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Using Pythagoras Theorem, the third side of a right-angled triangle can be calculated when two sides are given.
Suppose A = length of hypotenuse and
B & C = lengths of the sides containing the right angle
Then (A^2) = (B^2)+(C^2)
Proof:
If a = angle opposite side A ( =90 degrees)
b = angle opposite side B
c = angle opposite side C
then B = A sin a and C = A cos a
Squaring and adding,we get the result.
Pythagorean triplets:
3,4,5
5,12,13
8,15,17
58π 18π
For an electrical conductor, by Ohm`s law:
If V = Voltage across its ends ,
R= resistance offered to current flow
and I = Current flowing through it , then
1. V is directly proportional to I.
2. The ratio V/I is constant and equal to R.
If I = 2 Amperes and V = 20 volts then
R = 20/2 = 10 ohms.
60π 12π
"If there is paradise anywhere on earth, then it`s here", someone said of Kashmir.
A region of great strategic importance in South Asia, Kashmir is situated just below the former USSR , bordering Pakistan, India, China and Afghanistan.
It falls under India`s Himalayan mountain range. The second biggest peak after Mt. Everest, K2 , is in Chinese held Kashmir. The highest battle ground in the world Siachen glacier is in Indian held Kashmir.
Major religions are Islam,Budhism and Hinduism, although because of years of millitancy, Hindus have been leaving to India.
Kashmir is also the biggest source of conflict between India and Pakistan. Three of the four major India-Pakistan wars were fought over Kashmir in 1948,1965 and recently in 1999. See Pakistani Military Victories.
History: Kashmir in the Vedic period was ruled by Hindus. They developed beautiful temples while governing the state. The presence of Dal lake establishes the fact that agriculture too was a priority during the Hindu period. Till the 12th century Kashmir was ruled by seperate Hindu and Budhist kings before Muslim invasions began.
In the beginning of the 13th century, Muslim Pathans from Afghanistan conquered Kashmir. The new rulers gave Kashmiris three options - convert,die or leave. Those who did not convert or leave were brutally tortured and killed.
In 1587 Kashmir was merged into the Muslim Mughal empire and it became their hill station for the next two centuries.
At the same time Sikhism was born in Punjab.
In 1819 Sikhs freed Kashmir from Muslim rule. Sikh rule didn`t last long due to the British expanding their empire. In 1846 the first Anglo-Sikh war ended with the English emerging victorious.
Through the peace treaty of 9 March 1846 the Sikhs were compelled to pay a war indemnity amounting to 1.5 million sterling to the British. The Sikhs were unable to pay it fully and ceded in lieu thereof the hill territories between the Beas and the Indus rivers. A week later, on 16 March, another treaty was signed recognizing Sikhs as the new rulers of the newly formed Jammu and Kashmir.Sikh rule continued till the end of world war II.
However, outside Sikh territories, Muslims wanted special rights on religious basis under Jinnah`s leadership. Their initial demands for seperate voting rights slowly became demands for a seperate nation,Pakistan.
In August 1947, India was partitioned. Its muslim majority areas - West Punjab, Sindh, Frontier province ,Balochistan and East Bengal joined Pakistan. Pakistan`s map included Kashmir because of its Muslim majority, though the rulers were not Muslim.
Kashmir despite being Muslim-majority did not join Pakistan. Neither did it join India. It wanted to stay free, just like Nepal.
On 22 october 1947, Pakistan sent hundreds of tribesmen to forcefully occupy Kashmir.Kashmir had its own army but its Muslim soldiers fled and joined the tribesmen.In 1947 over half a million Hindus and Sikhs were killed in Pakistan`s Punjab riots. More than five million Hindus and Sikhs were forced to leave their homes behind and move to India. Fearing the worse at the hands of pakistani tribesmen , the King sought Indian military assistance. Indian government agreed to send in troops only if Kashmir accepted to be part of Indian dominion.
The King agreed to merge with India and troops were sent to drive out the infiltrators. The matter went into the newly constituted UN and a ceasefire was declared with Pakistan and India controlled areas staying with the respective countries.
Post 1948 Kashmir progressed as an attractive tourist destination and the largest saffron producing state in India. 1990 onwards both its tourist and saffron images have been ruined by the seperatist movement. Today Kashmir depends on India for its economic survival.
In 1999, Pakistan again sent tribesmen to occupy regions in Indian held Kashmir. India used Mirage fighter planes and Bofors field guns to pound and drive them out.
