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Economics Class 10 Notes

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Economics Class 10 Notes| Summary and Revision Points

Economics is a subject which studies the production, consumption and distribution of goods. Class 10th Economics deals with the topics such as development, sectors of Indian economy, Money and Credit, Globalisation and Consumer Rights. There are various case studies given in the book to make us understand these topics in more simple way. Thus, we have prepared the Economics Class 10 Notes for you so that you can easily understand all the important terms and points mentioned in the book. You can easily browse StudyRankers notes by clicking on the name of the chapter provided below.



Economics Class 10 Extra Questions

MCQ Test of Class 10th Economics
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Economics Class 10 Extra Questions

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Economics Class 10 Extra Questions Important Questions Answer Included

There are various questions present at the end of the each chapter in Economic Class 10 textbook which are called NCERT Solutions. However, these questions are not sufficient for the purpose of the examination. Therefore, we have provided Economics Class 10 Extra Questions which will help you acing in the exam. These questions also contains important question that could be asked in the examination. You can click on the name of the chapter to start learning.

  • Development Extra Questions
  • Sectors of the Indian Economy┬аExtra Questions
  • Money and Credit┬аExtra Questions
  • Globalisation and the Indian Economy┬аExtra Questions
  • Consumer Rights┬аExtra Questions
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Kshitiz Hindi Class 10 Notes

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Kshitiz Hindi Class 10 Notes| Summary and Important Points

Some of the chapters of Hindi are written in hard language thus it is not easy to get their meaning thoroughly. In this case┬аKshitiz Hindi Class 10 Notes prepared by StudyRankers comes to rescue. These notes are detailed and have meaning of each word so that you can get meaning easily. The poems of Kshitiz are arranged in Chronological order so the students can┬аbecome familiar with the development of the Hindi poetry. You can get the chapter notes by clicking on the chapter name provided below.


Kshitiz Hindi Class 10 Extra Questions

MCQ Test of Kshitiz Hindi Class 10

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Notes of Ch 5 Morphology in Flowering Plants| Class 11th Biology

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Study Material and Notes of┬аCh 5 Morphology in Flowering Plants Class 11th Biology

Topics in the Chapter

  • Classification
  • Numerical Taxonomy
  • Cytotaxonomy
  • Chemataxonomy
  • Algae
  • Reproduction in Algae
  • Bryophytes
  • Reproduction in Bryophytes
  • Pteridophytes
  • Gymnosperms
  • Angiosperms
  • Life Cycle and Alternation of Generations

Points to Remember

Morphology: The study of various external features, forms and relative position of different organs of the organism is known as morphology. It may be further divided into internal and external morphology.

External Morphology: It deals with external forms like shape, size, colour, structure and relative position of different organs.

Internal Morphology: Further divided into anatomy and histology.

Anatomy: It deals with the study of internal structure exposed after dissection and opening of various parts of an organ.

Histology: The study of tissues, their composition and structure.

Adaptation: Any alteration in the structure or function of an organism or any of its part that results from natural selection and by which the organism becomes better fitted to survive and multiply in its environment.

The Root

тЖТ The root is underground part of the plant and develops from elongation of radicle of the embryo.

Characteristics

тЖТ It lies inside the soild, chlorophyll is absent, absence of nodes and internodes, leaves and budgs; positive geotropic and hydrotropic and negative phototropic.

Main functions of root system

(i) Absorption of water and minerals from the soil.

(ii) Provides anchorage to plant parts.

(iii) Stores reserve food material and synthesises plant growth regulators (cytokinins)


Regions of Roots

Root Cap: The root is covered at the apex by the thimble-like structure which protect the tender apical part.

Region of meristematic activity

тЖТ Cells of this region have the capability to divide; cells are small, thin walled with dense protoplasm.

Region of elongation: Cell of this region are elongated and enlarged.This region is responsible for the growth of root in length.

Region of Maturation: This region has differnentiated and matured cells.

тЖТ Some epidermal cells form very fine and delicate thread like structures called root hairs.

Modifications of Root:

тЖТ Roots are modified for support, storage of food, respiration.
тАв For support: Prop roots in banyan tree, stilt roots inmaize and sugarcane.
тАв For respiration : Pneumatophores in Rhizophora (Mangrove).
тАв For storage of food: Fusiform (radish), Napiform (turnip), Conical (carrot), Fasiculated fleshy roots (Asparagus).

The Stem

тЖТ Stem is the aerial part of the plant and develops from plumule of the embryo. It bears nodes and internodes.

Functions of stem

тЖТ Exposure of leaves, conduction of water and minerals, translocation of food, exposure of flowers and fruits.

Modifications of Stem

тЖТ In some plants the stems are modified to perform the function of storage of food, support, protection and vegetative propagation.

тАв For food storage: Rhizome (ginger, turmeric), Tuber (potato), Bulb (onion), Corm (Colocasia, Amorphophallus/Zamin-kand)

тАв For support: Stem tendrils of wawtermelon, grapevine, cucumber, pumpkins.

тАв For protection: Axilliary buds of stem of Citrus, Bougainvillea get modified into pointed thorns. They protect the plants from animals.

тАв For vegetative propagation : Underground stems of grass (runner), strawberry (stolons), leateral branches of mint and jasmine, Eichhornia (offsets).

тАв For assimilation of food : Flattened stem of Opuntia and cylindrical stem of Euphorbia contains chlorophyll and performs photosynthesis.

The Leaf

тЖТ Develops from shoot apcial meristem, flattened, green structure acropetally arranged manufacture the food by photosynthesis. It has bud in axil.

тЖТ A typical leaf has leaf base, petiole and lamina (leaf blade).

тЖТ In some leguminous plants the leaf base may become swollen which is called as pulvinus.
┬а
Venation: The arrangement of veins and veinlets in the lamina of leaf.

Types of Venation

(i) Reticulate: Veinlets form a network as in leaves of dicotyledonous plants (China rose, peepal).

(ii) Parallel: Veins are parallel to each other as in leaves of monocotyledonous
plants (grass, maize,sugarcane).
Phyllotaxy: The pattern of arrangement of leaves on the stem or branch.

Functions of Leaf

Photosynthesis, gaseous exchange, transpiration, protection of buds and conduction.
Modifications of Leaves

(i)┬аTendrils тАФ┬аFunction: Climbing тАФ Example: Sweet Pea, Pea
(ii) Spines тАФ Function:┬аProtection тАФ Example: Aloe, Opuntia, Argemone
(iii) Pitcher тАФ┬аFunction:┬аNutrition тАФ Example: Nepenthes
(iv) Hook тАФ┬аFunction:┬аSupport тАФ Example: CatтАЩs nail
(v) Fleshy Leaves тАФ┬аFunction:┬аStoraged food тАФ Example: Onion and Garlic

Inflorescene: The arrangement of flowers on the floral axis (Peduncle)

Main types of Inflorescence

(i) Recemose:

тЖТ It is indefintie inflorescene.

тЖТ Main axis continues to grow and┬аflowers borne in acropetal succession.
e.g. : Radish, Mustard, Amaranthus

(ii) Cymose:

тЖТ It is defintie inflorescence.

тЖТ Main axis terminates in flowers and the┬аflowers borne in basipetal succession.
e.g. : Cotton, Jasmine, Calotropis

тАв Special Inflorescence typeтАФFicus, Salvia, Euphorbia,Sunflower

тАв FlowerтАФModified shoot meant for reproduction

On the basis of symmetry flower can be

(i)┬аActinomorphic (Radial symmetry)

тЖТ┬аFlower can be divided┬аinto two equal halves┬аin any radial plane┬аpassing through centre.┬аeg : Mustard, Datura,┬аChilli┬а

(ii)┬аZygomorphic┬а(Bilateral symmetry)

тЖТ┬аFlower can be divided into┬аtwo similar halves only in┬аone plane.┬аeg : Pea, bean, Gulmohar,┬аcassia

(iii)┬аAsymmetric┬а(Irregular)

тЖТ┬аFlower cannot be divided┬аin two similar halves by┬аany vertical plane passing┬аthrough centre.┬аeg : Canna

On the basis of floral appendages flower can be:

(i)┬аTrimerous┬а(multiples of 3)
(ii) Tetramerous (multiples of 4)
(iii) Pentamerous (multiples of 5)

On the basis of position of Calyx, corolla and androecium in respect of ovary, flower can be:

(i) Hypogynous (Superior Ovary): eg. Mustard, China rose, Brinjal
(ii) Perigynous (Half inferior ovary): eg. Plum, Rose, Peach
(iii) Epigynous (inferior ovary): eg. Guava, Cucumber, ray florets (sun flower)

тАв Thalamus/Receptacle: Swollen end of flower stalk (pedicel) which bears four whorls of flower viz., Calyx (K), Corolla (C), Androecium (A) and Gynoecium (G).

тАв Bract: Reduced leaf base found at the base of pedicel. Flowers with bracts are called bracteale and without bracts are called ebracteate.

тАв Perianth: If calyx and corolla are not distinguishable, they are called perianth.
Example : Lily

Aestivation

тЖТ The mode of arrangement of sepals or petals infloral bud.

Types of aestivation
(i) Valvate: Sepals or petals just touch one another at the margin, withut overlapping. e.g., Calotropis

(ii) Twisted: Sepals or petals overlap the next sepal or petal e.g., China rose, Cotton, ladyтАЩs finger.

(iii) Imbricate: The margins of sepals or petals overlap one another but not in any defintite direction, e.g., Cassia, Gulmohar.

(iv) Vexillary:The largest petal overlaps the two lateral petals which in turn overlap two smallest anterior petals, e.g., Bean, Pea.

Placentation

тЖТ The arrangement of ovules within the ovary.

Types of Placentation

(i) Marginal: Placenta forms a ridge along the ventral suture of ovary, e.g., Pea.

(ii) Axile: Margins of carpels fuse to form central axis, e.g., China rose, Tomato, Lemon

(iii) Perietal: Ovules develop on inner wall of ovary, e.g., Mustard, Argemone

(iv) Free central: Ovules borne on central axis, lacking septa, e.g., Dianthus, Primrose

(v) Basal: Placenta develop at the base of ovary, e.g., Sunflower, Marigold

тАв Placenta : Parenchymatous flattened cushion inside ovary where ovules are borne.

тАв The fruit : After fertilisation, the mature ovary develops into fruit. The parthenocarpic fruits are formed from ovary without fertilisation (seedless fruit-Banana)


Monocotyledonous seed

тЖТ Endosperm bulky and stores food, covered by proteinaceous Aleurone layer.┬а

тЖТ Seed has single large cotyledonтАУscutellum.

тЖТ Plumule is enclosed in Coleoptile and Radicle is enclosed in Coleorrhiza.

Dicotyledonous Seed


тАв Hilum: Is a scar on the seed coat through which seeds attached to the fruit.

тАв Micropyle: Small pore, above hilum

тАв Cotyledons: two; freshly, full of preserve food materials

тАв Embryonal axis: Radicle and plumule.

тАв Endospermous seed: endosperm present in mature seed. eg. castor

тАв Non-endospermous seed: endosperm not present in mature seeds, eg. bean,

NCERT Solutions of Class 12 Morphology in Flowering Plants
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Kshitiz Hindi Class 10 Extra Questions

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Kshitiz Hindi Class 10 Extra Questions┬аImportant Questions Answer Included

Various questions are provided at the end of each chapter which are called as NCERT Solutions. Before moving further, you must solve these questions. However, if you're preparing for the examination seriously then after seeing this you must move towards seeing extra questions that will give you edge over your classmates. Here, we have provided the┬аKshitiz Hindi Class 10 Extra Questions which will help you in preparing for the examination┬аand scoring┬аmore marks. You can visit the extra questions by clicking on name of the chapter given below.

  • Chapter 1 Pad Extra Questions
  • Chapter 2 Ram Laskhman Parshuram Samwad┬аExtra Questions
  • Chapter 3 Sawiya aur Kavitt┬аExtra Questions
  • Chapter 4 Aatmkathy┬аExtra Questions
  • Chapter 5 Utsaah aur At Nahi Rahi┬аExtra Questions
  • Chapter 6 Yeh Danturit Muskan aur Fasal┬аExtra Questions
  • Chapter 7 Chhaya Mat Chuna┬аExtra Questions
  • Chapter 8 Kanyadan┬аExtra Questions
  • Chapter 9 Sangatkar┬а┬аExtra Questions
  • Chapter 10 Netaji ka Chashma Extra Questions
  • Chapter 11 Balgobin Bhagat Extra Questions
  • Chapter 12 Lakhnavi Andaz Extra Questions
  • Chapter 13 Manviya Karuna ki Divy Chamak Extra Questions
  • Chapter 14 Ek Kahani Yeh Bhi Extra Questions
  • Chapter 15 Stri Shiksha keVirodhi Kutrkon ka Khandan Extra Questions
  • Chapter 16 Naubatkhane me Ibadat Extra Questions
  • Chapter 17 Sanskriti Extra Questions


Kshitiz Hindi Class 10 Notes

MCQ Test of Kshitiz Hindi Class 10

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Kritika Hindi Class 10 Notes

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Kritika Hindi Class 10 Notes| Summary and Important Points

Kritika is a supplementary reader of the Class 10 Hindi Course A. There are five chapters in the textbook however two of them are removed from the syllabus. Therefore, we are left three chapters. These chapters are very long and detailed. If you have less time or going to revise the it is not easy to do this in short time. At this time,┬аKritika Hindi Class 10 Notes prepared by StudyRankers can help you. We have included all the important points while preparing these notes which will ease your exam preparation activity. You can visit these notes clicking on the chapter name provided below.

  • Chapter 1 Mata ka Aanchal Notes
  • Chapter 2 George Pancha ki Naak Notes
  • Chapter 3 Sana-Sana Hath Jodi Notes
  • Chapter 4 Aiehi Thayian Jhulni Herani ho Rama Notes
  • Chapter 5 Main Kyon Likhta Hun Notes


Kritika Hindi Class 10 Extra Questions

MCQ Test of┬аKritika Hindi Class 10
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Kritika Hindi Class 10 Extra Questions

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Kritika Hindi Class 10 Extra Questions┬аImportant Questions Answer Included

Kritika book contains various questions at the end of each chapter. However, the quantity of questions are limited and not cover the whole chapter. Thus, you must prepare yourself to study more questions so excel in the examination. Thus, we have prepared┬аKritika Hindi Class 10 Extra Questions which will improve your understanding of the chapters. These questions also contains previous year questions that can be asked in the examinations. You only need to click on the chapter name to start reading.

