól OÆð‡Ë$ ÐólVýS… 7x = 94.50 × 200) = × 1200 = Æý‡*. 150 27 − x 27 + x x = Æý‡*.2700 = y Ò$/òÜ. f:2 4 + 3 +1 = 4 5 C§ýlªÆý‡$ Ð]lÅMýS$¢Ë Ð]l$«§lý Å ™ólyé= 600 &- 450 JMóS ¨Ô¶æÌZ Æð‡…yýl$ OÆð‡â¶æ$Ï {ç³Ä¶æ*×ìæõÜ¢ Ðésìæ 10. A™èlyìl ÐólVýS… = x MìS.Ò$./VýS…. = Æý‡*. 150 {ç³Ä¶æ*×ìæ…_¯]l M>Ë… = 6 VýS…rË$ ÐólVýS… = x − y f:1 5(27 − x) = 4(27 + x) 1 x2 + 2 2 135 − 5x = 108 + 4x GMýS$PÐ]l ÐólVýS…™ø ÐðlâôæÏ OÆð‡Ë$ ™èlMýS$PÐ]l ÐólVýS…™ø ™èlWY…_¯]l ™èlÆ>Ó™èl ÐólVýS… x = 2M 2 − 1 4. M1 = 120 W1 = 3 x 4x 2 135 − 108 = 9x ÐðlâôæÏ OÆð‡Ë$¯]l$ §ésôæ çÜÐ]l$Ķæ$… = 38 òÜMýS¯]l$Ï x− = 1 5 5 9x = 27 x = 3 MìS.Ò$. Æð‡…yýl$ OÆð‡â¶æ$Ï {ç³Ä¶æ*×ìæ…_¯]l Ððl¬™èl¢… §ýl*Æý‡…

D1 = 64 ∴ x2 , 2 Ë Ü ç VýSr$ = 2M2 −1 x §ýl*Æý‡… = M>Ë… × ÐólVýS… f:3 ç³° ç³NÇ¢ ^ólĶæ$yé°MìS ™èlWY…^éÍÞ¯]l ∴PR §ýl*Æý‡… = 27−3 = 24 MìS.Ò$. = 200 + 180 = 380 Ò$. ³ç °ÐéÇ Üç …QÅ = x Ððl¬§ýlr {ç³Ä¶æ*×ìæ…_¯]l §ýl*Æý‡…

2. Æð‡…yýl$ çÜ…QÅË Ððl¬™èl¢… =100 f:4 ÐlóVSý… = §lý*Ƈý… ⇒ x − y = 380 M>Ë…

38 M2 = (120 − x) Ððl¬§ýlsìæ çÜ…QÅ = x 7. ©Æý‡ƒ ^èl™èl$Æý‡{çÜ M>W™èl… ´÷yýlÐ]l# l, ÐðlyýlË$µ b = 6 × x = 6x D2 = (124 − 64) = 60 Æð‡…yø Üç …QÅ = 100−x V> ¡çÜ$Mö° Æð‡…yýl$ ¿êV>Ë$V> Ñ¿¶æhõÜ¢ x − y = 10–––– (i) ™èlWY¯]l ™èlÆ>Ó™èl {ç³Ä¶æ*×ìæ…_¯]l §ýl*Æý‡…

1 4x 24 x MýS.Ýë.VýS$. × VýS.Ýë.¿ê. = Æð‡…yýl$ çÜ…QÅË Æð‡…yýl$ OÆð‡â¶æ$Ï Ð]lņÆó‡Q ¨Ô¶æÌZ {ç³Ä¶æ*×ìæõÜ¢ = ×6= W2 = 3 5 5 ˺®… Ðésìæ ÐólVýS… = x + y l l M1D1 M 2 D2 §ýl*Æý‡…ÌZ ™ólyé = 5 MìS.Ò$.