During the 2002 military standoff between India and Pakistan, both nuclear giants came very close to an all-out war. But since then India and Pakistan have made steady progress on improving bilateral relations and a peaceful solution to Kashmir is expected.
What is the Kashmir dispute?
Pakistan claims it because it is Muslim majority. Pakistan`s argument in this regard is the two-nation theory, according to which there are two nations within india,one Hindu nation and the other Muslim nation.
India claims it because Kashmir chose to merge with India when Pakistan attacked it in 1948. India`s argument is that wherever Muslims are in majority they have driven Hindus out. If India is partitioned on religious basis like 1947 once again, where will Hindus go if Muslims become majority in other Indian states and start a Kashmir like power struggle.
Since 1990 Kashmiri seperatist movement has claimed over 50,000 lives. Over 300,000 Kashmiri Hindus have left their homes and today they have become refugees in their own land.
76π 40π
The standard unit of resistance offered to current flow by a conductor, used in electricity calculations.
Also see Ohm`s law.
For copper wire resistance is 2-100 ohms, but for a piece of wood it is over 1000 ohms.
130π 61π
Brave men who defend India. The 1.3 million strong Indian army is the third largest force in the world after China and USA.
The Indian Army strength at the beginning of the First World War was 155,423. It ended the war with 573,484 men defending the British empire.
During the Second World War the Indian Army had 189,000 men in 1939 who fought for Britain rising to 2,644,323 at peak strength in 1945.
After independence from Britain, Indian army was involved in these wars:
1.Kashmir in 1948 - came out victorious at several places in Kashmir and drove Pakistani invaders out until ceasefire was declared.
2.China in 1962 - lost to Chinese might and China voluntarily withdrew after taking some part of Kashmir.
3.Pakistan in 1965 - defeated Pakistani army, entered West Punjab and occupied Lahore.
4.Pakistan in 1971 - defeated Pakistan and captured over 90,000 Pakistani soldiers. They were released only when Pakistan agreed to the creation of Bangladesh.
5.Kashmir in 1999 - won through shelling Pakistani intruders by use of Bofors field guns. Pakistan withdrew after US intervention.
Indian army is twice the size of Pakistan army and has never lost to them.
168π 50π
The mother of all present-day european languages. Originated in India.
Indo-European Language Subfamilies:
* Indo-Iranian (Sanskrit, Hindi, Bengali, Persian)
* Hellenic (Greek)
* Armenian (Western Armenian, Eastern Armenian)
* Balto-Slavic (Russian, Polish, Czech, Lithuanian)
* Albanian (Gheg, Tosk)
* Celtic (Irish Gaelic, Welsh)
* Italic (Latin, Spanish, Italian, French)
* Germanic (German, English, Danish, Dutch, Swedish, Norwegian)
* Anatolian (extinct) (Hittite)
* Tocharian (extinct) (Tocharian A, Tocharian B)
Language Similarities:
* Indo-European voiceless stops (p, t, k) became Germanic voiceless fricatives (f, th, h):
o Indo-European pΓ
Βter, Germanic (English) father (contrast with non-Germanic: Latin pater)
o Indo-European treyes, Germanic (English) three (contrast with non-Germanic: Latin tres)
o Indo-European kerd, Germanic (English) heart, (compare with non-Germanic: Latin cord)
* Indo-European voiced stops (b, d, g) became Germanic voiceless stops (p, t, k):
o Indo-European abel, Germanic (English) apple (contrast with non-Germanic: Russian jabloko)
o Indo-European dent, Germanic (English) tooth (contrast with non-Germanic: Latin dentis)
o Indo-European grΓ
Βno, Germanic (English) corn (contrast with non-Germanic: Latin granum)
* voiced aspirated stops(bh, dh, gh) to voiced stops (b, d, g):
o Indo-European bhrater, Germanic (English) brother (contrast with non-Germanic: Latin frater)
Maater in Sanskrit = Mutter in German = Mother in English.
Pitar in Sanskrit = Vater in German = Father in English.
299π 75π
Enterprise and endeavour, these two words symbolize the essential spirit of the people of Punjab.
Punjab is a state in the Indian sub-continent where five rivers namely Satluj,Ravi,Jhelum,Chenab and Bias,meet.
Punjab is the richest state in India with the highest per capita income, a big number of Indian immigrants come from Punjab. Punjab is also the agricultural hub of India. It is the state where the "Green Revolution" (production of surplus wheat) began.
