1) (a+b)²+(a-b)² = 2(a²+b²)

2) (a-b)(a+b) = a²-b²

and

By Trigonometric identity:

sin²A+cos²A = 1 */

*/

/* By Trigonometric identity:

cos²A = 1-sin²A*/

Therefore,

Peggy and Maddie never got a reply of the letter they wrote to Wanda. There could be a possibility that Wanda never received the letter because her family had already moved. It could be that Wanda never wanted to reply to the girls who had been part of a group of students who had teased her and made her feel uneasy. But, her request to the teacher to gift her drawings to Peggy and Maddie implies that she received the letter, understood it was the girls' way of apologising to her and was mature enough to forgive their rude behaviour. Perhaps, she did not consider the possibility of friendship with the girls and chose not to write to them directly.
 

Maddie and Peggy did not get direct reply. However, Wanda did write a letter to the class teacher, Miss Mason, in which see mentioned both of them. Maddie was more anxious for a reply. She had dreams of standing up to the other girls with right to pick on Wanda, while Peggy had begin to forgot all about her. Maddie did feel worse than Peggy did because she herself was poor, and she always knew what they did to Wanda had been very wrong.
It was not like that Wanda didn't like those girls. So she replied their friendly letter indirectly.

Word processor is an application software, which is capable of creating ,editing, saving,and printing documents.
It's features are:
1.Ease and speed: an word processor provides an easier and faster method to type the text.
2.Editing feature:using a word processor ,you can apply editing operations to the text.
3.Storage:it stores all your documents for future use.
4.Graphic feature: you can add pictures, drawings,and charts, etc.,to your document.

Word processor is an application software, which is capable of creating ,editing, saving,and printing documents.
It's features are:
1.Ease and speed: an word processor provides an easier and faster method to type the text.
2.Editing feature:using a word processor ,you can apply editing operations to the text.
3.Storage:it stores all your documents for future use.
4.Graphic feature: you can add pictures, drawings,and charts, etc.,to your document.

a²-b² = (a - b) ( a+b)

Analyse, with illustrations, why Bhaktland Sufi thinkers adopted a variety of languages in which to express their opinions.

The Bhakti and Sufi thinkers used the languages of the common people to expressh their opinions. They often spoke in local languages. So they were well-understood by the common people. Had they used a few distinct languages, they would not have reached to all the people. They would have gone extinct. Hence their use of the local languages proved very significant.

(i) Sanskrit was used by traditional Bhakti saints to sing hymns at different occasions, places of worship and ceremonies.

(ii) The Alvars and Nayanars of Tamil Nadu travelled from place to place singing hymns in Tamil in praise of their Gods. These developed as centres of pilgrimage. Singing compositions of these poet-saints became part of temple rituals in these shrines, as did worship of the saint images.

(iii) Kabir’s poems have survived in several languages and dialects, and some are composed in the special language of nirguna poets, the sant bhasha. Others, known as ulatbansi (upside-down sayings), are written in a form in which everyday meanings are inverted.

(iv)    Baba Guru Nanak, Baba Farid, Ravidas (Raidas), composed their hymns in various languages such as Punjabi and Hindi etc.

(v)    Amir Khusrau wrote and sang in Hindavi or Persian, Punjabi, Urdu and some other form oflanguages.

(vi)    It was not just in sama that the Chishtis adopted local languages. In Delhi, those associated with the Chishti Silsila conversed in Hindavi, the language of the people. Other sufis such as Baba Farid composed verses in the local languages, which were incorporated in the Guru Granth Sahib.

(vii)    Other writers, thinkers, saints etc. composed long poems or masnavis to express ideas of divine love using human love as an allegory. For example, the prem-akhyan (love story) Padmavat composed by Malik Muhammad Jayasi revolved around the romance of Padmini and Ratansen, the king of Chittor. Their trials were symbolic of the soul’s journey to the divine. Such poetic compositions were often recited in hospices, usually during sama.

(viii) The poets of Bigapur and Karnatana wrote short poems in Dakhani, a variant of Urdu.

The growth of Magadha culminated in the emergence of the Mauryan Empire. Chandragupta Maurya, who founded the empire (c. 321 BCE), extended control as far northwest as Afghanistan and Baluchistan, and his grandson Asoka, arguably the most famous ruler of early India, conquered Kalinga (present-day Orissa). 
Such a huge empire needed a strong administration, hence here are the main features of how the empire was administered.

1. Division of empire into five major political centres- This centres were located at very strategic location for example both Taxila and Ujjayini were situated on important long-distance trade routes, while Suvarnagiri (literally, the golden mountain) was possibly important for tapping the gold mines of Karnataka.

2. Standing army- Such a diverse and vast region needed a strong army to control and protec it. Hence as Megasthenes has shown that the Mauryan had a very strong army. And he mentions six different committee with six subcommittees for coordinating military activity. Of these, one looked after the navy, the second managed transport and provisions, the third was responsible for foot-soldiers, the fourth for horses, the fifth for chariots and the sixth for elephants.