495 ×5 = x(100 −x) (i) 2 ³ç sìæ¯t ]l M>Ë… = 5 òÜMýS¯]l$Ï = 2 W1 W2 §lý*Ƈý…

24 x 380 100x − x2 = 2475 Ðl ó VS ý … = 6x − =5 ⇒ x + = y 2 x − 100x + 2475 = 0 x2 − 45x − 55x + 2475 = 0 x(x − 45) − 55(x − 45) = 0 (x − 45)(x − 55) = 0 x = 55 Ìôæ§é 45 Ððl¬§ýlsìæ Üç …QÅ = 55 Æð‡…yø Üç …QÅ = 100 − x = 100 − 55 = 45 Ðésìæ ¿ôæ§ýl… = 55 − 45 = 10

Æð‡…yø Ð]lÅMìS¢ ´÷…§ól ¿êVýS…

(ii) ³ ç r… ¯]l$…_ = 38 òÜ….Ò$.

120 × 64 (120 − x) × 60 = 2 1 3 3 120 × 64 = = (120 − x) × 60 2

64 = 120 − x x = 120 − 64 = 56 5.

f:1

3. Ððl¬§ýlsìæ Ð]lÅMìS¢ JMýS ÆøkÌZ ^ólõÜ ³ ç ° =1 6 Æð‡…yø Ð]lÅMìS¢ JMýS ÆøkÌZ ^ólõÜ ³ç ° = 1 8

Ððl¬§ýlsìæ Ð]lÅMìS¢ + Æð‡…yø Ð]lÅMìS¢ + MýS${Æ>yýl$ MýSÍíÜ 3 ÆøkË$ ç³°^ólõÜ¢ Ð]l¬VýS$YÆý‡$ MýSÍíÜ JMýS ÆøkÌZ ^ólõÜ ç³° = 1 3

MýS${Æ>yýl$ JMýS ÆøkÌZ ^ólõÜ ç³°

Ô¶æ…MýS$Ð]l# BM>Æý‡ç³# VýS$yéÆý‡… G™èl$¢ (h) = 14 Ayýl$VýS$Ë$ ÐéÅÝëÆý‡®… (r) = 6 Ayýl$VýS$Ë$ Ô¶æ…MýS$Ð]l# çœ$¯]lç³ÇÐ]l*×æ… = 1 × πr 2 h

b

l 2

l 2

f:2

3

1 22 = × × (6) 2 × 14 3 7 1 22 = × × 6 × 6 × 14 3 7

= 528 çœ$¯]l

b

Ayýl$VýS$Ë$ VýS$yéÆý‡…ÌZ° Ð]lÅMýS$¢Ë$ = 12 Ð]l$…¨ JMöPMýSP Ð]lÅMìS¢ ´÷…§ól çÜVýSr$ V>Í

(ii) b 2 b 2

l

M>Ë…

x + y = 76 –––(ii) i, iiË ¯]l$…_ x − y = 10 x + y = 76 2x = 86

5

5

6x =5 5 x=

25 1 =4 6 6

MìS.Ò$/VýS….

f: 2

b 2 b 2

l

(i) ç³r… ¯]l$…_ ©Æý‡ƒ^èl™èl$Æý‡{çÜ ^èl$r$tMöË™èl = 34 òÜ….Ò$. ©.^èl. ^èl$r$t MöË™èl = 2 ´÷yýlÐ]l# + 2 ÐðlyýlË$µ l = 2   + 2b = 34 2

l + 2b = 34 –––– (1)

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ÝëÐ]l$Æý‡¦Å…&2: Ð]lÅMîS¢MýSÆý‡×æ&çÜ–f¯é™èlÃMýS™èl Ë眬 çÜÐ]l*«§é¯]l {ç³Ô¶æ²Ë$ (3 Ð]l*Æý‡$PË$)