  • NCERT Solutions of┬ардкрд╛рда 1-┬ардорд╛рддрд╛ рдХрд╛ рдЖрдБрдЪрд▓
  • NCERT Solutions of┬ардкрд╛рда 2-┬ардЬреЙрд░реНрдЬ рдкрдВрдЪрдо рдХреА рдирд╛рдХ
  • NCERT Solutions of┬ардкрд╛рда 3-┬ард╕рд╛рдирд╛-рд╕рд╛рдирд╛ рд╣рд╛рде рдЬреЛрдбрд╝рд┐
  • NCERT Solutions of┬ардкрд╛рда 4-┬ардПрд╣реА рдареИрдпрд╛рдБ рдЭреБрд▓рдиреА рд╣реЗрд░рд╛рдиреА рд╣реЛ рд░рд╛рдорд╛!
  • NCERT Solutions of┬ардкрд╛рда 5-┬ардореИрдВ рдХреНрдпреЛрдВ рд▓рд┐рдЦрддрд╛ рд╣реВрдБ?


Kritika Hindi Class 10 Notes

MCQ Test of┬аKritika Hindi Class 10
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Sparsh Hindi Class 10 Notes

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Sparsh Hindi Class 10 Notes| Summary and Important Points

Class 10 Sparsh Hindi textbook consists of a number of stories and poems. The poems such as pad and dohe have very difficult meanings thus students found these hard. Stories are also sometimes vast making it lengthy for revision during examination. Therefore, StudyRankers have prepared Sparsh Hindi Class 10 Notes so that you can take help of these useful notes to make your preparation ease. These notes will make you understand the chapter in easy┬а and interesting way. We have also included all the hard words which are inside the chapter in the notes so that you don't need to turn the pages of book while reading. You can find the notes by clicking on the name of chapter provided below.


NCERT Solutions for Class 10th Hindi Sparsh

Sparsh Hindi Class 10 Extra Questions

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Sparsh Hindi Class 10 Extra Questions

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Sparsh Hindi Class 10 Extra Questions┬аImportant Questions Answer Included

Class 10 Sparsh Hindi textbook has various questions at the end of each chapter known as NCERT Solutions. However, if you want to pass the examination with good marks then you must practise more questions additional of these NCERT questions. Therefore, we have provided Sparsh Hindi Class 10 Extra Questions so that you can learn and understand more. These extra questions have been curated by StudyRankers experts which will provide in-depth knowledge to the students. These will ensure extra edge over your competitors. You can visit by clicking on the link provided below.

  • рдкрд╛рда 1- рд╕рд╛рдЦреА Extra Questions
  • рдкрд╛рда 2- рдкрдж Extra Questions
  • рдкрд╛рда 3- рджреЛрд╣реЗ Extra Questions
  • рдкрд╛рда 4- рдордиреБрд╖реНрдпрддрд╛ Extra Questions
  • рдкрд╛рда 5- рдкрд░реНрд╡рдд рдкреНрд░рджреЗрд╢ рдореЗрдВ рдкрд╛рд╡рд╕ Extra Questions
  • рдкрд╛рда 6- рдордзреБрд░-рдордзреБрд░ рдореЗрд░реЗ рджреАрдкрдХ рдЬрд▓ Extra Questions
  • рдкрд╛рда 7- рддреЛрдк Extra Questions
  • рдкрд╛рда 8- рдХрд░ рдЪрд▓реЗ рд╣рдо рдлрд╝рд┐рджрд╛ Extra Questions
  • рдкрд╛рда 9- рдЖрддреНрдорддреНрд░рд╛рдг Extra Questions
  • рдкрд╛рда 10- рдмрдбрд╝реЗ рднрд╛рдИ рд╕рд╛рд╣рдм Extra Questions
  • рдкрд╛рда 11- рдбрд╛рдпрд░реА рдХрд╛ рдПрдХ рдкрдиреНрдирд╛ Extra Questions
  • рдкрд╛рда 12- рддрддрд╛рдБрд░рд╛-рд╡рд╛рдореАрд░реЛ рдХрдерд╛ Extra Questions
  • рдкрд╛рда 13- рддреАрд╕рд░реА рдХрд╕рдо рдХреЗ рд╢рд┐рд▓реНрдкрдХрд╛рд░ рд╢реИрд▓реЗрдВрджреНрд░ Extra Questions
  • рдкрд╛рда 14- рдЧрд┐рд░рдЧрд┐рдЯ Extra Questions
  • рдкрд╛рда 15- рдЕрдм рдХрд╣рд╛рдБ рджреВрд╕рд░реЗ рдХреЗ рджреБрдЦ рд╕реЗ рджреБрдЦреА рд╣реЛрдиреЗ рд╡рд╛рд▓реЗ Extra Questions
  • рдкрд╛рда 16- рдкрддрдЭрд░ рдореЗрдВ рдЯреВрдЯреА рдкрддреНрддрд┐рдпрд╛рдБ Extra Questions
  • рдкрд╛рда 17- рдХрд╛рд░рддреВрд╕ Extra Questions
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Sanchyan Hindi Class 10 Notes

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Sanchyan Hindi Class 10 Notes| Summary and Important Points

Sanchyan Hindi Class 10 textbook is supplementary reader which contains only three stories however each of them are very vast which need a lot of time to read and understand. To simplify this process, StudyRankers has prepared Sanchyan Hindi Class 10 Notes which are detailed and contains all the important points which you need to consider during revision. These notes are easy to understand and comprehensible thus it will ensure you good marks in the examination. You don't need to open your book and start reading the chapter when you don't have enough time. You can revise and grasp the important events of the chapter completely by reading these notes. You can start reading these notes by clicking on the name chapter's name.

  • рдкрд╛рда 1-┬ард╣рд░рд┐рд╣рд░ рдХрд╛рдХрд╛ Notes
  • рдкрд╛рда 2-┬ард╕рдкрдиреЛрдВ рдХреЗ-рд╕реЗ рджрд┐рди Notes
  • рдкрд╛рда 3-┬ардЯреЛрдкреА рд╢реБрдХреНрд▓рд╛┬аNotes


Kritika Hindi Class 10 Extra Questions

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Sanchyan Hindi Class 10 Extra Questions

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Sanchyan Hindi Class 10 Extra Questions┬аImportant Questions Answer Included

Sanchyan Hindi Class 10 textbook has a number of questions in every chapter. But from the examination point of view, these questions are not sufficient. You need to answer more questions and practise them in order to obtain good marks. Therefore, we have prepared┬аSanchyan Hindi Class 10 Extra Questions which is included with all the important questions asked in the previous examination. The answers are very detailed and to the point. You can get the questions by clicking on the chapter's name provided below.



  • рдкрд╛рда 1-┬ард╣рд░рд┐рд╣рд░ рдХрд╛рдХрд╛ Notes
  • рдкрд╛рда 2-┬ард╕рдкрдиреЛрдВ рдХреЗ-рд╕реЗ рджрд┐рди Notes
  • рдкрд╛рда 3-┬ардЯреЛрдкреА рд╢реБрдХреНрд▓рд╛┬аNotes


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Summary of Amanda! by Robin Klein NCERT Class 10th

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Summary of Amanda! with Quick Revision Notes┬а First Flight Class 10

Summary of the Poem Amanda!

Amanda! by Robin Klein

Stanza 1

DonтАЩt bite your nails, Amanda!┬а
DonтАЩt hunch your shoulders, Amanda!┬а
Stop that slouching and sit up straight,┬а
Amanda!

In this stanza, the poet says that Amanda is getting instructed, most probably by her parents for biting nails and sitting lazily with her shoulders bent. The tone of instructions here is not a friendly one and thus fails to make any sense to Amanda. The poet here, focusses on the aspects related to the upbringing of a child (girl) and how parents go to any limit to bring proper sense to their child. Amanda is thus, getting trained for the society she is a part of. The pressure of making oneself presentable to the society triumphs over every other behaviour and manners. The last phrase or word 'Amanda!' is used with an exclamation mark which shows the irritation and frustration of the parent.

Stanza 2

(There is a languid, emerald sea,
where the sole inhabitant is meтАФ
a mermaid, drifting blissfully.)


It is quite interesting that the above lines are given within brackets. Brackets are used to provide more meaning to the phrase.
In this stanza, the poet uses it (brackets) to present the imagination of the little girl, the free-flow of pure thoughts. Amanda uses her imagination as an escape point from day to day commands of her parents. She feels suffocated in the real world and thus finds peace in her very own created world where there are no restrains. Amanda is lost in a world of her own away from the disorders and principles of the society. She imagines herself to be a joyful mermaid sailing without any confines alongside soft waves of the green sea. This world of Amanda is free and contained in itself and her happiness doesn't require any other human being. It is important to note that Amanda not requiring her father or mother points that she is being tortured by both of them. Her life is not going the way she wants, and there is no one to support her. For a child, mermaid is a symbol of freedom and wonder. Another meaning that is attached with mermaid is that they don't wish to be disturbed as they live in their own environs and would do anything to be like that. For this reason Amanda wishes to be a mermaid.

Stanza 3

Did you finish your homework, Amanda?┬а
Did you tidy your room, Amanda?┬а
I thought I told you to clean your shoes,

In this stanza, the poet says that Amanda is now being asked about whether she has finished her homework, or tidied up her room and also whether she has cleaned her shoes. These set of instructions marks a shift from the instructions given in first stanza. Now Amanda is being coached about the things that are related to her surroundings. The pattern of instructions explains that how every aspect of her is related to questioning and proper guidance. She is being disciplined for every little thing, making her lose every aspect of hers. Her innocence is eventually getting lost with passage of time. The way these instructions are delivered points out the regular nature of these lessons. Her name being called again with an exclamation mark shows that the parents seem to be losing their cool and are troubled. They are helpless in bringing correct 'senses to this girl as she is not paying proper heed to the instructions given by them.

Stanza 4

(I am an orphan, roaming the street.┬а
I pattern soft dust with my hushed, bare feet.┬а
The silence is golden, the freedom is sweet.)

In this stanza, the poet says that Amanda is again lost into her own world. After getting a fresh list of instructions from her parents, she wishes to be away from this daily routine life. The very first line is awfully depressing where Amanda hopes to be an orphan suggesting how much depressed she is because of her parents. This is indeed a very sorry place for a child to be in. Parents should be very careful in making their kids understand the ways of the world. While doing so, they should respect their child's awareness about the things around them. Amanda perceives herself as an orphan roaming on the streets, moving aimlessly without any purpose. She seems happy as she draws patterns using her bare feet. Patterning of dust by Amanda is important here as it brings order to the carefree world of hers. The shouting and yelling of her parents are too harsh for her to bear that she desires for this calmness.

Stanza 5

Don't eat that chocolate, Amanda!┬а
Remember your acne, Amanda!

In this stanza, the poet says that the set of instructions provided here indicates how much essential it is for Amanda to understand the value of external beauty, and steps to be taken to preserve it start from a very tender age. Amanda is stopped by her parents from eating a chocolate as previously that had caused her acne. Here, we see how a child is made conscious of a natural experience such as acne. However, Amanda is still lost in her own thoughts and doesn't care enough to look up to her scolding parents. This carelessness further angers the parents and they ask for her attention when she is being scolded. The role of appearance in the society is given more significance than the basic values and creativity.

Stanza 6

(I am Rapunzel, I have not a care;
life in a tower is tranquil and rare;┬а
I'll certainly never let down my bright hair!)

In this stanza, the poet says that Amanda is still lost in her own dreams. She pictures herself to be the long golden-haired Rapunzel who lived in a castle and had no care about anything. Amanda imagines that the life of Rapunzel must have been very peaceful and fantastic in the tower. But she wishes to evade the fate that was met out to Rapunzel as she is unwilling to let her hair down. Amanda doesn't want her peace to be disturbed anyhow. She seeks a life which is away from any other human form. We can see here how the presence of her parents and their inhuman behaviour had made her against any human connection. In the story of Rapunzel, it is because of a prince that Rapunzel is able to understand and receive happiness but Amanda doesn't require any prince, even though she is totally unaware about the feelings of love. The terrific effect of her parent's teaching on Amanda can be seen pretty apparently. Hence, she only wanted to live by herself as the presence of another being in her life would require her to act in a certain way. Amanda wanted to live free and happy.

Stanza 7

Stop that sulking at once, Amanda!┬а
YouтАЩre always so moody, Amanda!┬а
Anyone would think that I nagged at you, Amanda!

In this stanza, the poet says that the parents keep instructing Amanda on the do's and don'ts, but Amanda remains lost in her own dreams. The parents believe that Amanda is not reacting because she is annoyed. Amanda's behaviour has made her parents look bad and they are worried about their image. They are concerned about how society will perceive them if their child always remains in a foul mood. They want to prove themselves as responsible parents who manage to balance out what the child wants and what the society expects out of Amanda. However, they have already failed in their efforts.

Quick Revision Notes

тАв The poem deals with the upbringing of a small child, Amanda. It highlights the struggles faced by the child. Poet Robin Klein makes an important point that a child should never be denied freedom.

тАв Though it is parents who are responsible for proper upbringing of their child but that should not make a child feel trapped. Here, Amanda is prepared to be acceptable in society, and this training needs her freedom to be cut short.

тАв Her imagination is not given enough space; thus making her so angry that she wishes to be an orphan. The continuous nagging has, thus, made her moody.
тЖз

Summary of Animals by Walt Whitman NCERT Class 10th

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Summary of Animals with Quick Revision Notes┬а First Flight Class 10

Summary of the Poem Animals

Animals by Walt Whitman

Stanza 1

I think I could turn and live with animals, they are┬а
so placid and self-contained,┬а
I stand and look at them long and long.

