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ANS-12
Advantages: You get a stronger government with a majority coalition than a party trying to rule with a minority. More people's
views are represented in the policies implemented than if just one party ruled. Potentially a stronger/more talented team leading
the government, as the PM can then chose the talent from two parties, rather than just his own.
Disadvantages: Less stable, a coalition is more likely to fall apart and break up than a one-party government. It is less
accountable - who do you hold responsible for mistakes at the next election if there is more than one party in the government?
Politicians can easily just say 'it wasn't us, it was the Liberals' or whatever, reducing their accountability to both Parliament and
the electorate. One could also argue that they are less democratic - no one voted for a coalition, and as some of the policies of
every party involved will have to be dropped in the compromise, even those who voted for one of the coalition parties are not
getting all the policies/ideas they voted for.
It does, however, depend on the political system. Some systems work better than
others with coalition systems. In the Westminster Model, however, the negatives
usually outweigh the positives.
ANS-14
Gorakhpur is a city along the banks of Rapti river in the eastern part of the
state of Uttar Pradesh in India, near the border withNepal. It is the
administrative headquarters of Gorakhpur District and Gorakhpur Division.
The city is also home to Gorakhnath temple and many
historic Buddhist sites and the Gita Press, world's largest publisher
of Hindureligious texts. It is also the headquarters of North Eastern
Railways and serves an important center for education and trade.
Gorakhpur is a religious center containing many historic temples and sites
for both Hinduism and Buddhism. It is named after the ascetic Guru
Gorakshnath, a saint that popularized “Hath Yoga” a form of yoga which
concentrates on mastering natural power.
ANS-15
Babur (1526-1530)
Babar owns the credit of establishment of Mughal Empire in India after defeating Lodhi in 1526 at the battle of
Panipat. Babar ruled until 1530, and was succeeded by his son Humayun.
Achievements of Babur
 Defeated Ibrahim Lodhi in the first Battle of Panipat in 1526 to establish the greatest dynasty in India – the
Mughal Dynasty
 He extended his kingdom from Kabul and Kandahar in the north-west to Bihar in the east and from
Himalayas in the north to Gwalior in the south
 Though he ruled only for four years his love for art and architecture and fondness for nature is well known.
He made beautiful Moghul-style gardens in almost every fort and palace.
Gorakhpur
Humayun (1530-1540 and 1555-1556)
Achievements of Humayun
Humayun was the eldest son of the first emperor Babar of the Mughal Kingdom and became the second ruler of the
empire after succeeding his father in 1530. He ruled the country for about 10years but later in 1540 he was
defeatedby Sher ShahSuri.
Sher Shah Suri, the Afghan ruler who ruled for the short duration of 5 years from 1540 to 1545 but contributed a lot
to the country. He established efficient public administration and also set a revenue collectionsystem.
Humayun regain the throne in 1555 by defeating the Sikandar Suri, the successor of Sher Shah Suri but soon died
in 1556 at a young age of 48 years.
 The School of Mughal painting began with Humayun in 1549 when he invited two Persian painters to his
court.
 He was defeated by Sher Shah in the Battle of Chausa in 1539 but later with the help of the Iranian army he
regained lost power in 1555.
 He was well versed in Persian, Turki and subjects like Mathematics, Astronomy and Geography
 Humayun was tolerant towards all religions and invied various scholars in this court.
Akbar (1556-1605)
Akbar was Humayun's son and ascended the throne at the early age of 13 when his father died. The era of Akbar’s
rule holds a certain eminence in history for the same reason he is also known as Akbar the great. He was great
administrator as well the efficient ruler of the country. He introduced impartial justice towards non Muslims and
treated every religion with respect. Akbar’s popular Mansabdari system system became the basis of Mughal military
organization and civil administration.
Akbar ruled the country for nearly 50 years and died in 1605 and was buried outside of Agra at Sikandra.
Achievements of Akbar
 Akbar’s generals Bairam Khan and Khan Zaman I defeated Hemu, the Hindu ruler of North India in the
second battle of Panipat in 1556
 Akbar was a great patron of architecture and built the first Mughal monument, the Humayun’s tomb.