™ðlË…V>×æ {ç³fË$ Æý‡${§é§ýl$Ë$ Ððl$^ólarr$Ï Ä¶æ¬§ýl®… ^ólíÜ ÑfĶæ$… Ý뫨…^éÆý‡$ A¯]lyýl…ÌZ MýSÑ E§ólªÔ¶æ… HÑ$sìæ? º™èl$MýS$ ™øÐ]l ^èl*õ³ M>Ë… A…sôæ HÑ$sìæ? ™ðlË…V>×æ ÝëÓ™èl…{™èlÅ ´ùÆ>r… GÌê Mö¯]lÝëW…¨? "Ò ™ðlË$VýS$ Æó‡VýSyìlÌZ hW Ððl$…yýl$ Ð]l*™èlÆø' A¯]l² MýSÑ Ð]l*rÌZÏ A…™èlÆ>Æý‡¦… HÑ$sìæ? ™ðlË…V>×æ ÒÆý‡$Ë ç³Æ>{MýSÐ]l*°² ÑÐ]lÇ…^èl…yìl. "¯éyýl$, ¯ólyýl$¯]l* ™ðlË…V>×æ Ððl*yýlÌôæ§ýl$' A¯]l² MýSÑ Ð]l*r˯]l$ çÜÐ]l$ǦçÜ*¢ Æ>Ķæ$…yìl. "ÒÆý‡ ™ðlË…V>×æ' ´ëuý‡… B«§éÆý‡…V> §éÔ¶æÆý‡¤ Æý‡^èl¯é OÔðæÍ° ÑÐ]lÇ…^èl…yìl. "™ðlË…V>×æÌZ E{¨MýS¢™èl MýSÍW…_¯]l ¯]lÐéº$Ë BfqËMýS$ M>Ë… ^ðlÍÏ´ùƇ¬…¨' A¯]lyýl…ÌZ MýSÑ E§ólªÔ¶æ… HÑ$sìæ? ´ëu>Å…Ô¶æ…ÌZ õ³ÆöP¯]l² ™ðlË…V>×æ Æ>kË {ç³™ólÅMýS™èl HÑ$sìæ?

ÐéÅçÜÆý‡*ç³ çÜÐ]l*«§é¯]l {ç³Ô¶æ²Ë$ 1.

2.

(6 Ð]l*Æý‡$PË$) ÒÆý‡ ™ðlË…V>×æ ´ëu>Å…Ô¶æ… §éÓÆ> Ò$Æý‡$ {VýSíßæ…_¯]l ÑçÙĶæ*Ë$ HÑ$sìæ? °gê… Æ>k™ø ™ðlË…V>×æ {ç³fË$ H Ñ««§ýl…V> Ķ欧ýl®… ^ólÔ>Æý‡$?

çÜ–f¯é™èlÃMýS {ç³Ô¶æ²Ë$ 1.

2.

(6 Ð]l*Æý‡$PË$) ™ðlË…V>×æ ÒÆý‡$Ë Vöç³µ™èl¯é°² ÑÐ]lÇçÜ*¢ MýSÑ™èl Æ>Ķæ$…yìl. ™ðlË…V>×æ ÒÆý‡$Ë ™éÅV>˯]l$ çÜÃÇçÜ*¢ Ñ${™èl$°MìS ÌôæQ Æ>Ķæ$…yìl.

çÜÐ]l*ÝëË$ 1.

2.

3.

4.

5.

™ðlË$VýS$ 3.

4.

™ðlË…V>×æ ÒÆý‡$Ë Vöç³µ™èl¯é°² AÀ¯]l…¨çÜ*¢ AÀ¯]l…§ýl¯é ç³{™èl… Æ>Ķæ$…yìl. ™ðlË…V>×æ ÝëÓ™èl…{™èlÅ ´ùÆ>r Äñæ*«§ýl$° B™èlÃMýS£ýl¯]l$ FíßæçÜ*¢ Æ>Ķæ$…yìl.

AÆ>¦Ë$ 1.

2.

3.

5.

7.

9.

6.

ÝëÐ]l$Æý‡¦Å… &3 : ¿êÚë…Ô>Ë$ (糧ýlgêË…)

(10 Ð]l*Æý‡$PË$)

§ýl…{íÙtMýS = MøÆý‡ ¡…{yìl…^èl$ = {ç³M>Õ…^èl$ gZ§ýl$ÌŒæ = ÒÆý‡$Ë$ A{¿¶æÐ]l¬ = Ðól$çœ$Ð]l¨Ñ = BM>Ô¶æ… fË«¨ = çÜÐ]l¬{§ýl…

4. EfjÓË = {ç³M>Õ…^ól 6. MýS–´ë×æÐ]l¬ = MýS†¢ 8. Ô¶æ${MýS$yýl$ = C…{§ýl$yýl$ 10. Ñ$…r¯Œæ = BM>Ô¶æ…ÌZ

¯é¯éÆ>¦Ë$ 1.