In this stanza, the poet here desires to turn into an animal and live with them as he is impressed by their calmness and the purity of their mind. Unlike humans, animals seem so contained with their lives and are happy in their natural surroundings. The simple lives of animals help them maintain self-control and their rationality. He stands and looks at them for a long time. In the phrase тАШlong and longтАЩ the implied meaning is the longing that the poet feels for these two qualities in human beings.

Stanza 2

They do not sweat and whine about their condition,┬а
They do not lie awake in the dark and weep for their sins,┬а
They do not make me sick discussing their duty to God,

The poet is quite happy with the fact that animals do not make complaints and cry about their conditions like humans. They eat and sleep peacefully as they have nothing to worry about, while humans, because of their wrong actions are unable to do so and thus cannot sleep without worrying about them. Humans, even after committing sins, talk about God and rightness, while animals are simple creatures and they do not need to worry about praying to God. The poet here means that since animals are so pure, they do not pray to God for forgiveness or ask God to fulfil their desires like humans.

Stanza 3

Not one is dissatisfied, not one is demented with┬а
the mania of owning things,┬а
Not one kneels to another, nor to his kind that┬а
lived thousands of years ago,┬а
Not one is respectable or unhappy over the whole earth.

In this stanza, the poet says that Animals do not possess material things like humans and they are happy and satisfied without all the worldly items, the desire of which has affected human beings very badly. This desire to own things has been called madness by the poet. Animals are free from the habit of praying to their ancestors. When the poet says 'not one is respectable' he means that since all of them are equal, there is no question of respect to some and insult to others. All these features of animals make them happy and uncomplaining.

Stanza 4

So they show their relations to me and I accept them,┬а
They bring me tokens of myself, they evince┬а
them plainly in their possession
I wonder where they get those tokens,┬а
Did I pass that way huge times ago and negligently drop them?

In this stanza, the poet feels that animals represent human beings in some way. This means that animals seem to have what humans once had, i.e. virtues like kindness, Self-containment and innocence. They symbolise the lost values of the human race. He believed that civilisation has corrupted human beings and instead of teaching values to them, it has taught them greed. He believes in this poem that humans dropped these virtues a long time ago and have forgotten them.

Quick Revision Notes

тАв In the poem 'Animals', the poet Walt Whitman praises animals for being better than human beings and for possessing all such qualities that humans lack or have forgotten.

тАв Those qualities are calmness, the lack of greed and the ability to stay happy and contained among others.

тАв The poet wants to live among animals and experience a life where no one complains and where they are free of sins and sorrow. The most important theme of the poem is not to praise how good animals are, but to compare humans with them in order to highlight the flaws of their nature.

тАв The poet believes that probably a very long time ago, humans possessed all these qualities mentioned above, but they have now lost them.
тЖз
тЖз

Notes of Ch 7 Coordinate Geometry| Class 10th Math

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Revision Notes for Ch┬а7 Coordinate Geometry Class 10th Mathematics

Coordinate Geometry

тАв┬аCoordinate Geometry: The branch of Mathematics in which algebraic methods are used to solve geometrical problems is known as coordinate geometry.

Coordinate System

тАв As shown in the figure, the line XOXтА▓ is known as the X-axis and YOYтА▓ is known as Y-axis.

тАв The point O is called the origin. For any point P (x y), the ordered pair (x y)┬аis called the coordinate of point P.

тАв The distance of a point from Y-axis is called its abscissa and the distance of a point from X-axis is called its ordinate.
тАв Distance between Two Points
The distance between two points P (x1, y1) and Q (x2, y2) is given by:
This is also known as Distance Formula.
Note: The distance of any point P(x,y) from the origin O(0,0) is given by:

тАв Section Formula

Let P (x,y) be a point on the line segment joining A(x1, y1) and B(x2, y2) such that it divides AB internally in the ratio m:n. The coordinates of the point P are given by
This is known as Section Formula.

Note:
(i) If the point P divides the line segment joining A(x1, y1)┬аand B(x2, y2)┬аinternally in the ratio k:1, its coordinates are given by:

Example:┬аIn what ratio does the point (2,- 5) divide the line segment joining the points A(-3, 5) and B(4, -9).

Solution:

Let the ratio be ╬╗ : 1



The required ratio is 5:2.

Mid -Point Formula

The mid-point of the line joining A(x1, y1) and B(x2, y2) is given as


Centroid of the Triangle
The Centroid of the triangle is the point of intersection of medians of the triangle. For a triangle A(x1, y1), B(x2, y2) and C(x3, y3) we can say that the co-ordinates of centroid is given as



Areas of Triangle



Condition for Collinearity of three Points

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рдЭрд╛рдБрд╕реА рдХреА рд░рд╛рдиреА - рдкрдарди рд╕рд╛рдордЧреНрд░реА рдФрд░ рд╕рд╛рд░ NCERT Class 6th Hindi

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рдЭрд╛рдБрд╕реА рдХреА рд░рд╛рдиреА рд╕рд╛рд░ рд╡рд╕рдВрдд рднрд╛рдЧ┬а- 1 (Summary of Jhansi ki Rani Vasant)

рдЗрд╕ рдХрд╡рд┐рддрд╛ рдореЗрдВ┬ардЭрд╛рдБрд╕реА рдХреА рд░рд╛рдиреА рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рдХреА рд╡реАрд░рддрд╛ рдХрд╛ рдмрдЦрд╛рди рдХрд┐рдпрд╛ рдЧрдпрд╛ рд╣реИ| рдпрд╣ рдХрд╡рд┐рддрд╛ рд╕рдиреН 1857 рдХреЗ рд╕реНрд╡рддрдВрддреНрд░рддрд╛ рд╕рдВрдЧреНрд░рд╛рдо рдХреА рдкрд░рд┐рд╕реНрдерд┐рддрд┐рдпреЛрдВ рдХреА рдЭрд▓рдХ рджреЗрддрд╛ рд╣реИ|

рдЕрдВрдЧреНрд░реЗреЫреЛрдВ рдХреЗ рдмреЭрддреЗ рдЕрддреНрдпрд╛рдЪрд╛рд░ рдХреЗ рдЦрд┐рд▓рд╛рдл рдФрд░┬ард╕реНрд╡рддрдВрддреНрд░рддрд╛ рдХреА рд▓рдбрд╝рд╛рдИ рдХреЗ рд▓рд┐рдП┬арднрд╛рд░рдд рдХреЗ рд░рд╛рдЬрд╛рдУрдВ рдореЗрдВ рд╣рд▓рдЪрд▓ рд╣реБрдИ рдЬрд┐рд╕рд╕реЗ┬ард╕рд┐рдВрд╣рд╛рд╕рди рд╣рд┐рд▓ рдЧрдПред рд░рд╛рдЬрд╡рдВрд╢ рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдкрд░ рдЧреБрд╕реНрд╕рд╛┬ард╣реЛ рдЧрдПред рдЧреБрд▓рд╛рдореА рдХреЗ рдЬрдВрдЬреАрд░ рдореЗрдВ рдЬрдХреЬреЗ┬ардЬрд░реНрдЬрд░ рдмреВрдврд╝реЗ рднрд╛рд░рдд рдореЗрдВ рдлрд┐рд░ рд╕реЗ┬ардирдпрд╛ рдЬреЛрд╢ рдХрд╛ рд╕рдВрдЪрд╛рд░ рд╣реБрдЖред рд╕рднреА┬ард░рд╛рдЬрд╛ рдЕрдкрдиреА рдЦреЛрдИ рд╣реБрдИ рдЖрдЬрд╛рджреА рдХрд╛ рдореВрд▓реНрдп рд╕рдордЭрдиреЗ рд▓рдЧреЗ рдереЗ рдЗрд╕рд▓рд┐рдП рдЙрдиреНрд╣реЛрдВрдиреЗ рдлрд┐рд░рдВрдЧреА рдпрд╛рдиреА┬ардЕрдВрдЧреНрд░реЗреЫреЛ┬ардХреЛ рднрд╛рд░рдд рд╕реЗ рднрдЧрд╛рдиреЗ рдХрд╛ рдирд┐рд╢реНрдЪрдп рдХрд░ рд▓рд┐рдпрд╛ рдерд╛ред рднрд╛рд░рдд рдХреА рдкреБрд░рд╛рдиреА рддрд▓рд╡рд╛рд░ рд╕рдиреН 1857 рдореЗрдВ рдЪрдордХ рдЙрдареАред рдЭрд╛рдБрд╕реА рдХреА рд░рд╛рдиреА рдЙрд╕ рдпреБрджреНрдз рдореЗрдВ рд╡реАрд░ рдкреБрд░реБрд╖реЛрдВ рдХреА рднрд╛рдБрддрд┐ рд▓рдбрд╝реАред рдЙрд╕рдХреА рдпрд╣ рдХрд╣рд╛рдиреА рд╣рдордиреЗ рдмреБрдВрджреЗрд▓рдЦрдгреНрдб рдХреЗ рд╣рд░рдмреЛрд▓реЛрдВ рд╕реЗ рд╕реБрдиреА рдереАрдВред

рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рдХрд╛рдирдкреБрд░ рдХреЗ рдирд╛рдирд╛ рд╕рд╛рд╣рдм рдХреА рдореБрдБрд╣рдмреЛрд▓реА рдмрд╣рди рдереА рдЬрд┐рдирдХрд╛┬ардмрдЪрдкрди рдХрд╛ рдирд╛рдо рдЫрдмреАрд▓реА рдерд╛ред рд╡рд╣┬ардЕрдкрдиреЗ рдкрд┐рддрд╛ рдХреА рдЕрдХреЗрд▓реА рд╕рдВрддрд╛рди рдереАрдВред рдЙрдирдХрд╛ рдмрдЪрдкрди рдирд╛рдирд╛ рд╕рд╛рд╣рдм рдХреЗ рд╕рд╛рде рдкреЭрддреЗ рдФрд░ рдЦреЗрд▓рддреЗ рдмрд┐рддрд╛ рдерд╛ред рд╡рд╣ рдЕрдкрдиреЗ рдЙрдореНрд░ рдХреА рд▓реЬрдХрд┐рдпреЛрдВ рдХреЛ рд╕рд╣реЗрд▓реА рдирд╣реАрдВ рдмрдирд╛рдХрд░┬ардмрд░рдЫреА, рдврд╛рд▓, рдХреГрдкрд╛рдг рдХреЛ рд╡рд╣ рдЕрдкрдиреА рд╕рд╣реЗрд▓реА рдорд╛рдирддреА рдереАред рдЙрдиреНрд╣реЗрдВ┬ард╢рд┐рд╡рд╛рдЬреА рдЬреИрд╕реЗ рд╡реАрд░реЛрдВ рдХреА рдХрд╣рд╛рдирд┐рдпрд╛рдБ рдЬрдмрд╛рдиреА рдпрд╛рдж рдереАрдВред рдХрд╡рдпрд┐рддреНрд░реА рдХрд╣рддреА рд╣реИрдВ┬ардХрд┐ рд╣рдордиреЗ рдмреБрдВрджреЗрд▓реЗ рд╣рд░рдмреЛрд▓реЛрдВ рдХреЗ рдореБрдБрд╣ рд╕реЗ рд╕реБрдирд╛ рд╣реИ рдХрд┐ рд░рд╛рдиреА рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рд╡реАрд░ рдкреБрд░реБрд╖реЛрдВ рдХреА рднрд╛рдБрддрд┐ рдмрд╣рд╛рджреБрд░реА рд╕реЗ рд▓рдбрд╝реА рдереАрдВред

рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рдХреЛ рджреЗрдЦрдХрд░┬ардРрд╕рд╛ рд▓рдЧрддрд╛ рдерд╛ рдХрд┐ рдорд╛рдиреЛ рд╡рд╣ рд╡реАрд░рддрд╛ рдХреА рдЕрд╡рддрд╛рд░ рд▓рдХреНрд╖реНрдореА рдпрд╛ рджреБрд░реНрдЧрд╛ рд╣реИрдВ| рдЙрдирдХреА┬арддрд▓рд╡рд╛рд░реЛрдВ рдХреА рдЪреЛрдЯреЗрдВ рджреЗрдЦрдХрд░ рдорд░рд╛рдареЗ рдкреНрд░рд╕рдиреНрди рд╣реЛрддреЗ рдереЗред рдирдХрд▓реА рдпреБрджреНрдз рдХрд░рдирд╛, рдЪрдХреНрд░рд╡реНрдпреВрд╣ рдмрдирд╛рдирд╛, рдЦреВрдм рд╢рд┐рдХрд╛рд░ рдХрд░рдирд╛, рд╢рддреНрд░реБ рдХреА рд╕реЗрдирд╛ рдХреЛ рдШреЗрд░рдирд╛,┬ард╢рддреНрд░реБ рдХреЗ рдХрд┐рд▓реЗ рддреЛрдбрд╝рдирд╛ рдЙрдирдХреЗ рдкреНрд░рд┐рдп рдЦреЗрд▓ рдереЗред рдорд╣рд╛рд░рд╛рд╖реНрдЯреНрд░ рдХреА рдХреБрд▓рджреЗрд╡реА рднрд╡рд╛рдиреА рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рдХреА рдЖрд░рд╛рдзреНрдп рдереАрдВред