Providing the impetus for the "White revolution", it was Punjab that recorded the highest per capita availability of milk. Its average growth rate of 10% is amongst the highest in the country, clearly reflecting the progressive economy of the state.
Punjab is home to Sikhs,the bravest people in India. The Sikh Golden Temple located in Amritsar has more tourist visits than the Taj Mahal. Punjabi music and bhangra is popular in India and abroad among the sub-continental people.
Life in Punjab began with the Harappan civilisation. This culture existed along the Punjab state (in present day Pakistan). It was named after the city of Harappa which it was centered around. This city is well known for its impressive, organized and regular layout. Over one hundred other towns and villages also existed in this region. The Harappan people were literate and used the Dravidian language.
The presence of five rivers and the fertile land invited invasions. The first alien settlers in Punjab were fair-skinned Aryans who came from Central Asia , Tibet and parts of Russia.
Punjab was originally given the name Paanchaal by Aryans. During the Ramayana period , Punjab was where the sons of Prince Ram , Luv and Kusha were born. The cities of Lahore (Luv Pore) and Kasur (Kush Pore) were named after them.
During the the Mahabharata period, Punjab or Paanchaal was the state Draupadi,the Pandava(the five brothers) wife came from. Hence the name Paanchaali.
The oldest scriptures in all of India and the most important are called the vedas. All Hindus recognize the Vedas as the true origin of their faith because of the spiritual meaning behind them. The scriptures served as a base for inner searching among the Indo-Aryan people as they were composed by seers or ancient prophets while in a state of inspiration.
There are four Vedas: Rig Veda, Sama Veda, Yajur Veda and Atharva Veda. Each is divided into two groups: works and knowledge. The first is made of hymns and instructions regarding rights, ceremonies and rules of conduct. The latter is concerned with knowledge of who god is.
The Vedas form the basis of Hinduism and the caste system. Punjab was the place where Vedas were created by the Aryans after they invaded and settled in the Indus valley. These Vedas were passed on orally for many generations. They were first written in Vedic, an early form of Sanskrit. Then around 300 B.C. the Vedas were written down in Sanskrit the form we have them in today.
The religion that sprang forth from the Vedas helped shape Indian society. The Veda describes how the god sacrificed himself to himself. Each of the pieces of his body developed into a different portion of society. His mouth became the Brahmin or priests; his arms became the Kshatriyas or warriors; his thighs became the Vaisya or merchants, farmers, herders and artisans; and the feet became the Harijana or slaves and servants. Thus, while each part of society had its own role, it was still and single body.
The birth of Islam and occupation of Sindh threatened Punjab as well due to its geographical proximity to modern day Afghanistan. Muslim rulers attacked seventeen times but failed. They however didn`t fail the eighteenth chance and Punjab came under Islamic rule.
The first centre of Islamic existence was established at Multan. For the locals, Muslim rule meant abandoning their original faith and culture or they faced punishment according to Islamic laws. Many refused to convert and were killed or mercilessly tortured.
This went on unabated until the birth of Sikhism , a religion that initially rose above the blind religious practices of Hindus and Muslims, disapproved the caste system , proposed the existence of a single God but later on became a fighting force to deal with the oppressive Muslim rule. Had it not been for Sikh`s efforts, entire north India would have become Pakistan.
After the fall of Muslims in Punjab, Sikhs tried to re-establish themselves in the Muslim-majority Punjab but were successfully defeated by the British and the state came under direct British rule.
Punjab contributed the most brave men towards freedom struggle. The Arya Samaj,a Hindu reformist movement that disapproved of idol worship and the caste system ,originated and grew popular in Punjab.
Punjab`s contribution to Colonial British forces during the first and second world war was significant. Many fought against the Japanese at Singapore and Burma alongside Gurkhas.
The partition of India divided this state. Muslim-majority areas including capital Lahore went to Pakistan. Over 5 million Pakistani Punjab`s Hindus and Sikhs were forced to abandon their homes and move to India. Rest were killed in riots.
1947 onwards the state has seen a movement demanding a seperate Sikh state , a military campaign to flush out Sikh millitants from the Golden Temple and a dead prime minister but nevertheless economic progress has been outstanding, compared to other Indian states.
I am from Punjab.
Punjab is famous because of:
1. Sikhism
2. Folk music
3. Bhangra dance
4. Awesome food
5. Economic Progress(in India)
6. Its hardworking community
729π 560π