2.

MýSâêÅ×æ… = Ô¶æ$¿¶æ…, Ð]l$…VýSâ¶æ…, ò³…yìlÏ Æ>k = {糿¶æ$Ð]l#, C…{§ýl$yýl$, ^èl…{§ýl$yýl$, Ķæ$„ýS$yýl$

7.

8.

9.

10.

M>MýS¡Ä¶æ¬Ë MýS…^èl$VýS…r = M>MýS¡Ä¶æ¬Ë Äñæ¬MýSP MýS…^èl$VýS…r (çÙïÙx ™èl™èl$µÆý‡$çÙ çÜÐ]l*çÜ…)

MýSâêÅ×æ çœ$…rË$= MýSâêÅ×æ… MöÆý‡MýS$ çœ$…rË$ (^èl™èl$Ǧ ™èl™èl$µÆý‡$çÙ çÜÐ]l*çÜ…) {º™èl$MýS$ {™øÐ]l = {º™èl$MýS$¯]lMýS$ {™øÐ]l (çÙïÙx ™èl™èl$µÆý‡$çÙ çÜÐ]l*çÜ…) Ð]l$àÆý‡Ð]lÐ]l¬ = Ð]l$àĶæ$Ƈ¬¯]l Æý‡Ð]lÐ]l(ÑÔóæçÙ×æ ç³NÆý‡Ó糧ýl…) ÑM>Æý‡ §ýl…{çÙtË$= ÑM>Æý‡OÐðl$¯]l §ýl…{çÙtË$ (ÑÔóæçÙ×æ ç³NÆý‡Ó糧ýl…)

M>…† ÐéÆý‡$¦Ë$ = M>…† A¯ðlyìl ÐéÆý‡$¦Ë$ (Æý‡*ç³MýS çÜÐ]l*çÜ…) ™ðlË…V>×æ Æ>{çÙt… = ™ðlË…V>×æ A¯ól õ³Æý‡$VýSË Æ>{çÙt… (ççÜ…¿êÐ]l¯]l ç³NÆý‡Ó糧ýl…) Ð]l$™èl í³Ô>_= Ð]l$™èl… A¯ðlyìl í³Ô>_( Æý‡*ç³MýS çÜÐ]l*çÜ…) {Ô>Ð]l×ê{¿¶æÐ]l¬ = {Ô>Ð]l×æÐ]l$…§ýlÍ A{¿¶æÐ]l(çÜç³¢Ò$ ™èl™èl$µÆý‡$çÙ çÜÐ]l*çÜ…) ¯]lË$ ¨MýS$PË$= ¯éË$VýS$ çÜ…QÅ VýSË ¨MýS$PË$ (¨ÓVýS$ çÜÐ]l*çÜ…)

AË…M>Æ>Ë$

E§é: 1. ±sìæÌZ ç³yìl¯]l ™ólË$ ™ólË$™èl$…§é 2. AÆý‡sìæ ™öMýSP ™öMýSPÆ>§ýl$ 3. °ç³#µÌZ ò³yìl™ól M>Ë$ M>Ë$™èl$…¨ 4. ÒÆý‡$ ÒÆý‡$ÌŒæ ç³Æ>Æý‡$¦ÌŒæ Oò³ E§éçßæÆý‡×æË$ ç³ÇÖÍõÜ¢ ™ólË$&™ólË$, ™öMýSP&™öMýSP, M>Ë$&M>Ë$, ÒÆý‡$&ÒÆý‡$ A¯ól 糧éË$ Ððl…r Ððl…r¯ól {ç³Äñæ*W…^éÆý‡$. M>± Ðésìæ AÆý‡¦…ÌZ ™ólyé E…¨. CÌê çßæË$ÏË f…r AÆý‡¦¿ôæ§ýl…™ø Ððl…r Ððl…r¯ól {ç³Äñæ*WõÜ¢ A¨ bólM>¯]l${´ëçÜ AË…M>Æý‡….