3. Appointing royal princes as the governor of the major political centres, because being a royal princes they could be trusted.

4. During Asoka, he tried to hold his empire together by propagating dhamma, the principles of which were simple and virtually universally applicable. This, according to him, would ensure the well-being of people in this world and the next.

5. Strong means of communication along land and rivers were developed aso as to administer the vast empire.

Among the five points we see that it was his attempts to hold the empire using dhamma as means to be most prominent theme in the inscription which were inscribed on natural stones, pollished pillars.

Q u e s t i o n :
A n s w e r : What is meant by the expression ‘Aya Ram, Gaya Ram’?
The expression ‘Aya Ram, Gaya Ram’ is meant to describe the practice of frequent floor-crossing by legislators.

Because the net charge inside a conductor remains zero , the total charge of a conductor resides on its surface , as charges want to attain equilibrium so they come on surface , to minimize the  repulsion among them .As the  charge inside a conductor is zero therefore , if we apply Gauss' theorem to find the electric field inside a conductor , we find it zero . 

The three sets of questions are :

(i)Questions about what, which are related to the identification of patterns of natural and cultural features.

(ii)Questions about where. Some questions are related to the distribution of the natural and cultural features.

(iii)Questions related to why. It is related to the explanation or the causal relationship between feature and phenomena.

Contrast between the composition of the caste and the tribe.

(a) A tribe theoretically is a territorial group while a caste is a socio-cultural group. When a tribe loses its territorial character, it takes the form of a caste.

(b) Each tribe has its own distinct language than the other but it is not the case with a caste. A tribe never imposes restrictions on its members regarding the choice of occupation but a caste usually promotes hereditary occupations and the principle of birth.

(c) Caste and tribe emphasise and perpetuate collective identities in strikingly similar ways. A caste or tribe may change its name and also its mode of livelihood and still retains its collective identity.

(d) The tribes have segmentary, egalitarian system and are not mutually inter-dependent like the castes which show a system of stratification and organic solidarity.

1. Archaeologists trace socio-economic differences in Harappan society by adopting the following methods and techniques:

1. Burials. a. Difference in burial pits.
                b. Presence of artefacts in the burial.
 
Archaeologist have found out that in Burials
  a. There is difference in burial pits, some are just hollowed out space whereas others are lined with bricks.
   b. Although Harappans rarely buried precious material along with their death one, however some graves did contain pottery, ornaments, jewellery which were made of semi precious stones.

   

2. Availability of Luxury goods.

Archaeologists assume objects to be luxuries if they are rare or made from costly, non-local materials or with complicated technologies.

Archaeologist have noticed that,

a. Larger settlements like Harappa and Mohenjodaro has large concerntration of Luxury goods whereas smaller settlements like kalibangan etc did not.

a n s w e r is
Stereotypes: A fixed and inflexible characterisation of a group of people. A fixed, often simplistic generalisation, about a particular group or class of people.

The main features of the Mahajanapadas are as follow:
1. Mahajanapadas were forms of early states and were mostly ruled by kings. However there were oligarchy also known as Gana and Sanghas, where group of people shared power and were collectively known as Rajas.

2. Mahajanapadas had its own capital and it was fortified. It was where the king lived.

3. Mahajanapadas developed gradually a standing armies and bureaucracy.

4. There was the system of taxation, taxes were collected fromt the masses.

5. There developed a notion where king was supposed to come from Kshatriya, with its roles and duties.

Piecing together parts of Harappa history C 

i. Cunningham’s confusion- Harappan artifacts were found fairly often during the nineteenth century and some of these reached Cunningham, he did not realise how old these were but unsuccessfully tried to place it within the time-frame of c. sixth century BCE-fourth century CE. 

ii. John Marshall`s Ignorance- Marshall tended to excavate along regular horizontal units, measured uniformly throughout the mound, ignoring the stratigraphy of the site. This meant that all the artefacts recovered from the same unit were grouped together, even if they were found at different stratigraphic layers. As a result, valuable information about Harappan civilisation was irretrievably lost. 

 iii. R.E.M. Wheeler`s problems- R.E.M. Wheeler took over as Director-General of the ASI in 1944, rectified many problems. Wheeler recognized that it was necessary to follow the stratigraphy of the mound rather than dig mechanically along uniform horizontal lines. 

 iv. Daya Ram SahniSeals- were discovered at Harappa by archaeologists such as Daya Ram Sahni in the early decades of the twentieth century, in layers that were definitely much older than Early Historic levels. It was then that their significance began to be realized. 

v. Rakhal Das Banerji- in 1924,John Marshall, Director-General of the ASI, announced the discovery of a new civilization in the Indus valley to the world. 

vi. S.N. Roy- As S.N. Roy noted in The Story of Indian Archaeology, “Marshall left India three thousand years older than he had found her.”This was because similar, till-then-unidentified seals were found at excavations at Mesopotamian sites. It was then that the world knew not only of a new civilization interesting results in the future.