рд╡реАрд░рд╛рдВрдЧрдирд╛ рдЫрдмреАрд▓реА рдХрд╛ рд╡рд┐рд╡рд╛рд╣ рдЭрд╛рдБрд╕реА рдХреЗ рд░рд╛рдЬрд╛ рдЧрдВрдЧрд╛рдзрд░ рд░рд╛рд╡ рдХреЗ рд╕рд╛рде рд╣реБрдЖ рддрдм рд╡рд╣ рд░рд╛рдиреА рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рдмрдирдХрд░ рдЭрд╛рдБрд╕реА рдЖ рдЧрдИред рд░рд╛рдЬрдорд╣рд▓ рдореЗрдВ рдмрдзрд╛рдИ рдХреЗ рдмрд╛рдЬреЗ рдмрдЬрдиреЗ рд▓рдЧреЗред рдЙрдирдХреЗ рд╡рд┐рд╡рд╛рд╣ рдХреЗ рдЕрд╡рд╕рд░ рдкрд░ рдЭрд╛рдБрд╕реА рдХреЗ рд░рд╛рдЬрдорд╣рд▓ рдореЗрдВ рдмрдзрд╛рдЗрдпрд╛рдБ рдмрдЬреАрдВ рдФрд░ рдЦреБрд╢рд┐рдпрд╛рдБ рдЫрд╛ рдЧрдИрдВред рдорд╛рдиреЛ, рд╡рд╣ рдЭрд╛рдБрд╕реА рдореЗрдВ рд╡реАрд░ рдмреБрдВрджреЗрд▓реЛрдВ рдХреА рдХреАрд░реНрддрд┐ рдмрдирдХрд░ рдЖ рдЧрдИ рд╣реЛред┬ардРрд╕рд╛ рд▓рдЧрд╛ рдЬреИрд╕реЗ рдЪрд┐рддреНрд░рд╛ рдХреЛ рд╡реАрд░ рдЕрд░реНрдЬреБрди рдорд┐рд▓ рдЧрдпрд╛ рдпрд╛ рд╢рд┐рд╡ рд╕реЗ рднрд╡рд╛рдиреА рдорд┐рд▓реА рд╣реЛред

рд░рд╛рдиреА рдХреЗ рд╡рд┐рд╡рд╛рд╣ рдХреЗ рдмрд╛рдж рдЭрд╛рдБрд╕реА рдХрд╛ рд╕реМрднрд╛рдЧреНрдп рдЬрд╛рдЧ рдЧрдпрд╛ред рдорд╣рд▓реЛрдВ рдореЗрдВ рдкреНрд░рд╕рдиреНрдирддрд╛ рдХрд╛ рдкреНрд░рдХрд╛рд╢ рд╣реЛ рдЧрдпрд╛, рдХрд┐рдиреНрддреБ рд╕рдордп рдХреЗ рд╕рд╛рде рджреБрд░реНрднрд╛рдЧреНрдп рдХреЗ рдмрд╛рджрд▓ рднреА рдШрд┐рд░ рдЖрдПред рджреБрд░реНрднрд╛рдЧреНрдп рдХреЛ рддреАрд░ рдЪрд▓рд╛рдиреЗ рд╡рд╛рд▓реЗ рд╣рд╛рдереЛрдВ рдХрд╛ рдЪреВрдбрд╝рд┐рдпрд╛рдБ рдкрд╣рдирдирд╛ рдЕрдЪреНрдЫрд╛ рдирд╣реАрдВ рд▓рдЧрд╛ рдФрд░ рд╣рд╛рдп рд░рд╛рдиреА рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рд╡рд┐рдзрд╡рд╛ рд╣реЛ рдЧрдИред рднрд╛рдЧреНрдп рдХреЛ рднреА рдЙрди рдкрд░ рджрдпрд╛ рдирд╣реАрдВ рдЖрдИред рд░рд╛рдЬрд╛ рдЧрдВрдЧрд╛рдзрд░ рд░рд╛рд╡ рдирд┐:рд╕рдВрддрд╛рди рдорд░ рдЧрдПред рд░рд╛рдиреА рд╢реЛрдХ рдореЗрдВ рдбреВрдм рдЧрдИред

рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рд╡рд┐рд╡рд╛рд╣ рдХреЗ рдмрд╛рдж рдЬрдм рдЭрд╛рдБрд╕реА рдореЗрдВ рдЖрдИ рддреЛ рд╡рд╣рд╛рдБ рдХрд╛ рд╕реМрднрд╛рдЧреНрдп рдЬрд╛рдЧ рдЧрдпрд╛| рдорд╣рд▓реЛрдВ рдореЗрдВ рдЙрдЬрд╛рд▓рд╛ рдЫрд╛ рдЧрдпрд╛ред рдХрд┐рдВрддреБ рд╣рдерд┐рдпрд╛рд░ рдЙрдард╛рдиреЗ рд╡рд╛рд▓реЗ рд╣рд╛рдереЛрдВ рдХреЛ рдЪреВрдбрд╝рд┐рдпрд╛рдБ рдХрдм рд╢реЛрднрд╛ рджреЗрддреА рд╣реИрдВ? рджреБрд░реНрднрд╛рдЧреНрдп рдХреЛ рддреАрд░ рдЪрд▓рд╛рдиреЗ рд╡рд╛рд▓реЗ рд╣рд╛рдереЛрдВ рдХрд╛ рдЪреВрдбрд╝рд┐рдпрд╛рдБ рдкрд╣рдирдирд╛ рдЕрдЪреНрдЫрд╛ рдирд╣реАрдВ рд▓рдЧрд╛|┬ард░рд╛рдЬрд╛ рдХреА рдореГрддреНрдпреБ рд╣реЛ рдЧрдИ рдФрд░ рд░рд╛рдиреА рд╡рд┐рдзрд╡рд╛ рд╣реЛ рдЧрдИред рднрд╛рдЧреНрдп рдХреЛ рднреА рдЙрди рдкрд░ рджрдпрд╛ рдирд╣реАрдВ рдЖрдИред рд░рд╛рдЬрд╛ рдЧрдВрдЧрд╛рдзрд░ рд░рд╛рд╡ рдирд┐:рд╕рдВрддрд╛рди рдорд░ рдЧрдПред рд░рд╛рдиреА рд╢реЛрдХ рдореЗрдВ рдбреВрдм рдЧрдИред

рдЭрд╛рдБрд╕реА рдХрд╛ рджреАрдкрдХ рдмреБрдЭ рдЬрд╛рдиреЗ рдкрд░ рдЕрд░реНрдерд╛рдд рд░рд╛рдЬрд╛ рдХреЗ рдорд░ рдЬрд╛рдиреЗ рдкрд░ рдЕрдВрдЧреНрд░реЗрдЬ рдЧрд╡рд░реНрдирд░ рд▓реЙрд░реНрдб рдбрд▓рд╣реМрдЬреА рдХреЛ рдмрдбрд╝реА рдкреНрд░рд╕рдиреНрдирддрд╛ рд╣реБрдИ, рдХреНрдпреЛрдВрдХрд┐ рдЙрд╕реЗ рдЭрд╛рдБрд╕реА рдХрд╛ рд░рд╛рдЬреНрдп рд╣рдбрд╝рдкрдиреЗ рдХрд╛ рдЕрдЪреНрдЫрд╛ рдЕрд╡рд╕рд░ рдорд┐рд▓ рдЧрдпрд╛ред рдЙрд╕рдиреЗ рддреБрд░рдиреНрдд рдЕрдкрдиреА рдлреМрдЬреЗрдВ рднреЗрдЬ рдЭрд╛рдБрд╕реА рдХреЗ рдХрд┐рд▓реЗ рдкрд░ рдЕрдкрдирд╛ рдЭрдВрдбрд╛ рдлрд╣рд░рд╛ рджрд┐рдпрд╛ред рдЗрд╕ рдкреНрд░рдХрд╛рд░ рдЙрд╕ рд╡рд╛рд░рд┐рд╕ рд░рд╣рд┐рдд рдЭрд╛рдБрд╕реА рдХреЗ рд░рд╛рдЬреНрдп рдХрд╛ рд╡рд╛рд░рд┐рд╕ рдмреНрд░рд┐рдЯрд┐рд╢ рд░рд╛рдЬреНрдп рдмрди рдЧрдпрд╛редрд░рд╛рдиреА рдиреЗ рдЖрдБрд╕реВ рднрд░рдХрд░ рджреЗрдЦрд╛ рдХрд┐ рдЭрд╛рдБрд╕реА рдЙрдЬрдбрд╝ рд░рд╣реА рдереАред

рдЬрдм рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдиреЗ рдЭрд╛рдБрд╕реА рдХреЛ рдЕрдкрдиреЗ рд░рд╛рдЬреНрдп рдореЗрдВ рдорд┐рд▓рд╛рдпрд╛, рддрдм рд░рд╛рдиреА рдиреЗ рдЙрдирд╕реЗ рдЕрдиреЗрдХ рддрд░рд╣ рд╕реЗ рд╡рд┐рдирдореНрд░ рдкреНрд░рд╛рд░реНрдердирд╛ рдХреА рдкрд░рдиреНрддреБ рд╕рдм рдмреЗрдХрд╛рд░ рд░рд╣рд╛ред рдЕрдВрдЧреНрд░реЗрдЬрд╝ рдЬрдм рднрд╛рд░рдд рдореЗрдВ рдИрд╕реНрдЯ рдЗрдВрдбрд┐рдпрд╛ рдХрдВрдкрдиреА рдХреЗ рд░реВрдк рдореЗрдВ рдЖрдП рддреЛ рд╡реЗ рд╕рд╛рдзрд╛рд░рдг рд╡реНрдпрд╛рдкрд╛рд░реА рдереЗред рдЙрд╕ рд╕рдордп рд╡реЗ┬ардпрд╣рд╛рдБ рдХреЗ рд░рд╛рдЬрд╛рдУрдВ рдХреА рджрдпрд╛ рдЪрд╛рд╣рддреЗ рдереЗред рдбрд▓рд╣реМрдЬреА рдиреЗ рдзреАрд░реЗ-рдзреАрд░реЗ рдЕрдВрдЧреНрд░реЗрдЬреА рд╢рд╛рд╕рди рдХрд╛ рд╡рд┐рд╕реНрддрд╛рд░ рдХрд┐рдпрд╛ рдФрд░ рдзреАрд░реЗ-рдзреАрд░реЗ┬ардкрд░рд┐рд╕реНрдерд┐рддрд┐рдпрд╛рдБ рдЙрдирдХреЗ рдкрдХреНрд╖ рдореЗрдВ рдЖ рдЧрдИрдВ|┬ардЬрд┐рди рд░рд╛рдЬрд╛рдУрдВ рдФрд░ рдирд╡рд╛рдмреЛрдВ рд╕реЗ рд╡реЗ рддрдм рджрдпрд╛ рдорд╛рдБрдЧрддреЗ рдереЗ, рдЙрдиреНрд╣реАрдВ рдХреЛ рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдиреЗ рдкреИрд░реЛрдВ рд╕реЗ рдареБрдХрд░рд╛рдпрд╛ рд╣реИред рдЕрдм рдЕрдВрдЧреНрд░реЗрдЬрд╝реА рд░рд╛рдЬреНрдп рдХреА рджрд╛рд╕реА рдереА рдФрд░ рджрд╛рд╕реА рдХреЗ рд╕рдорд╛рди рд░рд╣рдиреЗ рд╡рд╛рд▓реА рдЕрдВрдЧреНрд░реЗрдЬрд╝реА рд╢рд╛рд╕рди рдХреА рд╡рд┐рдХреНрдЯреЛрд░рд┐рдпрд╛ рдЕрдм рд╣рдорд╛рд░реЗ рджреЗрд╢ рдХреА рдорд╣рд╛рд░рд╛рдиреА рдмрди рдЧрдИ рдереА рдпрд╛рдиреА┬ардЕрдВрдЧреНрд░реЗрдЬреА рд╕рд╛рдореНрд░рд╛рдЬреНрдп рдкреВрд░реЗ┬арднрд╛рд░рдд рдореЗрдВ реЮреИрд▓ рдЧрдпрд╛ред

рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдиреЗ рджрд┐рд▓реНрд▓реА рдЫреАрди рд▓реА рдФрд░ рдЙрд╕ рдкрд░ рдЕрдкрдирд╛ рдЕрдзрд┐рдХрд╛рд░ рдХрд░ рд▓рд┐рдпрд╛ред рд▓рдЦрдирдК рдХреЛ рднреА рдЙрдиреНрд╣реЛрдВрдиреЗ рдЬреАрдд рд▓рд┐рдпрд╛ред рдмрд┐рдареВрд░ рдХреЗ рдкреЗрд╢рд╡рд╛ рдмрд╛рдЬреАрд░рд╛рд╡ рдХреЛ рдмрдВрджреА рдмрдирд╛ рд▓рд┐рдпрд╛ рдЧрдпрд╛ рддрдерд╛ рдирд╛рдЧрдкреБрд░ рдкрд░ рднреА рдШрд╛рддрдХ рд╣рдорд▓рд╛ рд╣реБрдЖред рдЗрд╕реА рдкреНрд░рдХрд╛рд░ рдЙрджрдпрдкреБрд░, рддрдВрдЬреМрд░, рд╕рддрд╛рд░рд╛, рдХрд░реНрдирд╛рдЯрдХ рдЖрджрд┐ рднреА рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдХреЗ рд╕рд╛рдордиреЗ рди рдард╣рд░ рд╕рдХреЗред┬ард╕рд┐рдВрдз, рдкрдВрдЬрд╛рдм, рдореНрдпрд╛рдВрдорд╛рд░ (рдмрд░реНрдорд╛) рдЖрджрд┐ рдХрд╛ рднреА рдкрддрди рд╣реЛ рдЧрдпрд╛ред рдпрд╣реА рд╣рд╛рд▓рдд рдмрдВрдЧрд╛рд▓ рдФрд░ рдорджреНрд░рд╛рд╕ (рдЪреЗрдиреНрдирдИ) рдХреА рднреА рд╣реБрдИред