 Akbar also built the entire city of Fatehpur Sikri which is made of low arches and huge domes
 In his capital city of Agra, Akbar built the remarkable Red Fort which has exquisite carvings and canopied
roofs with sandstone.
 He formed a new religion called the Din-i-Ilahi which had the best elements of all religions drawn mostly
from Islam and Hinduism
 That Akbar was tolerant towards all religions is evident from the fact that he repealed the Jizya tax from
non-Muslims.
Jehangir (1605-1627)
Jehangir was the son of Akbar whose real name was Salim but was given the title of Jehangir, "Conqueror of the
World". He was married to Mehr-un-Nisa and gave her the title of Nur Jahan (light of the world).He further
strengthened the Mughal Empire in India after his father Akbar’s death. He was found of art and literature, famous
Mughal gardens at Srinagar are the evidence of his artistic taste. He died in 1627.
Achievements of Jahangir
 Mughal painting reached great heights during the rule of Jahangir. He promoted Persian culture and
patronised European and Persian painters.
 The Shalimar Gardens in Kashmir was built during Jahangir’s reign
 He sketched his own autobiography named Tuzk-e-Jahangiri.
 It was under Jahangir’s reign that the the seamless celestial globe was built by the Mughal scientists.
Shah Jahan: (1628-1658)
Jehangir was succeeded by his second son Khurram in 1628. Khurram alias Shah Jahan, was the fifth Mughal ruler
of India. He expanded his Empire to Kandhar in the north and conquered most of Southern India. The Mughal
Empire prospered greatly during this reign. The arts and culture of the Mughal Empire is admired even today. The
Red Fort, Jama Masjid and Taj Mahal are some of the great monuments of that era.
Achievements of Shah Jahan
 He built the Taj Mahal in Agra, one the best Mughal architecture in memory of his loving wife Mumtaz
Mahal.
 He built the Peacock throne made out of precious stones and gold.
 Shah Jahan shifted his capital to Delhi and built the Red Fort
 The Moti Masjid, the Jama Masjid and several mosques in Lahore were built by Shah Jahan.
Aurangzeb (1658-1707)
Aurangzeb was the son of Shah Jahan and was the sixth ruler of the Mughal Empire. He was a devout Muslim and
was very particular that his state follows Islam strictly. In terms of tenure he matched the reign of Akbar. The vision
to unite entire India was well realized during his tenure and in terms of area captured the Mughal rule was at its
peak. The only negative aspect was that he never trained any of his sons into administration.
Achievements of Aurangzeb
 Under his rule, the Mughal Empire reached its peak stretching from Kashmir in the north to Jinji to the south
and from Chitagong in the east to Hindukush in the west
 Only a few monuments were built by him as he was not too passionate about art and architecture.
ANS-16
Essay on environmental degradation
The deterioration of the environment by natural or human forces is known as environmental degradation.
Natural happenings like heavy rain, floods, storms, earthquakes, volcanoes etc. are not under human control
and they play havoc with environment time to time by making the land unfit lor cultivation. Here man is
helpless.
He can do nothing except to see the havoc. But when man himself plays a vital role in degrading the
environment in which he lives, and then the problem becomes more serious.
Needless to say that environmental degradation is one of the major global issues. The overuse of resources is it
land or water and the industrialisation process are the major causes of this phenomenon. Man has been felling
the tress for his various purposes.
He never minds if this process goes on without check it will lead to soil erosion, floods, silting of irrigation
canals and cultivated lands, which finally degrade our environment.
ANS-21 slang
An informal nonstandard variety of speechcharacterized by newly coined and rapidly changing words and phrases.
In his book Slang: The People's Poetry (OUP, 2009), Michael Adams argues that "slang is not merely a lexical phenomenon, a type of
word, but a linguistic practice rooted in social needs and behaviors, mostly the complementary needs to fit in and to stand out." (See
Examples and Observations, below.)
ANS-22 Heteronyms
Heteronyms are words that are spelled identically but have different meaningswhen pronounced
differently. For example:
Lead, pronounced LEED, means to guide. However, lead, pronounced LED, means a metallic element.
Compare heteronyms to homographs, homophones, and homonyms.