Aç³Ç_™èl VýS§ýlÅ…

ç³Æ>ÅĶæ$ 糧éË$ fË«¨ = ÐéǦ, çÜÐ]l¬{§ýl…, ÝëVýSÆý‡…, A…º$«¨ ™èlÍÏ = AÐ]l$Ã, Ð]l*™èl, f¯]l° ¿ê¯]l$yýl$ = çÜ*Æý‡$Åyýl$, B¨™èl$Åyýl$, ¿êçÜPÆý‡$yýl$ Ķ欧ýl®… = Æý‡×æ…, çÜÐ]l$Æý‡…, ´ùÆý‡$ 5. MýS–´ë×æ… = MýS†¢, Qyýl…Y , AíÜ 6. ¨Ñ = BM>Ô¶æ…, °…W, VýSVýS¯]l…, Ñ$…r 7. ³ç £ýl… = Ð]l*Æý‡…Y , §éÇ, »êr 1.

2.

3.

4.

{ç³MýS–† & ÑMýS–™èl$Ë$ Äñæ*«§ýl$Ë$ & gZ§ýl$Ë$ çÜÐ]l¬{§ýl… & çÜ…{§ýl…

M>Æý‡Å… & MýSÆý‡j… Üç …«§lý Å & Üç …f 6. {´ëĶæ$Ð]l¬ & ç³Æý‡$Ð]lÐ]l1.

2.

3.

5.

4. ¨Ô¶æ

& §ðlÜç

7. AÐ]l$Ã & A…º

fË«¨= fË…™ø «§ýlÇ…^ól¨& çÜÐ]l¬{§ýl…

MýS–´ë×æ…= §ýlĶæ$¯]l$ ´ùVör$t¯]l¨& MýS†¢ Ð]lçÜ$«§ýl= º…V>Æ>°² VýSÆý‡ÂÐ]l¬¯]l…§ýl$ MýS˨& ¿¶æ*Ñ$

ÝëÐ]l$Æý‡¦Å…&4 : ¿êÚë…Ô>Ë$ (ÐéÅMýSÆý‡×ê…Ô>Ë$) çÜ…«§ýl$Ë$ 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

çÜ*^èl¯]l: VýS™èl…ÌZ CMýSPyýl JMýS Aç³Ç_™èl õ³Æ>{V>‹œ C_a {ç³Ô¶æ²Ë$ C^ólaÐéÆý‡$. M>± Ð]l*ǯ]l ç³È„ýSË çÜ…çÜPÆý‡×æÌZÏ ¿êVýS…V> CMýSPyýl HO§ðl¯é JMýS çÜ–f¯é™èlÃMýS™èl A…Ô¶æ…

CçÜ$¢¯é²Æý‡$.

E§é: ÌôæQ/ MýSÆý‡ç³{™èl…/ MýSÑ™èl/ B™èlÃMýS£ýl/ AÀ¯]l…§ýl¯é ç³{™èl…/ {ç³Ô>²Ð]lã Ððl¬§ýlOÌñæ¯]lÑ.

{ç³Ô¶æ²Ë Æý‡MýS…: 1. õ³Æ>

Ð]l#Å™èlµ™èl¢ÅÆ>¦Ë$ 1.

2.

3.