рдЬрд┐рди рд░рд╛рдЬрд╛рдУрдВ рдХреЗ рд░рд╛рдЬрдкрд╛рдЯ рдЫрд┐рдиреЗ рдЙрдирдХреА рд░рд╛рдирд┐рдпрд╛рдБ рд░рдирд┐рд╡рд╛рд╕реЛрдВ рдореЗрдВ рд░реЛ рд░рд╣реА рдереАрдВ рдФрд░ рдЬрд┐рди рдирд╡рд╛рдмреЛрдВ рдХреА рд░рд┐рдпрд╛рд╕рдд рдЫрд┐рдиреА рдЙрдирдХреА рдмреЗрдЧрдореЗрдВ рднреА рдмрд╣реБрдд рджреБрдЦреА рдереАрдВред рдЙрдирдХреЗ рдмрд╣реБрдореВрд▓реНрдп рдХрдкрдбрд╝реЗ рдФрд░ рдЧрд╣рдиреЗ рдХрд▓рдХрддреНрддрд╛ рдХреЗ рдмрд╛рдЬрд╛рд░ рдореЗрдВ рдмрд┐рдХ рд░рд╣реЗ рдереЗред рдЕрдВрдЧреНрд░реЗрдЬреА рдЕрдЦрдмрд╛рд░ рдиреАрд▓рд╛рдореА рдХреА рдЦрдмрд░реЗрдВ рд╕рдмрдХреЗ рдмреАрдЪ рдкрд╣реБрдБрдЪрд╛ рд░рд╣реЗ рдереЗред┬ардирд╛рдЧрдкреБрд░ рдХреЗ рдЬреЗрд╡рд░реЛрдВ рдФрд░ рд▓рдЦрдирдК рдХреЗ рдкреНрд░рд╕рд┐рджреНрдз рдиреМрд▓рдЦреЗ рд╣рд╛рд░ рдмрд╛рдЬрд╛рд░реЛрдВ рдореЗрдВ рдмрд┐рдХ рд░рд╣реЗ рдереЗред рд╡реЗ рдЧрд╣рдиреЗ рдЬреЛ рдФрд░рддреЛрдВ рддрдерд╛ рд░рд╛рдирд┐рдпреЛрдВ рдХреА рд╢реЛрднрд╛ рдереЗ, рдкрд░реНрджреЗ рдХреА рдЗрдЬреНрдЬрдд рдереЗ, рджреВрд╕рд░реЛрдВ рдХреЗ рд╣рд╛рдереЛрдВ рдмрд┐рдХ рд░рд╣реЗ рдереЗред

рдЬрдм рдЭрд╛рдБрд╕реА рдкрд░ рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдХрд╛ рдХрдмреНрдЬрд╛ рд╣реЛ рдЧрдпрд╛ рддреЛ рдЭрд╛рдБрд╕реА рдХреЛ рдореБрдХреНрдд рдХрд░рд╛рдиреЗ рдХреЗ рд▓рд┐рдП рдкреНрд░рдпрд╛рд╕ рд╣реЛрдиреЗ рд▓рдЧреЗред рдЬреЛ рдХреБрдЯрд┐рдпрд╛ рдореЗрдВ рд░рд╣рддреЗ рдереЗ рд╡реЗ рдмрд╣реБрдд рджреБрдЦреА рдереЗ рдФрд░ рдорд╣рд▓реЛрдВ рдореЗрдВ рд░рд╣рдиреЗ рд╡рд╛рд▓реЗ рднреА рдЕрдкрдорд╛рдирд┐рдд рдорд╣рд╕реВрд╕ рдХрд░ рд░рд╣реЗ┬ардереЗред рдЭрд╛рдБрд╕реА рдХреЗ рд╡реАрд░ рд╕реИрдирд┐рдХреЛрдВ рдХреЗ рдорди рдореЗрдВ рдЕрдкрдиреЗ рд╡реАрд░ рдкреВрд░реНрд╡рдЬреЛрдВ рдХреА рд╡реАрд░рддрд╛ рдХрд╛ рдЕрднрд┐рдорд╛рди рднреА рдерд╛ред рд╡реЗ рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рд╕реЗ рдмрджрд▓рд╛ рд▓реЗрдиреЗ рдХреЗ рд▓рд┐рдП рддреИрдпрд╛рд░ рдереЗред рдирд╛рдирд╛ рдзреБрдВрдзреВрдкрдВрдд рдФрд░ рдкреЗрд╢рд╡рд╛ рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдХреЗ рд╡рд┐рд░реБрджреНрдз рдпреБрджреНрдз рдХрд░рдиреЗ рдХреЗ рд▓рд┐рдП рдЖрд╡рд╢реНрдпрдХ рд╕рд╛рдорд╛рди рдЬреБрдЯрд╛ рд░рд╣реЗ рдереЗред рдЙрдирдХреА рдмрд╣рди рдЫрдмреАрд▓реА рдпрд╛рдиреА рд░рд╛рдиреА рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рдиреЗ рднреА рд░рд╛рдЬреНрдп рдХреА рд╕реНрддреНрд░рд┐рдпреЛрдВ рдореЗрдВ рджреЗрд╡реА рджреБрд░реНрдЧрд╛ рдХреЗ рд░рдгрдЪрдВрдбреА рд░реВрдк рдХреЛ рдЬрд╛рдЧреГрдд рдХрд░ рд░рд╣реА рдереА рдЕрд░реНрдерд╛рддреН рдпреБрджреНрдз рдХрд╛ рдкреНрд░рд╢рд┐рдХреНрд╖рдг рджреЗрдХрд░ рдЕрдкрдиреА рд╕реЗрдирд╛ рдореЗрдВ рд╢рд╛рдорд┐рд▓ рдХрд░ рд░рд╣реА рдереАред┬а┬ардЗрд╕ рдкреНрд░рдХрд╛рд░ рд╕рднреА рдиреЗ рд╕реНрд╡рддрдВрддреНрд░рддрд╛ рд░реВрдкреА рдпрдЬреНрдЮ рдореЗрдВ рд╕реЛрдИ рд╣реБрдИ рдЬреНрдпреЛрддрд┐ рдХреЛ рдЬрдЧрд╛рдиреЗ рдХрд╛ рдирд┐рд╢реНрдЪрдп рдХрд░ рд▓рд┐рдпрд╛ рдерд╛ред

рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рд╕реЗ рдЕрдкрдиреА рдЖрдЬрд╛рджреА рдЫреАрди рд▓реЗрдиреЗ рдХреА рдмрд╛рдд рдорд╣рд▓реЛрдВ рдореЗрдВ рдЖрдЧ рдХреА рддрд░рд╣ рдлреИрд▓ рд░рд╣реАрдВ рдереАрдВ рддреЛ рд╕рд╛рде рд╣реА рдЭреЛрдкреЬреА рдпрд╛рдиреА┬ардЧрд░реАрдм┬ард╡рд░реНрдЧ рдореЗрдВ рднреА рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдХреЗ рдкреНрд░рддрд┐ рдЧреБрд╕реНрд╕рд╛ рдерд╛ред рдЖрдЬрд╛рджреА рдкреНрд░рд╛рдкреНрдд рдХрд░рдиреЗ рдХрд╛ рдпрд╣ рдЬреЛрд╢, рдЬреБрдиреВрди рдЙрдирдХреЗ рд╣реГрджрдп рд╕реЗ рдирд┐рдХрд▓ рд░рд╣рд╛ рдерд╛ред рдЭрд╛рдБрд╕реА рдФрд░ рджрд┐рд▓реНрд▓реА рдЬрд╛рдЧ рдЪреБрдХреА рдереА рддреЛ рд▓рдЦрдирдК рдореЗрдВ рднреА┬ард▓реЛрдЧ рдЕрдВрдЧреНрд░реЗрдЬреА рд╕реЗрдирд╛ рдХреЗ рд╡рд┐рд░реБрджреНрдз рддреИрдпрд╛рд░ рдЦрдбрд╝реЗ рдереЗред рдореЗрд░рда, рдкрдЯрдирд╛, рдХрд╛рдирдкреБрд░ рдореЗрдВ рдЖрдЬрд╛рджреА рдкреНрд░рд╛рдкреНрдд рдХрд░рдиреЗ рдХреА рдмрд╛рдд рд╕рдмрдХреЗ рджрд┐рд▓реЛрдВ рдореЗрдВ рдереАред рдЬрдмрд▓рдкреБрд░ рдФрд░ рдХреЛрд▓реНрд╣рд╛рдкреБрд░ рдХреЗ рд▓реЛрдЧреЛрдВ рдореЗрдВ рдпрд╣ рдмрд╛рдд рднрд░рдиреА рдереА рдпрд╛рдиреА рдЙрдирдХреЛ рднреА рдкреНрд░реЗрд░рд┐рдд рдХрд░рдирд╛ рдерд╛ред

рдЬрдм рд╕реНрд╡рддрдВрддреНрд░рддрд╛ рд░реВрдкреА рдорд╣рд╛рдпрдЬреНрдЮ рдЖрд░рдВрдн рд╣реБрдЖ рддреЛ рдЕрдиреЗрдХ рд╡реАрд░ рдпреЛрджреНрдзрд╛рдУрдВ рдиреЗ рдЕрдкрдирд╛ рдмрд▓рд┐рджрд╛рди рджрд┐рдпрд╛ред рдЗрдирдореЗрдВ рдирд╛рдирд╛ рдзреБрдВрдзреВрдкрдВрдд, рддрд╛рдБрддрд┐рдпрд╛, рдЕрдЬреАрдореБрд▓реНрд▓рд╛-рдЕрд╣рдордж рд╢рд╛рд╣ рдореМрд▓рд╡реА, рдХреБрд░ рдХреБрдБрд╡рд░ рд╕рд┐рдВрд╣ рдЬреИрд╕реЗ рд╡реАрд░ рд╕реИрдирд┐рдХ рдереЗред рдЖрдЬрд╛рджреА рдХреЗ рдЗрд╕ рдорд╣рд╛рдпрдЬреНрдЮ рдореЗрдВ рдХрдИ рд╡реАрд░реЛрдВ рдХреЛ рдЕрдкрдиреА рдХреБрд░реНрдмрд╛рдиреА рджреЗрдиреА рдкрдбрд╝реАред рднрд╛рд░рдд рдХреА рд╕реНрд╡рддрдВрддреНрд░рддрд╛ рдХреЗ рдЗрддрд┐рд╣рд╛рд╕ рд░реВрдкреА рдЖрдХрд╛рд╢ рдореЗрдВ рдЗрдирдХрд╛ рдирд╛рдо рд╕реВрд░рдЬ-рдЪрд╛рдБрдж рдХреА рддрд░рд╣ рд╣рдореЗрд╢рд╛ рдЕрдорд░ рд░рд╣реЗрдЧрд╛ред рдЙрдирдХреА рдЗрд╕ рдХреБрд░реНрдмрд╛рдиреА, рддреНрдпрд╛рдЧ рдФрд░ рдмрд▓рд┐рджрд╛рди рдХреЛ рдЕрдВрдЧреНрд░реЗрдЬ рдЬреБрд░реНрдо рдЕрд░реНрдерд╛рддреН рдЕрдкрд░рд╛рдз рдХрд╣рддреЗ рдереЗред

рд╣рдо рдЕрдиреНрдп рдкреНрд░рджреЗрд╢реЛрдВ рдХреА рдмрд╛рддреЗрдВ рдЫреЛрдбрд╝рдХрд░ рдЭрд╛рдБрд╕реА рдХреЗ рдореИрджрд╛рдиреЛрдВ рдХрд╛ рджреГрд╢реНрдп рджреЗрдЦрддреЗ рд╣реИрдВ, рдЬрд╣рд╛рдБ рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рдорд░реНрджреЛ рдореЗрдВ рдорд░реНрдж рдмрдиреА рдЦрдбрд╝реА рд╣реИ рдЕрд░реНрдерд╛рддреН рдорд░реНрджреЛ рд╕реЗ рдмрдврд╝рдХрд░ рд╡реАрд░ рдпреЛрджреНрдзрд╛ рдХреЗ рд░реВрдк рдореЗрдВ рд▓рдбрд╝ рд░рд╣реА рдереАрдВред рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдХреА рдУрд░ рд╕реЗ рд▓реЗрдлреНрдЯрд┐рдиреЗрдВрдЯ рд╡реЙрдХрд░ рдиреЗ рдЕрдкрдиреЗ рдЬрд╡рд╛рдиреЛрдВ рдХреЗ рд╕рд╛рде┬ардЭрд╛рдБрд╕реА рдкрд░ рд╣рдорд▓рд╛ рдХрд┐рдпрд╛ред рд░рд╛рдиреА рдиреЗ рднреА рдЙрд╕рдХрд╛ рд╡рд┐рд░реЛрдз рдХрд░рдиреЗ рдХреЗ рд▓рд┐рдП рддрд▓рд╡рд╛рд░ рдЦреАрдВрдЪ рд▓реА рдЕрд░реНрдерд╛рдд рдпреБрджреНрдз рдХреА рдШреЛрд╖рдгрд╛ рдХрд░ рджреА рдереАред рджреЛрдиреЛрдВ рдореЗрдВ рднреАрд╖рдг рдпреБрджреНрдз рд╣реБрдЖред рдзреВрд▓ рд╕реЗ рдЖрдХрд╛рд╢ рдврдХ рдЧрдпрд╛ред рдЕрдВрдЧреНрд░реЗрдЬ рд╕реЗрдирд╛рдкрддрд┐ рдШрд╛рдпрд▓ рд╣реЛрдХрд░ рднрд╛рдЧ рдЧрдпрд╛ред рдЙрд╕реЗ рд░рд╛рдиреА рдХреА рд╡реАрд░рддрд╛ рджреЗрдЦрдХрд░ рдмрд╣реБрдд рдЖрд╢реНрдЪрд░реНрдп рд╣реБрдЖред