Homographs are words that are spelled the same but differ in meaning, derivation, or pronunciation.
Homophones are words that are pronounced the same but differ in meaning, derivation, or spelling.
Homonyms are words that are spelled and pronounced the same but have different meanings. There is
overlap among these categories.
Heteronyms are specific types of homographs in which the different pronunciations are associated with
different meanings. Many heteronyms are the result of one pronunciation being a verb and another being a
noun.
ANS-24
Palindrome Examples
A palindrome is a word or a number or a sequence of units that is able to be read the same way from either direction, be it forwards or backwards.
Punctuation and spaces between the words or lettering is allowed. Composing literature that is categorized as a palindrome is known as ‘constrained
writing.’ Single Word
Palindromes
 Stressed or desserts
 Rewarder or redrawer
 Departer or retraped
 Stop or pots
 Snap or pans
 Evil or live
 Star or rats
 Diaper or repaid
 Never odd or even
ANS-26
hard” and “hardly”
A lot of words in English vocabulary are very similar, but have different meanings that you need to understand
if you really want to learn English well.
The problem with HARDLY is that it looks like an adverb ( for example; quickly, differently, slowly) formed
from an adjective. But hardly is not the adverb of hard.
The definition of hardly is:
with great difficulty, almost not, just
I could hardly hear him speaking, he should have used a microphone
Mike had hardly walked through the front door when the phone rang
HARD can be both an adjective and an adverb
Examples as an adjective:
Diamonds are extremely hard stones
The basketball trainer is very hard if you miss the rebound you have to do 20 push-ups
Examples as adverbs:
Tom worked very hard to make his business profitable
The little boy held his father’s hand hard, he didn’t want to lose him
ANS-27
somehow vs anyhow
But somehow the tension remained.
It was a rough job, but somehow it didn't look that different with the skin stretched over straw instead of ribs.
But somehow all their endeavours had come to nothing
I don't quite know why, but anyhow if they do feel old at 75, then they ought to be shaken up a bit.
FML 556 But anyhow have you if you have a look here there's erm er the er er I think we ought to be thinking about er
GTC 354 It is not known who suggested this alteration, but anyhow the problem was solved; in the words of John Farey
As I gave a detailed account of Tommy's behavior and schoolwork, I prayed for the right words to bring these
two (Tommy's divorced parents) together, to help them see what they were doing to their son. But ____ the
words wouldn't come. Perhaps if they saw one of his smudged, carelessly done papers.
A. somehow B. anyhow Anonymous
Only 'somehow' fits the meaning.
ANS-37 Pendulum
pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its
resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium
position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium
position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period
depends on the length of the pendulum, and also to a slight degree on the amplitude, the width of the pendulum's swing.
ANS-40
Pythagoras, from a 1920s textbook. Photograph: © Blue Lantern Studio/Corbis
Pythagoras (circa 570-495BC)
Vegetarian mystical leader and number-obsessive, he owes his standing as the most famous name in maths due to a theorem about right-angled triangles, although it now
appears it probably predated him. He lived in a community where numbers were venerated as much for their spiritual qualities as for their mathematical ones. His elevation of
numbers as the essence of the world made him the towering primogenitor of Greekmathematics, essentially the beginning of mathematics as we know it now. And, famously, he
didn't eat bean
Hypatia (cAD360-415)
Hypatia (375-415AD), a Greek woman mathematician and philosopher. Photograph: © Bettmann/Corbis
Women are under-represented in mathematics, yet the history of the subject is not exclusively male. Hypatia was a scholar at the library in Alexandria in the 4th century CE. Her
most valuable scientific legacy was her edited version of Euclid's The Elements, the most important Greek mathematical text, and one of the standard versions for centuries after
her particularly horrific death: she was murdered by a Christian mob who stripped her naked, peeled away her flesh with broken pottery and ripped apart her limbs.
Girolamo Cardano (1501 -1576)
Girolamo Cardano (1501-1576), mathematician, astrologer and physician. Photograph: SSPL/Getty
Italian polymath for whom the term Renaissance man could have been invented. A doctor by profession, he was the author of 131 books. He was also a compulsive gambler. It
was this last habit that led him to the first scientific analysis of probability. He realised he could win more on the dicing table if he expressed the likelihood of chance events using
numbers. This was a revolutionary idea, and it led to probability theory, which in turn led to the birth of statistics, marketing, the insurance industry and the weather forecast.