(5 Ð]l*Æý‡$PË$)

fVýSÐðl$ËÏ = fVýSÐ]l¬+GËÏ çÜĶæ*ÅrÌêyðl¯Œæ = çÜĶæ*ÅrË$+Byðl¯Œæ §éÇ°_aÇ = §éÇ°+ C_aÇ «§ýlÆ>™èlËÐðl$ËÏ = «§ýlÆ>™èlËÐ]l¬ + GËÏ ¨Ô>…^èlËÐ]l¬ = ¨Ô¶æ+A…^èlËÐ]l(çÜÐ]lÆý‡~ ©Æý‡ƒ çÜ…«¨) {Ô>Ð]l×ê{¿¶æÐ]l¬= {Ô>Ð]l×æ+A{¿¶æÐ]l(çÜÐ]lÆý‡~ ©Æý‡ƒ çÜ…«¨) Ðól$¯]l™èl¢ = Ðól$¯]l+A™èl¢ (AM>Æý‡ çÜ…«¨) ç³Æ>Æý‡$¦Ë$ = ³ç Æý‡ + AÆý‡$¦Ë$ (çÜÐ]lÆý‡~ ©Æý‡ƒ çÜ…«¨) ò³§ýlÐ]l#ÌŸ†¢¯]l = ò³§ýlÐ]l#Ë$+ J†¢¯]l (EM>Æý‡ çÜ…«¨) ¯éËPË$ Ýë^èl$^èl$= ¯éËPË$+^é^èl$^èl$ (VýSçÜyýl§ýlÐé §ólÔ¶æ çÜ…«¨)

10 Ð]l*Æý‡$PË$ (EM>Æý‡ çÜ…«¨) (EM>Æý‡ çÜ…«¨) (CM>Æý‡ çÜ…«¨) (EM>Æý‡ çÜ…«¨)

B«§éÆý‡…V> {ç³Ô¶æ²Ë$ ™èlĶæ*Æý‡$^ólĶæ$yýl…

2. {ç³Ô¶æ²ËMýS$ fÐéº$Ë$ Æ>Ķæ$yýl…

3. õ³Æ> B«§éÆý‡…V> ç³sìætMýS¯]l$ ç³NÇ…^èlyýl…

4. Rêä˯]l$ ç³NÇ…^èlyýl…

5. ™èl´÷µç³#µË¯]l$ VýS$Ç¢…^èlyýl…

E§é: f¯]l糧ýl… A…sôæ ç³ÌñæÏr*Æý‡$. f¯]l糧éËÌZ E…yól ÐéÇ° gê¯]l糧ýl$Ë$ A…sêÆý‡$. ÐéÆý‡$ ´ëyýl$MýS$¯ól ´ër˯]l$ gê¯]l糧ýl VóSĶæ*Ë$ A…sêÆý‡$. Òsìæ¯ól B…VýSÏ…ÌZ ¸ùMŠæ Ýë…VŠæÞ A…sêÆý‡$. E™èl¢Æý‡ ¿êÆý‡™èl§ólÔ¶æ…ÌZ gê¯]l糧ýl VóSĶæ*˯]l$ ÌZMŠæ Ýëíßæ™èlÅ Ìôæ§é ÌZMŠæX™Œæ A…sêÆý‡$. gê¯]l糧ýl VóSĶæ*°MìS JMýS {ç³™ólÅMýS MýSÑ A…r* GÐ]lÆý‡* E…yýlÆý‡$. C¨ JMýS çÜÐ]l$íÙt ç܅糧ýl. AƇ¬™ól ™ðlË$VýS$ ¿êçÙÌZ G…™ø gê¯]l糧ýl VóSĶæ$ ç܅糧ýl E¯]l²ç³µsìæMîS ¿¶æ{§ýlç³Ç^ólÐéÆý‡$ ÌôæMýS G…™ø MýS¯]l$Ð]l$Æý‡$OVðS…¨. CsîæÐ]lË M>Ë…ÌZ gê¯]l糧ýl Ýëíßæ™èlÅ… Ð]l$Æý‡Ìê ç³#…kMøÐ]lyýl…

CsîæÐ]lË íܱ Ýëíßæ™èlÅ… §éÓÆ> Ð]l$¯]l… VýSÐ]l$°…^èlÐ]l^èl$a.

Oò³ õ³Æ> ^èl¨Ñ I§ýl$ {ç³Ô¶æ²Ë$ ™èlĶæ*Æý‡$^ólĶæ$…yìl (5 Ð]l*Æý‡$PË$)