рд░рд╛рдиреА рдЭрд╛рдБрд╕реА рд▓рдЧрд╛рддрд╛рд░ рд╕реМ рдореАрд▓ рдХреА рдпрд╛рддреНрд░рд╛ рдХрд░рдХреЗ рдХрд╛рд▓рдкреА рдЖ рдЧрдИред рдЗрддрдирд╛ рд╕рдлрд╝рд░ рдХрд░рдиреЗ рдХреЗ рдХрд╛рд░рдг рдЙрдирдХрд╛ рдШреЛрдбрд╝рд╛ рдердХрдХрд░ рдзрд░рддреА рдкрд░ рдЧрд┐рд░ рдкрдбрд╝рд╛ рдФрд░ рддреБрд░рдиреНрдд рдорд░ рдЧрдпрд╛ред рд╡рд╣рд╛рдБ рдпрдореБрдирд╛ рдХреЗ рдХрд┐рдирд╛рд░реЗ рдлрд┐рд░ рдЕрдВрдЧреНрд░реЗрдЬрд╝ рд░рд╛рдиреА рд╕реЗ рд╣рд╛рд░ рдЧрдПред рдХрд╛рд▓рдкреА рдЬреАрддрдХрд░ рд░рд╛рдиреА рдлрд┐рд░ рдЖрдЧреЗ рдмрдврд╝реА рдФрд░ рдЙрд╕рдиреЗ рдЧреНрд╡рд╛рд▓рд┐рдпрд░ рдкрд░ рдЕрдзрд┐рдХрд╛рд░ рдХрд░ рд▓рд┐рдпрд╛ред рдЧреНрд╡рд╛рд▓рд┐рдпрд░ рдХрд╛ рд░рд╛рдЬрд╛ рд╕рд┐рдВрдзрд┐рдпрд╛ рдЕрдВрдЧреНрд░реЗрдЬрд╝реЛрдВ рдХрд╛ рдорд┐рддреНрд░ рдерд╛ред рдЙрд╕реЗ рд░рд╛рдиреА рд╕реЗ рдкрд░рд╛рдЬрд┐рдд рд╣реЛрдХрд░ рд░рд╛рдЬрдзрд╛рдиреА рдЫреЛрдбрд╝рдиреА рдкрдбрд╝реАред

рд░рд╛рдиреА рдХреА рдЬреАрдд рд╣реБрдИ рдкрд░ рдлрд┐рд░ рд╕реЗ рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рдХреА рд╕реЗрдирд╛ рд░рд╛рдиреА рдХреЛ рдШреЗрд░рддреА рд╣реБрдИ рдЖ рдкрд╣реБрдБрдЪреАред рдЗрд╕ рдмрд╛рд░ рд╕рд╛рдордиреЗ рд╕реЗ рдЖ рд░рд╣реА рдЯреБрдХрдбрд╝реА рдХрд╛ рдиреЗрддреГрддреНрд╡ рдЬрдирд░рд▓ рд╕реНрдорд┐рде рдХрд░ рд░рд╣рд╛ рдерд╛ред рдЙрдзрд░ рд░рд╛рдиреА рдХреЗ рд╕рд╛рде рдЙрд╕рдХреА рджреЛ рд╕рд╣реЗрд▓рд┐рдпрд╛рдБ рдХрд╛рдирд╛ рдФрд░ рдордВрджрд░рд╛ рднреА рдЖрдИ рдереАрдВ рдФрд░ рдЙрдиреНрд╣реЛрдВрдиреЗ рдпреБрджреНрдз рдореЗрдВ рдмрд╣реБрддрд╕реЗ рд╢рддреНрд░реБрдУрдВ рдХреЛ рдорд╛рд░рд╛|┬ардкрд░рдВрддреБ рддрднреА рдкреАрдЫреЗ рд╕реЗ рдпреВрд░реЛрдЬ рдиреЗ рдЖрдХрд░ рдЖрдХреНрд░рдордг рдХрд░ рджрд┐рдпрд╛ред рдЗрд╕ рдкреНрд░рдХрд╛рд░ рд░рд╛рдиреА рджреЛрдиреЛрдВ рдУрд░ рд╕реЗ рдШрд┐рд░ рдЧрдИ|

рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ рджреЛрдиреЛрдВ рдУрд░ рд╕реЗ рдШрд┐рд░ рдЬрд╛рдиреЗ рдкрд░ рднреА рдорд╛рд░-рдХрд╛рдЯ рдХрд░рддреА рд╣реБрдИ рдЖрдЧреЗ рдмрдврд╝ рдЧрдИ рдФрд░ рд╕реЗрдирд╛ рдХреЛ рдкрд╛рд░ рдХрд░рддреА рд╣реБрдИ рдирд┐рдХрд▓ рдЧрдИред рддрднреА рдЕрдЪрд╛рдирдХ рд╕рд╛рдордиреЗ рдПрдХ рдмрд╣реБрдд рдмрдбрд╝рд╛ рдирд╛рд▓рд╛ рдЖ рдЧрдпрд╛ред рд░рд╛рдиреА рдХреЗ рд▓рд┐рдП рдпрд╣ рдПрдХ рднрд╛рд░реА рд╕рдВрдХрдЯ рдерд╛ред рд░рд╛рдиреА рдХрд╛ рдирдпрд╛ рдШреЛрдбрд╝рд╛ рдЙрд╕реЗ рдкрд╛рд░ рди рдХрд░рдиреЗ рдХреЗ рд▓рд┐рдП рдЕрдбрд╝ рдЧрдпрд╛ред рдЗрддрдиреЗ рдореЗрдВ рдкреАрдЫрд╛ рдХрд░рддреЗ рд╣реБрдП рдЕрдВрдЧреНрд░реЗрдЬ рд╕реИрдирд┐рдХ рдЖ рдЧрдП рдФрд░ рджреЛрдиреЛрдВ рдУрд░ рд╕реЗ рд╡рд╛рд░ рдкрд░ рд╡рд╛рд░ рд╣реЛрддреЗ рдЪрд▓реЗ рдЧрдПред рд╢реЗрд░рдиреА-рд╕реА рд░рд╛рдиреА рдШрд╛рдпрд▓ рд╣реЛрдХрд░ рдЧрд┐рд░ рдЧрдИ рдФрд░ рд╡реАрд░рдЧрддрд┐ рдХреЛ рдкреНрд░рд╛рдкреНрдд рд╣реБрдИред

рд░рд╛рдиреА рд╕реНрд╡рд░реНрдЧ рд╕рд┐рдзрд╛рд░ рдЧрдИ рдЕрдм рдЙрд╕рдХреА рдЕрдиреЛрдЦреА рд╕рд╡рд╛рд░реА рдЪрд┐рддрд╛ рд╣реА рдереАред рддреЗрдЬ-рд╕реЗ-рддреЗрдЬ рдорд┐рд▓ рдЧрдпрд╛ рдЕрд░реНрдерд╛рдд рд░рд╛рдиреА рдХрд╛ рдЖрддреНрдорд░реВрдкреА рддреЗрдЬ рдкреНрд░рднреБ рдХреЗ рддреЗрдЬ рд╕реЗ рдорд┐рд▓ рдЧрдпрд╛ред рд╡рд╣ рддреЗрдЬ рдХреА рд╕рдЪреНрдЪреА рдЕрдзрд┐рдХрд╛рд░реА рднреА рдереАред рдЕрднреА рд╡рд╣ рдХреЗрд╡рд▓┬арддреЗрдИрд╕ рд╡рд░реНрд╖ рдХреА рдереА рдФрд░ рддреЗрдИрд╕ рд╡рд░реНрд╖реЛрдВ рдореЗрдВ рдЙрдиреНрд╣реЛрдВрдиреЗ рдЬреЛ рд╡реАрд░рддрд╛ рджрд┐рдЦрд╛рдИ рдЙрд╕рд╕реЗ рд▓рдЧрддрд╛ рд╣реИ рд╡рд╣ рдордиреБрд╖реНрдп рдирд╣реАрдВ рдХреЛрдИ рджреЗрд╡рддрд╛ рдереАрдВред рд╡рд╣ рд╕реНрд╡рддрдВрддреНрд░рддрд╛ рдХреА рджреЗрд╡реА рдмрдирдХрд░ рд╣рдореЗрдВ рдЬреАрд╡рд┐рдд рдХрд░рдиреЗ рдЖрдИ рдереАрдВред рд╡рд╣ рд╣рдореЗрдВ рдмрд▓рд┐рджрд╛рди рдХрд╛ рдорд╛рд░реНрдЧ рджрд┐рдЦрд╛ рдЧрдИрдВ рдФрд░ рдЬреЛ рд╕реАрдЦ рджреЗрдиреА рдереА рджреЗ рдЧрдИрдВред

рдХрд╡рдпрд┐рддреНрд░реА рдХрд╣рддреА рд╣реИ рдХрд┐ рд░рд╛рдиреА рд▓рдХреНрд╖реНрдореАрдмрд╛рдИ, рддреБрдо рддреЛ рд╕реНрд╡рд░реНрдЧ рдХреЛ рдЬрд╛рдУ рдкрд░рдиреНрддреБ рд╕реНрд╡рддрдВрддреНрд░рддрд╛ рдЖрдВрджреЛрд▓рди┬а рдореЗрдВ рдЖрдкрдХреЗ┬ардпреЛрдЧрджрд╛рди рдХреЛ рдХрднреА рднреБрд▓рд╛рдпрд╛ рдирд╣реАрдВ рдЬрд╛ рд╕рдХрддрд╛ред рдЖрдкрдХрд╛ рдпрд╣ рдмрд▓рд┐рджрд╛рди рд╣рдореЗрдВ рдХрднреА рди рдирд╖реНрдЯ рд╣реЛрдиреЗ рд╡рд╛рд▓реА рдЖрдЬрд╛рджреА рдХреЗ рдкреНрд░рддрд┐ рд╕рдЪреЗрдд рдХрд░рддрд╛ рд░рд╣реЗрдЧрд╛ред рдЗрддрд┐рд╣рд╛рд╕ рдЪрд╛рд╣реЗ рдХреБрдЫ рднреА рди рдХрд╣реЗ рдФрд░ рд╕рдЪреНрдЪрд╛рдИ рдХрд╛ рдЧрд▓рд╛ рдШреЛрдВрдЯ рджрд┐рдпрд╛ рдЬрд╛рдП| рдЕрдВрдЧреНрд░реЗрдЬреЛрдВ рджреНрд╡рд╛рд░рд╛ рд╡рд┐рдЬрдп рдкреНрд░рд╛рдкреНрдд рдХрд░
рднреА рд▓реА рдЬрд╛рдП рдпрд╛ рд╡реЗ рдЭрд╛рдБрд╕реА рдХреЛ рдЧреЛрд▓реЛрдВ рд╕реЗ рдирд╖реНрдЯ рдХрд░ рджреЗрдВ рдкрд░ рднрд╛рд░рддрд╡рд╛рд╕реА рдпрд╣ рдмрд▓рд┐рджрд╛рди рдирд╣реАрдВ рднреВрд▓ рд╕рдХреЗрдВрдЧреЗред рд╣реЗ рд░рд╛рдиреА! рддреВ рдЕрдкрдирд╛ рд╕реНрдорд╛рд░рдХ рд╕реНрд╡рдпрдВ рд╣реЛрдЧреА рдпрд╛рдиреА рдЖрдк┬арддреЛ рдЕрдкрдиреЗ рдЖрдк рдореЗрдВ рд╣реА рдЕрдкрдиреА рдпрд╛рдж рдХрд╛ рдЪрд┐рд╣реНрди рдереАред

рдХрдард┐рди рд╢рдмреНрджреЛрдВ рдХреЗ рдЕрд░реНрде -

тАв рднреГрдХреБрдЯреА рддрд╛рдирдирд╛ - рдХреНрд░реЛрдз рдХрд░рдирд╛
тАв рдЧреБрдореА рд╣реБрдИ - рдЦреЛрдИ рд╣реБрдИ
тАв рдлрд┐рд░рдВрдЧреА - рд╡рд┐рджреЗрд╢реА (рдЕрдВрдЧреНрд░реЗрдЬрд╝)
тАв рдорди рдореЗрдВ рдард╛рдирдирд╛ - рдкрдХреНрдХрд╛ рдЗрд░рд╛рджрд╛ рдХрд░рдирд╛
тАв рд╣рд░рдмреЛрд▓реЗ - рд╣рд░ рд╡реНрдпрдХреНрддрд┐ рдХреЗ рдореБрдБрд╣ рд╕реЗ
тАв рдХреГрдкрд╛рдг - рддрд▓рд╡рд╛рд░
тАв рдЕрд╡рддрд╛рд░ - рд╡рд┐рд╢реЗрд╖ рд░реВрдк рд╕реЗ рдЬрдиреНрдо рд▓реЗрдирд╛
тАв рдкреБрд▓рдХрд┐рдд - рдкреНрд░рд╕рдиреНрди
тАв рд╡реНрдпреВрд╣-рд░рдЪрдирд╛ - рдореЛрд░реНрдЪрд╛ рдмрдирд╛рдирд╛
тАв рджреБрд░реНрдЧ рддреЛрдбрд╝рдирд╛ тАУ рдХрд┐рд▓рд╛ рддреЛрдбрд╝рдирд╛
тАв рдЦрд┐рд▓рдмрд╛рдбрд╝ - рдЦреЗрд▓
тАв рднрд╡рд╛рдиреА┬а -рдкрд╛рд░реНрд╡рддреА
тАв рд╕реБрдордЯ - рдЕрдЪреНрдЫреЗ рд╡реАрд░
тАв рд╡рд┐рд░реБрджрд╛рд╡рд▓рд┐ - рдкреНрд░рд╢рдВрд╕рд╛ рдХреА рдХрд╣рд╛рдиреА
тАв рдЙрджрд┐рдд рд╣реБрдЖ - рдЬрдЧрд╛
тАв рдореБрджрд┐рдд - рдкреНрд░рд╕рдиреНрди
тАв рдХрд╛рд▓рдЧрддрд┐ - рдореГрддреНрдпреБ рдХреА рдЪрд╛рд▓
тАв рдХрд╛рд▓реА рдШрдЯрд╛ рдШреЗрд░ рд▓рд╛рдирд╛ - рдореБрд╕реАрдмрддреЗрдВ рдЖрдирд╛
тАв рдЕрд╢реНрд░реБрдкреВрд░реНрдг - рдЖрдБрд╕реБрдУрдВ рд╕реЗ рднрд░реЗ рд╣реБрдП
тАв рдмрд┐рд░рд╛рдиреА - рдкрд░рд╛рдИ
тАв рдЕрдиреБрдирдп-рд╡рд┐рдирдп - рдкреНрд░рд╛рд░реНрдердирд╛
тАв рд╡рд┐рд╖рдо - рдХрдард┐рди
тАв рдкреИрд░ рдкрд╕рд╛рд░рдирд╛ - рд╡рд┐рд╕реНрддрд╛рд░ рдХрд░рдирд╛
тАв рдХрд╛рдпрд╛ рдкрд▓рдЯрдирд╛ - рдмрджрд▓рд╛рд╡ рдЖрдирд╛
тАв рдШрд╛рдд - рдЖрдХреНрд░рдордг
тАв рдХреМрди рдмрд┐рд╕рд╛рдд - рдХреНрдпрд╛ рдФрдХрд╛рдд
тАв рд╡рдЬреНрд░ рдирд┐рдпрд╛рдд - рдХрд░рд╛рд░реА рдЪреЛрдЯ
тАв рдмреЗрдЬрд╛рд░ - рдкреАрдбрд╝рд┐рдд
тАв рд╕рд░реЗрдЖрдо - рд╕рдмрдХреЗ рд╕рд╛рдордиреЗ
тАв рдиреМрд▓рдЦрд╛ - рдмрд╣реБрдореВрд▓реНрдп рд╣рд╛рд░
тАв рд░рдгрдЪрдВрдбреА - рджреБрд░реНрдЧрд╛ рдХрд╛ рдПрдХ рд░реВрдк
тАв рдЖрд╣реНрд╡рд╛рди - рдкреБрдХрд╛рд░рдирд╛
тАв рдЕрдВрддрд░рддрдо - рд╣реГрджрдп
тАв рдЪреЗрддреА - рдЬрд╛рдЧреНрд░рдд рд╣реЛ рдЧрдИ
тАв рд▓рдкрдЯреЗрдВ рдЫрд╛рдирд╛ - рднрдпрдВрдХрд░ рд░реВрдк рд╕реЗ рдлреИрд▓ рдЬрд╛рдирд╛
тАв рдЙрдХрд╕рд╛рдирд╛ - рдкреНрд░реЗрд░рд┐рдд рдХрд░рдирд╛
тАв рдЕрднрд┐рд░рд╛рдо - рд╕реБрдиреНрджрд░
тАв рдореБрдБрд╣ рдХреА рдЦрд╛рдирд╛ - рд╣рд╛рд░рдирд╛,
тАв рд╡реАрд░ рдЧрддрд┐ рдкрд╛рдирд╛ - рдпреБрджреНрдз рдореЗрдВ рд╢рд╣реАрдж рд╣реЛрдирд╛
тАв рджрд┐рд╡реНрдп - рдЕрд▓реМрдХрд┐рдХ
тАв рдорджрдорд╛рддреА - рдорд╕реНрдд рдХрд░рдиреЗ рд╡рд╛рд▓реА
тАв рдЕрдорд┐рдЯ - рди рдорд┐рдЯрдиреЗ рд╡рд╛рд▓реАред