Leonhard Euler (1707- 1783)
Leonhard Euler (1707-1783). Photograph: Science and Society Picture Library
The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous formula eiπ + 1
= 0, where e is the mathematical constant sometimes known as Euler's number and i is the square root of minus one, is widely considered the most beautiful in mathematics. He
later took an interest in Latin squares – grids where each row and column contains each member of a set of numbers or objects once. Without this work, we might not have had
sudoku.
Carl Friedrich Gauss (1777-1855)
Carl Friedrich Gauss (1777-1855). Photograph: Bettmann/CORBIS
Known as the prince of mathematicians, Gauss made significant contributions to most fields of 19th century mathematics. An obsessive perfectionist, he didn't publish much of his
work, preferring to rework and improve theorems first. His revolutionary discovery of non-Euclidean space (that it is mathematically consistent that parallel lines may diverge) was
found in his notes after his death. During his analysis of astronomical data, he realised that measurement error produced a bell curve – and that shape is now known as a
Gaussian distribution.
Georg Cantor (1845-1918)
Georg Ferdinand Cantor (1845-1918), German mathematician. Photograph: © Corbis
Of all the great mathematicians, Cantor most perfectly fulfils the (Hollywood) stereotype that a genius for maths and mental illness are somehow inextricable. Cantor's most
brilliant insight was to develop a way to talk about mathematical infinity. His set theory lead to the counter-intuitive discovery that some infinities were larger than others. The result
was mind-blowing. Unfortunately he suffered mental breakdowns and was frequently hospitalised. He also became fixated on proving that the works of Shakespeare were in fact
written by Francis Bacon.
Paul Erdös (1913-1996)
Paul Erdos (1913-96).
Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel. He rarely published alone, preferring to
collaborate – writing about 1,500 papers, with 511 collaborators, making him the second-most prolific mathematician after Euler. As a humorous tribute, an "Erdös number" is
given to mathematicians according to their collaborative proximity to him: No 1 for those who have authored papers with him; No 2 for those who have authored with
mathematicians with an Erdös No 1, and so on.
ohn Horton Conway (b1937)
John Horton Conway.
The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles. In 1970, he came up with the rules for the Game of Life, a game in
which you see how patterns of cells evolve in a grid. Early computer scientists adored playing Life, earning Conway star status. He has made important contributions to many
branches of pure maths, such as group theory, number theory and geometry and, with collaborators, has also come up with wonderful-sounding concepts like surreal numbers,
the grand antiprism and monstrous moonshine.
Grigori Perelman (b1966)
Russian mathematician Grigory Perelman. Photograph: © EPA/Corbis
Perelman was awarded $1m last month for proving one of the most famous open questions in maths, the Poincaré Conjecture. But the Russian recluse has refused to accept the
cash. He had already turned down maths' most prestigious honour, the Fields Medal in 2006. "If the proof is correct then no other recognition is needed," he reportedly said. The
Poincaré Conjecture was first stated in 1904 by Henri Poincaré and concerns the behaviour of shapes in three dimensions. Perelman is currently unemployed and lives a frugal
life with his mother in St Petersburg.
Terry Tao (b1975)
Terry Tao. Photograph: Reed Hutchinson/UCLA
An Australian of Chinese heritage who lives in the US, Tao also won (and accepted) the Fields Medal in 2006. Together with Ben Green, he proved an amazing result about prime
numbers – that you can find sequences of primes of any length in which every number in the sequence is a fixed distance apart. For example, the sequence 3, 7, 11 has three
primes spaced 4 apart. The sequence 11, 17, 23, 29 has four primes that are 6 apart. While sequences like this of any length exist, no one has found one of more than 25 primes,
since the primes by then are more than 18 digits long.