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Notes of Ch 8 Introduction to Trigonometry| Class 10th Math

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Revision Notes for Ch┬а8 Introduction to Trigonometry Class 10th Mathematics


Trigonometry and Trigonometric Ratios

тЖТ Trigonometry is the branch of mathematics which deals with measurements of angles and the problems related to relationship between sides and angles.

Trigonometric Ratios:

тЖТ It is the ratios of two sides of a right angle triangle.

тЖТ Suppose we have a right angled triangle ABC.


тЖТ Thus the trigonometric Ratios are defined as the largest side of a right angle triangle is known as hypotenuse.

Also, by Pythagoras theorem, we know that h2┬а=b2+p2.

Here, ╬╕ is pronounced as theta, тИаA=╬╕. We write trigonometric ratios according to angle ╬╕.



Trigonometric Ratios for Few Particular Angels



Note:- Some Angles like cosec╬╕ for ╬╕=0┬░ is not defined. We know that cosec╬╕ = 1/sin╬╕ = 1/0. 1/0 is not defined hence cosec0┬░┬аis not defined.

Trigonometric Identities

тЖТ Identities are equations which are valid for any conditions. Trigonometric identities are equations involving trigonometric ratios.

Some Trigonometric Identities are:

(i) sin2╬╕+cos2тБб╬╕=1



(iv) sec2╬╕-tan2╬╕=1

(v) cosec2╬╕-cot2тБб╬╕=1

Trigonometric Ratios for Complementary Angles

(i) sin (90 тАУ ╬╕) = cos╬╕
(ii) cos (90 тАУ ╬╕) = sin╬╕
(iii) tan (90 тАУ ╬╕) = cot╬╕
(iv) cot (90 тАУ ╬╕) = tan╬╕
(v) sec (90 тАУ ╬╕) = cosec╬╕
(vi) cosec (90 тАУ ╬╕) = sec╬╕
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рдЬреЛ рджреЗрдЦрдХрд░ рднреА рдирд╣реАрдВ рджреЗрдЦрддреЗ рд╕рд╛рд░ NCERT Class 6th Hindi

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рдЬреЛ рджреЗрдЦрдХрд░ рднреА рдирд╣реАрдВ рджреЗрдЦрддреЗ┬ард╡рд╕рдВрдд рднрд╛рдЧ┬а- 1 (Summary of Jo Dekhkar bhi nhi dekhte Vasant)

рдпрд╣ рдкрд╛рда рд╣реЗрд▓реЗрди рдХреЗрд▓реЗрд░ рджреНрд╡рд╛рд░ рд▓рд┐рдЦрд╛ рдПрдХ рдирд┐рдмрдВрдз рд╣реИ рдЬреЛ рджреГрд╖реНрдЯрд┐рд╣реАрди рдПрд╡рдВ рдмрдзрд┐рд░ рдереАред рдЙрдирдХреА рд╕рд╣реЗрд▓реА рдХреБрдЫ рд╕рдордп рдкрд╣рд▓реЗ рдЬрдВрдЧрд▓ рдХреА рд╕реИрд░ рдХрд░рдХреЗ рдЖрдИ рдереАрдВ рдкрд░рдиреНрддреБ рдкреВрдЫрдиреЗ рдкрд░┬ардЙрд╕рдиреЗ рдХрд╣рд╛ рдЙрд╕рдиреЗ рдХреБрдЫ рдЦрд╛рд╕ рдирд╣реАрдВ рджреЗрдЦрд╛ред рдЪреВрдБрдХрд┐ рдРрд╕рд╛ рд╕реБрдирдиреЗ рдХреА рд▓реЗрдЦрд┐рдХрд╛ рдХреЛ рдЖрджрдд рдкреЬ рдЪреБрдХреА рдереА рдЗрд╕рд▓рд┐рдП рдЙрдиреНрд╣реЗрдВ рдХреЛрдИ рдЖрд╢реНрдЪрд░реНрдп рдирд╣реАрдВ рд╣реБрдЖ|┬ард╕рд╛рде рд╣реА рдЙрдиреНрд╣реЗрдВ рдпрд╣ рднреА рд▓рдЧрддрд╛ рдерд╛ рдХреА┬ардХреЛрдИ рдЗрддрдирд╛ рдШреВрдордХрд░ рднреА рд╡рд┐рд╢реЗрд╖ рдЪреАреЫ рдХреИрд╕реЗ рдирд╣реАрдВ рджреЗрдЦ рд╕рдХрддрд╛,┬ардЬрдмрдХрд┐ рд╡реЗ рдЕрдВрдзреА рд╣реЛрддреЗ рд╣реБрдП рднреА рд╕рдм рдХреБрдЫ рджреЗрдЦ рд▓реЗрддреА рд╣реИред┬а

рд╡реЗ рд░реЛреЫрд╛рдирд╛ рд╕реИрдХреЬреЛрдВ рдЪреАреЫреЛрдВ рдХреЛ рдЫреВрдХрд░ рдФрд░ рдорд╣рд╕реВрд╕ рдХрд░ рдкрд╣рдЪрд╛рди рд▓реЗрддреА рд╣реИрдВ рдЬреИрд╕реЗ┬арднреЛрдЬрдкрддреНрд░ рдХреА рдЪрд┐рдХрдиреА рдЫрд╛рд▓, рдЪреАрдбрд╝ рдХреА рдЦреБрд░рджрд░реА рдЫрд╛рд▓, рд╡рд╕рдВрдд рдореЗрдВ рдЦрд┐рд▓реА рдХрд▓рд┐рдпрд╛рдБ рддрдерд╛ рдлреВрд▓реЛрдВ рдХреА рдкрдВрдЦреБрдбрд╝рд┐рдпреЛрдВ рдХреА рдордЦрдорд▓реА рд╕рддрд╣ рдЖрджрд┐|┬ардЗрди рд╕рдмрдХреЛ рд╕реНрдкрд░реНрд╢ рдХрд░рдиреЗ рд╕реЗ рдЙрдиреНрд╣реЗрдВ рдЖрдирдВрдж рдкреНрд░рд╛рдкреНрдд рд╣реЛрддрд╛ рд╣реИ|┬ардЕрдкрдиреА┬ардЕрдБрдЧреБрд▓рд┐рдпреЛрдВ рдХреЗ рдмреАрдЪ рдмрд╣рддреЗ рдкрд╛рдиреА рдХреЛ рдорд╣рд╕реВрд╕ рдХрд░рдиреЗ рд╕реЗ рдЙрдиреНрд╣реЗрдВ рдЖрдирдВрдж рдорд┐рд▓рддрд╛┬ард╣реИ| рдмрджрд▓рддрд╛ рд╣реБрдЖ рдореМрд╕рдо рдЙрдирдХреЗ рдЬреАрд╡рди рдореЗрдВ рдЦреБрд╢рд┐рдпрд╛рдБ рднрд░ рджреЗрддрд╛ рд╣реИ|┬ард▓реЗрдЦрд┐рдХрд╛ рдХреЛ рд▓рдЧрддрд╛ рд╣реИ рдЬрдм рдЗрди┬ард╕рдм рдЪреАрдЬреЛрдВ рдХреЛ рдЫреВрдиреЗ рдорд╛рддреНрд░ рд╕реЗ рд╣реА рдЗрддрдиреА┬ардЦреБрд╢реА рдорд┐рд▓рддреА рд╣реИ рдЕрдЧрд░ рд╡реЗ┬ардЗрди рд╕рдмрдХреЛ рджреЗрдЦрддреАрдВ рддреЛ рдЙрди рдореЗрдВ рдЦреЛ рдЬрд╛рддреАрдВред┬а

рдЙрдирдХреЗ рдЕрдиреБрд╕рд╛рд░ рдЬрд┐рдирдХреА рдЖрдБрдЦреЗрдВ рд╣реЛрддреА рд╣реИрдВ рд╡реЗ рд▓реЛрдЧ рдмрд╣реБрдд рд╣реА рдХрдо рджреЗрдЦрддреЗ рд╣реИрдВред рд╡реЗ рдкреНрд░рдХреГрддрд┐ рдХреЛ рд▓реЗрдХрд░ рдЕрд╕рдВрд╡реЗрджрдирд╢реАрд▓ рд╣реЛрддреЗ рд╣реИрдВ| рдордиреБрд╖реНрдп рдХреЗ рдкрд╛рд╕ рдЬрд┐рд╕ рдЪреАреЫ┬ардХреА рдХрдореА рд╣реЛрддреА рд╣реИ, рд╡рд╣ рдЙрд╕реЗ рдкреНрд░рд╛рдкреНрдд рдХрд░рдиреЗ рдХреЗ рд▓рд┐рдП рд▓рд╛рд▓рд╛рдпрд┐рдд рд░рд╣рддрд╛ рд╣реИред рдИрд╢реНрд╡рд░ рд╕реЗ рдорд┐рд▓реА рджреГрд╖реНрдЯрд┐ рдХреЛ рдорд╛рдирд╡ рдПрдХ рд╕рд╛рдзрд╛рд░рдг-рд╕реА рдЪреАрдЬрд╝ рд╕рдордЭрдХрд░ рдЙрд╕рдХрд╛ рдЙрдЪрд┐рдд рдкреНрд░рдпреЛрдЧ рдирд╣реАрдВ ред рдХрд░рддрд╛ рд╣реИ, рдЬрдмрдХрд┐ рдЗрд╕рдХреЗ рдЙрдЪрд┐рдд рдкреНрд░рдпреЛрдЧ рд╕реЗ рдЬреАрд╡рди рдореЗрдВ рдЦреБрд╢рд┐рдпреЛрдВ рдХреЗ рдЗрдВрджреНрд░рдзрдиреБрд╖реА рд░рдВрдЧ рднрд░реЗ рдЬрд╛ рд╕рдХрддреЗ рд╣реИрдВред

рдХрдард┐рди рд╢рдмреНрджреЛрдВ рдХреЗ рдЕрд░реНрде -

тАв рдкрд░рдЦрдиреЗ - рдЬрд╛рдБрдЪрдиреЗ┬а
тАв рдЕрдЪрд░рдЬ - рдЖрд╢реНрдЪрд░реНрдп, рд╣реИрд░рд╛рдиреА
тАв рд░реЛрдЪрдХ - рдЕрдЪреНрдЫреА рд▓рдЧрдиреЗ рд╡рд╛рд▓реА┬а
тАв рд╕рдорд╛рдБ - рд╡рд╛рддрд╛рд╡рд░рдг┬а
тАв рдореБрдЧреНрдз - рдореЛрд╣рд┐рдд┬а
тАв рдХреНрд╖рдорддрд╛ - рддрд╛рдХрдд
тАв рдХрджрд░ - рдкрд╣рдЪрд╛рдирдирд╛
тАв рдЖрд╕ - рдЙрдореНрдореАрдж┬а
тАв рдирд┐рдпрд╛рдордд - рдИрд╢реНрд╡рд░ рдХреА рджреЗрди┬а
тАв рдЗрдВрджреНрд░рдзрдиреБрд╖реА рд░рдВрдЧ - рдЕрдиреЗрдХ рдкреНрд░рдХрд╛рд░ рдХреЗ рд░рдВрдЧ

NCERT Solutions of┬ардЬреЛ рджреЗрдЦрдХрд░ рднреА рдирд╣реАрдВ рджреЗрдЦрддреЗ

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рд╕рдВрд╕рд╛рд░ рдкреБрд╕реНрддрдХ рд╣реИ рд╕рд╛рд░ NCERT Class 6th Hindi