Alex Bellos is the author of Alex's Adventures in Numberland

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  • 1. ANS-12 Advantages: You get a stronger government with a majority coalition than a party trying to rule with a minority. More people's views are represented in the policies implemented than if just one party ruled. Potentially a stronger/more talented team leading the government, as the PM can then chose the talent from two parties, rather than just his own. Disadvantages: Less stable, a coalition is more likely to fall apart and break up than a one-party government. It is less accountable - who do you hold responsible for mistakes at the next election if there is more than one party in the government? Politicians can easily just say 'it wasn't us, it was the Liberals' or whatever, reducing their accountability to both Parliament and the electorate. One could also argue that they are less democratic - no one voted for a coalition, and as some of the policies of every party involved will have to be dropped in the compromise, even those who voted for one of the coalition parties are not getting all the policies/ideas they voted for. It does, however, depend on the political system. Some systems work better than others with coalition systems. In the Westminster Model, however, the negatives usually outweigh the positives. ANS-14 Gorakhpur is a city along the banks of Rapti river in the eastern part of the state of Uttar Pradesh in India, near the border withNepal. It is the administrative headquarters of Gorakhpur District and Gorakhpur Division. The city is also home to Gorakhnath temple and many historic Buddhist sites and the Gita Press, world's largest publisher of Hindureligious texts. It is also the headquarters of North Eastern Railways and serves an important center for education and trade. Gorakhpur is a religious center containing many historic temples and sites for both Hinduism and Buddhism. It is named after the ascetic Guru Gorakshnath, a saint that popularized “Hath Yoga” a form of yoga which concentrates on mastering natural power. ANS-15 Babur (1526-1530) Babar owns the credit of establishment of Mughal Empire in India after defeating Lodhi in 1526 at the battle of Panipat. Babar ruled until 1530, and was succeeded by his son Humayun. Achievements of Babur  Defeated Ibrahim Lodhi in the first Battle of Panipat in 1526 to establish the greatest dynasty in India – the Mughal Dynasty  He extended his kingdom from Kabul and Kandahar in the north-west to Bihar in the east and from Himalayas in the north to Gwalior in the south  Though he ruled only for four years his love for art and architecture and fondness for nature is well known. He made beautiful Moghul-style gardens in almost every fort and palace. Gorakhpur
  • 2. Humayun (1530-1540 and 1555-1556) Achievements of Humayun Humayun was the eldest son of the first emperor Babar of the Mughal Kingdom and became the second ruler of the empire after succeeding his father in 1530. He ruled the country for about 10years but later in 1540 he was defeatedby Sher ShahSuri. Sher Shah Suri, the Afghan ruler who ruled for the short duration of 5 years from 1540 to 1545 but contributed a lot to the country. He established efficient public administration and also set a revenue collectionsystem. Humayun regain the throne in 1555 by defeating the Sikandar Suri, the successor of Sher Shah Suri but soon died in 1556 at a young age of 48 years.  The School of Mughal painting began with Humayun in 1549 when he invited two Persian painters to his court.  He was defeated by Sher Shah in the Battle of Chausa in 1539 but later with the help of the Iranian army he regained lost power in 1555.  He was well versed in Persian, Turki and subjects like Mathematics, Astronomy and Geography  Humayun was tolerant towards all religions and invied various scholars in this court. Akbar (1556-1605) Akbar was Humayun's son and ascended the throne at the early age of 13 when his father died. The era of Akbar’s rule holds a certain eminence in history for the same reason he is also known as Akbar the great. He was great administrator as well the efficient ruler of the country. He introduced impartial justice towards non Muslims and treated every religion with respect. Akbar’s popular Mansabdari system system became the basis of Mughal military organization and civil administration. Akbar ruled the country for nearly 50 years and died in 1605 and was buried outside of Agra at Sikandra. Achievements of Akbar  Akbar’s generals Bairam Khan and Khan Zaman I defeated Hemu, the Hindu ruler of North India in the second battle of Panipat in 1556  Akbar was a great patron of architecture and built the first Mughal monument, the Humayun’s tomb.  Akbar also built the entire city of Fatehpur Sikri which is made of low arches and huge domes  In his capital city of Agra, Akbar built the remarkable Red Fort which has exquisite carvings and canopied roofs with sandstone.  He formed a new religion called the Din-i-Ilahi which had the best elements of all religions drawn mostly from Islam and Hinduism  That Akbar was tolerant towards all religions is evident from the fact that he repealed the Jizya tax from non-Muslims. Jehangir (1605-1627) Jehangir was the son of Akbar whose real name was Salim but was given the title of Jehangir, "Conqueror of the