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рд╕рдВрд╕рд╛рд░ рдкреБрд╕реНрддрдХ рд╣реИ┬ард╡рд╕рдВрдд рднрд╛рдЧ┬а- 1 (Summary of Sansar Pustak hai Vasant)

рдпрд╣ рдкрд╛рда рдкрдВрдбрд┐рдд рдЬрд╡рд╛рд╣рд░рд▓рд╛рд▓ рдиреЗрд╣рд░реВ рджреНрд╡рд╛рд░рд╛ рдЕрдкрдиреА рдкреБрддреНрд░реА рдХреЛ рд▓рд┐рдЦрд╛ рдЧрдпрд╛ рдПрдХ рдкрддреНрд░ рд╣реИред рдЗрд╕┬ардкрддреНрд░ рдХреЗ рдорд╛рдзреНрдпрдо рд╕реЗ рджреБрдирд┐рдпрд╛ рдФрд░ рдЫреЛрдЯреЗ рджреЗрд╢реЛрдВ рдХреЗ рдмрд╛рд░реЗ рдореЗрдВ рдЕрдкрдиреА рдкреБрддреНрд░реА рдХреЛ рдмрддрд╛рдирд╛ рдЪрд╛рд╣рддреЗ рдереЗред┬ардиреЗрд╣рд░реВ рдЬреА рдЗрд▓рд╛рд╣рд╛рдмрд╛рдж рдореЗрдВ рдереЗ рдФрд░ рдЙрдирдХреА рджрд╕ рд╡рд░реНрд╖реАрдп рдкреБрддреНрд░реА рдЗрдВрджрд┐рд░рд╛ рдЧрд╛рдБрдзреА рдорд╕реВрд░реА рдореЗрдВ рдереАрдВред рд╡реЗ рдкрддреНрд░реЛрдВ рджреНрд╡рд╛рд░рд╛ рдЕрдкрдиреА рдмреЗрдЯреА рдХреЛ рджреБрдирд┐рдпрд╛ рдХреА рдЬрд╛рдирдХрд╛рд░реА рджреЗрдирд╛ рдЪрд╛рд╣рддреЗ рдереЗ|┬а

рд╡рд╣ рдЕрдкрдиреА рдмреЗрдЯреА рд╕реЗ рдХрд╣рддреЗ рд╣реИрдВ рдХрд┐┬арддреБрдордиреЗ рдЗрдВрдЧреНрд▓реИрдВрдб рддрдерд╛ рд╣рд┐рдВрджреБрд╕реНрддрд╛рди рдХреЗ рд╡рд┐рд╖рдп рдореЗрдВ рдЗрддрд┐рд╣рд╛рд╕ рдореЗрдВ рдкрдврд╝рд╛ рд╣реЛрдЧрд╛ рд▓реЗрдХрд┐рди рдпрджрд┐ рджреБрдирд┐рдпрд╛ рдХреЛ рдЬрд╛рдирдирд╛ рд╣реИ рддреЛ рд╕рдордЭрдирд╛ рдХрд┐ рд╕рд╛рд░рд╛ рд╕рдВрд╕рд╛рд░ рдПрдХ рд╣реИред рдЗрд╕рдореЗрдВ рд░рд╣рдиреЗ рд╡рд╛рд▓реЗ рд╕рднреА рднрд╛рдИ-рдмрд╣рди рд╣реИрдВред┬ардпрд╣ рдзрд░рддреА рд▓рд╛рдЦреЛрдВ-рдХрд░реЛрдбрд╝реЛрдВ рд╡рд░реНрд╖ рдкреБрд░рд╛рдиреА рд╣реИред рдПрдХ рд╕рдордп рдерд╛ рдЬрдм рдзрд░рддреА рдмреЗрд╣рдж рдЧрд░реНрдо рдереА рдФрд░ рдЗрд╕ рдкрд░ рдХреЛрдИ рдЬреАрд╡рд┐рдд рдирд╣реАрдВ рд░рд╣ рд╕рдХрддрд╛ рдерд╛ред рдЗрддрд┐рд╣рд╛рд╕ рдХреЛ рдХрд┐рддрд╛рдмреЛрдВ рдореЗрдВ┬ардкреЭрд╛ рдЬрд╛ рд╕рдХрддрд╛ рд╣реИ рдкрд░рдиреНрддреБ┬ардкреБрд░рд╛рдиреЗ рдЬрдорд╛рдиреЗ рдореЗрдВ рдЬрдм рдЖрджрдореА рдирд╣реАрдВ рдерд╛, рддрдм рдХрд┐рддрд╛рдмреЗрдВ рдХреМрди рд▓рд┐рдЦрддрд╛? рдкрд╣рд╛рдбрд╝, рд╕рдореБрджреНрд░, рд╕рд┐рддрд╛рд░реЛрдВ, рдирджрд┐рдпрд╛рдБ, рдЬрдВрдЧрд▓ рдЖрджрд┐ рдХреЗ рдорд╛рдзреНрдпрдо рд╕реЗ рднреА рдкреБрд░рд╛рдиреА рджреБрдирд┐рдпрд╛ рдХрд╛ рдкрддрд╛ рд▓рдЧ рд╕рдХрддрд╛ рд╣реИред рдЗрд╕рдХреЗ рд▓рд┐рдП рд╕рдВрд╕рд╛рд░ рд░реВрдкреА рдкреБрд╕реНрддрдХ рдХреЛ рдкрдврд╝рдирд╛ рд╣реЛрдЧрд╛ред┬ард╕рдВрд╕рд╛рд░ рд░реВрдкреА рдкреБрд╕реНрддрдХ рдХреЛ рдкрдврд╝рдиреЗ рдХреЗ рд▓рд┐рдП рдкрддреНрдерд░реЛрдВ рдФрд░ рдкрд╣рд╛рдбрд╝реЛрдВ рдХреЛ рдкрдврд╝рдирд╛ рдЪрд╛рд╣рд┐рдПред рд╕рдбрд╝рдХ рдкрд░ рдпрд╛ рдкрд╣рд╛рдбрд╝ рдХреЗ рдиреАрдЪреЗ рдХрд╛ рдЫреЛрдЯрд╛-рд╕рд╛ рдкрддреНрдерд░ рдХрд╛ рдЯреБрдХрдбрд╝рд╛ рднреА рдкреБрд╕реНрддрдХ рдХрд╛ рдкреГрд╖реНрда рдмрди рдЬрд╛рддрд╛ рд╣реИ|┬а

рдЬреИрд╕реЗ рд╣рдо рдХреЛрдИ рднрд╛рд╖рд╛ рд╕реАрдЦрдиреЗ рдХреЗ рд▓рд┐рдП рдЕрдХреНрд╖рд░ рдЬреНрдЮрд╛рди рдкреНрд░рд╛рдкреНрдд рдХрд░рддреЗ рд╣реИрдВ рдЙрд╕реА рдкреНрд░рдХрд╛рд░ рдкреНрд░рдХреГрддрд┐ рдХреЛ рд╕рдордЭрдиреЗ рдХрд╛ рдЬреНрдЮрд╛рди рд╣рдо┬ардкрддреНрдерд░реЛрдВ рдФрд░ рдЪрдЯреНрдЯрд╛рдиреЛрдВ рд╕реЗ рдкреНрд░рд╛рдкреНрдд рдХрд░ рд╕рдХрддреЗ рд╣реИрдВ|┬ардХреЛрдИ рдЪрд┐рдХрдирд╛-рд╕рд╛ рдкрддреНрдерд░ рднреА рдЕрдкрдиреЗ рдмрд╛рд░реЗ рдореЗрдВ рдмрд╣реБрдд рдХреБрдЫ рдмрддрд╛рддрд╛ рд╣реИ рдХрд┐ рдпрд╣ рдЧреЛрд▓, рдЪрд┐рдХрдирд╛, рдЪрдордХреАрд▓рд╛ рдФрд░ рдЦреБрд░рджреБрд░реЗ рдХрд┐рдирд╛рд░реЗ рдХреИрд╕реЗ рд╣реЛ рдЧрдпрд╛ред рдЕрдВрдд рдореЗрдВ рд╡рд╣ рдмрд╛рд▓реВ рдХрд╛ рдХрдг рдХреИрд╕реЗ рд╣реЛ рдЧрдпрд╛рдФрд░ рд╕рд╛рдЧрд░ рдХреЗ рдХрд┐рдирд╛рд░реЗ рдЬрдо рдЧрдпрд╛ред┬ардЕрдЧрд░ рдЫреЛрдЯрд╛-рд╕рд╛ рдкрддреНрдерд░ рдЗрддрдиреА рдЬрд╛рдирдХрд╛рд░реА рджреЗ рд╕рдХрддрд╛ рд╣реИ, рддреЛ рдкрд╣рд╛рдбрд╝реЛрдВ рдФрд░ рдЕрдиреНрдп рдЪреАрдЬреЛрдВ рд╕реЗ рд╣рдореЗрдВ рдХрдИ┬ардмрд╛рддреЗрдВ рдкрддрд╛ рдЪрд▓┬ард╕рдХрддреА рд╣реИрдВред

рдХрдард┐рди рд╢рдмреНрджреЛрдВ рдХреЗ рдЕрд░реНрде -

тАв рдЕрдХрд╕рд░ - рдкреНрд░рд╛рдпрдГ┬а
тАв рдЦрдд - рдкрддреНрд░
тАв рдЖрдмрд╛рдж - рдмрд╕рд╛ рд╣реБрдЖ┬а
тАв рдЧреМрд░ рд╕реЗ - рдзреНрдпрд╛рди рд╕реЗ
тАв рдЬрд░реНрд░рд╛ - рдХрдг┬а
тАв рджрд╛рдордитАУрддрд▓рд╣рдЯреА
тАв рдЦреБрд░рджрд░рд╛-рдЬрд┐рд╕рдХреА рд╕рддрд╣ рдЪрд┐рдХрдиреА рди рд╣реЛ
тАв рдШрд░реМрдВрджрд╛-рдмрдЪреНрдЪреЛрдВ рджреНрд╡рд╛рд░рд╛ рдмрдирд╛рдпрд╛ рдорд┐рдЯреНрдЯреА рдХрд╛ рдЫреЛрдЯрд╛-рд╕рд╛ рдШрд░


тЖз

Notes of Ch 9 Some Applications of Trigonometry| Class 10th Math

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Revision Notes for Ch┬а9 Some Application of Trigonometry Class 10th Mathematics


Introduction

тЖТ This chapter is an application of trigonometry. In trigonometry, we use to measure sides of triangle, when particular angle was given. Most the buildings, walls, towers we see around are perpendicular to ground. The chapter deals with measurement of heights and distance from certain points with the help of trigonometry if particular angles are known.

Line of Sight: When an observer looks from a point O at an object A, then OA is called line of sight.


Angle of Elevation: Suppose that from a point O, you look up at point A, then the angle, the which the line of sight makes with the horizontal line through O is called the angle of elevation of A, as we seen from O.

Here OX is horizontal line. is here angle of elevation.

Angle of depression: Suppose that from the point O, you look down at an object B, placed below the level of your eye. Then the angle which the line of sight makes with the horizontal line through O is called angle of depression of B for O.

Here, OX is horizontal line. ╬▓ is here angle of deviation.


An Example of Angle of Elevation and Depression

A man standing on a building will look at a building higher than his. If he sees at the top, he will look at the top he will form angle of elevation. If he look at the bottom he will form angle of depression with bottom of the building.

Solved Example based on The Concept

Q. The angle of elevation of a cloud 60m above a lake is 30┬░ and the angle of reflection of the cloud in the lake is 60┬░. Find height of the cloud.

Answer

The situation is depicted by the following diagram.


Let AB be the surface of the lake and let P be the point vertically above A such that AP=60m
Let C be the position of cloud and let D be its reflection in the lake.
Let the height of Cloud be H meters.
Then BC=BD=H (Let)
Draw PQ Perpendicular to CD
тЗТтИаQPC=30┬░,тИаQPD=60┬░
BQ=AP=60m
CQ=(H-60)m,DQ=(H+60)m

From right triangle тИЖ CQP, we have
Let AB be the surface of the lake and let P be the point vertically above A such that AP=60m
Let C be the position of cloud and let D be its reflection in the lake.
Let the height of Cloud be H meters.
Then BC=BD=H (Let)
Draw PQ Perpendicular to CD
тЗТтИаQPC=30┬░,тИаQPD=60┬░
BQ=AP=60m
CQ=(H-60)m,DQ=(H+60)m
From right triangle тИЖ CQP, we have
PQ/CQ=cotтБб30┬░
PQ/(H-60) = тИЪ3
PQтЗТ(H-60) тИЪ3 m (i)
From the right triangle тИЖ DQP
PQ/DQ=cotтБб60┬░
тЗТPQ=(H+60)/тИЪ3 (ii)
From (i) and (ii), we get
(H-60) тИЪ3=(H+60)/тИЪ3
тЗТ3H-180=H+60
тЗТH=240
So, height of the cloud is H=240m.


Ladder Problem


Answer

The angle of elevation of a ladder leaning against a wall is 45┬░ and foot of the ladder is 10m away from the wall. Find the length of ladder. The following diagram depicts the situation


Let OY is the ladder. Let OY=l. YX is the wall on which ladder is leaning on. It is given, ladder is leaned at 45┬░. Also, distance from the wall to foot of ladder is 10m, OX=d=10m. It is given тИЪ2=1.414
From the diagram,
cos 45┬░= OX/OY = d/l
тЗТ l=d/cos 45┬░
We know that cos 45┬░ = 1/тИЪ2
So, l = d/(1/тИЪ2) = тИЪ2 d
l = тИЪ2├Ч10 m = 10тИЪ2 m = 10├Ч1.414 = 14.14m
So, length of ladder is 14.14m
тЖз

French Revolution Mind Map - Class 9th History

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French Revolution Mind Map - Class 9th History

Behind French Revolution, there were various social, political, economic causes. This revolutions ended monarchy in France and introduced constitutional monarchy and then republic. But it was for short time, Napoleon Bonaparte again became rule of France in 1804.

In this mindmap, different important events are listed that happened during French Revolution.
French Revolution Mind Map

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