  • 3. World". He was married to Mehr-un-Nisa and gave her the title of Nur Jahan (light of the world).He further strengthened the Mughal Empire in India after his father Akbar’s death. He was found of art and literature, famous Mughal gardens at Srinagar are the evidence of his artistic taste. He died in 1627. Achievements of Jahangir  Mughal painting reached great heights during the rule of Jahangir. He promoted Persian culture and patronised European and Persian painters.  The Shalimar Gardens in Kashmir was built during Jahangir’s reign  He sketched his own autobiography named Tuzk-e-Jahangiri.  It was under Jahangir’s reign that the the seamless celestial globe was built by the Mughal scientists. Shah Jahan: (1628-1658) Jehangir was succeeded by his second son Khurram in 1628. Khurram alias Shah Jahan, was the fifth Mughal ruler of India. He expanded his Empire to Kandhar in the north and conquered most of Southern India. The Mughal Empire prospered greatly during this reign. The arts and culture of the Mughal Empire is admired even today. The Red Fort, Jama Masjid and Taj Mahal are some of the great monuments of that era. Achievements of Shah Jahan  He built the Taj Mahal in Agra, one the best Mughal architecture in memory of his loving wife Mumtaz Mahal.  He built the Peacock throne made out of precious stones and gold.  Shah Jahan shifted his capital to Delhi and built the Red Fort  The Moti Masjid, the Jama Masjid and several mosques in Lahore were built by Shah Jahan. Aurangzeb (1658-1707) Aurangzeb was the son of Shah Jahan and was the sixth ruler of the Mughal Empire. He was a devout Muslim and was very particular that his state follows Islam strictly. In terms of tenure he matched the reign of Akbar. The vision to unite entire India was well realized during his tenure and in terms of area captured the Mughal rule was at its peak. The only negative aspect was that he never trained any of his sons into administration. Achievements of Aurangzeb  Under his rule, the Mughal Empire reached its peak stretching from Kashmir in the north to Jinji to the south and from Chitagong in the east to Hindukush in the west  Only a few monuments were built by him as he was not too passionate about art and architecture. ANS-16 Essay on environmental degradation The deterioration of the environment by natural or human forces is known as environmental degradation. Natural happenings like heavy rain, floods, storms, earthquakes, volcanoes etc. are not under human control and they play havoc with environment time to time by making the land unfit lor cultivation. Here man is helpless. He can do nothing except to see the havoc. But when man himself plays a vital role in degrading the environment in which he lives, and then the problem becomes more serious.
  • 4. Needless to say that environmental degradation is one of the major global issues. The overuse of resources is it land or water and the industrialisation process are the major causes of this phenomenon. Man has been felling the tress for his various purposes. He never minds if this process goes on without check it will lead to soil erosion, floods, silting of irrigation canals and cultivated lands, which finally degrade our environment. ANS-21 slang An informal nonstandard variety of speechcharacterized by newly coined and rapidly changing words and phrases. In his book Slang: The People's Poetry (OUP, 2009), Michael Adams argues that "slang is not merely a lexical phenomenon, a type of word, but a linguistic practice rooted in social needs and behaviors, mostly the complementary needs to fit in and to stand out." (See Examples and Observations, below.) ANS-22 Heteronyms Heteronyms are words that are spelled identically but have different meaningswhen pronounced differently. For example: Lead, pronounced LEED, means to guide. However, lead, pronounced LED, means a metallic element. Compare heteronyms to homographs, homophones, and homonyms. Homographs are words that are spelled the same but differ in meaning, derivation, or pronunciation. Homophones are words that are pronounced the same but differ in meaning, derivation, or spelling. Homonyms are words that are spelled and pronounced the same but have different meanings. There is overlap among these categories. Heteronyms are specific types of homographs in which the different pronunciations are associated with different meanings. Many heteronyms are the result of one pronunciation being a verb and another being a noun. ANS-24 Palindrome Examples A palindrome is a word or a number or a sequence of units that is able to be read the same way from either direction, be it forwards or backwards. Punctuation and spaces between the words or lettering is allowed. Composing literature that is categorized as a palindrome is known as ‘constrained writing.’ Single Word Palindromes  Stressed or desserts  Rewarder or redrawer  Departer or retraped  Stop or pots  Snap or pans  Evil or live  Star or rats  Diaper or repaid  Never odd or even ANS-26 hard” and “hardly” A lot of words in English vocabulary are very similar, but have different meanings that you need to understand if you really want to learn English well. The problem with HARDLY is that it looks like an adverb ( for example; quickly, differently, slowly) formed from an adjective. But hardly is not the adverb of hard. The definition of hardly is:
  • 5. with great difficulty, almost not, just I could hardly hear him speaking, he should have used a microphone Mike had hardly walked through the front door when the phone rang HARD can be both an adjective and an adverb Examples as an adjective: Diamonds are extremely hard stones The basketball trainer is very hard if you miss the rebound you have to do 20 push-ups Examples as adverbs: Tom worked very hard to make his business profitable The little boy held his father’s hand hard, he didn’t want to lose him ANS-27 somehow vs anyhow But somehow the tension remained. It was a rough job, but somehow it didn't look that different with the skin stretched over straw instead of ribs. But somehow all their endeavours had come to nothing I don't quite know why, but anyhow if they do feel old at 75, then they ought to be shaken up a bit. FML 556 But anyhow have you if you have a look here there's erm er the er er I think we ought to be thinking about er GTC 354 It is not known who suggested this alteration, but anyhow the problem was solved; in the words of John Farey As I gave a detailed account of Tommy's behavior and schoolwork, I prayed for the right words to bring these two (Tommy's divorced parents) together, to help them see what they were doing to their son. But ____ the words wouldn't come. Perhaps if they saw one of his smudged, carelessly done papers. A. somehow B. anyhow Anonymous Only 'somehow' fits the meaning. ANS-37 Pendulum pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on the amplitude, the width of the pendulum's swing. ANS-40 Pythagoras, from a 1920s textbook. Photograph: © Blue Lantern Studio/Corbis Pythagoras (circa 570-495BC) Vegetarian mystical leader and number-obsessive, he owes his standing as the most famous name in maths due to a theorem about right-angled triangles, although it now appears it probably predated him. He lived in a community where numbers were venerated as much for their spiritual qualities as for their mathematical ones. His elevation of numbers as the essence of the world made him the towering primogenitor of Greekmathematics, essentially the beginning of mathematics as we know it now. And, famously, he didn't eat bean
  • 6. Hypatia (cAD360-415) Hypatia (375-415AD), a Greek woman mathematician and philosopher. Photograph: © Bettmann/Corbis Women are under-represented in mathematics, yet the history of the subject is not exclusively male. Hypatia was a scholar at the library in Alexandria in the 4th century CE. Her most valuable scientific legacy was her edited version of Euclid's The Elements, the most important Greek mathematical text, and one of the standard versions for centuries after her particularly horrific death: she was murdered by a Christian mob who stripped her naked, peeled away her flesh with broken pottery and ripped apart her limbs. Girolamo Cardano (1501 -1576) Girolamo Cardano (1501-1576), mathematician, astrologer and physician. Photograph: SSPL/Getty Italian polymath for whom the term Renaissance man could have been invented. A doctor by profession, he was the author of 131 books. He was also a compulsive gambler. It was this last habit that led him to the first scientific analysis of probability. He realised he could win more on the dicing table if he expressed the likelihood of chance events using numbers. This was a revolutionary idea, and it led to probability theory, which in turn led to the birth of statistics, marketing, the insurance industry and the weather forecast. Leonhard Euler (1707- 1783) Leonhard Euler (1707-1783). Photograph: Science and Society Picture Library The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous formula eiπ + 1 = 0, where e is the mathematical constant sometimes known as Euler's number and i is the square root of minus one, is widely considered the most beautiful in mathematics. He later took an interest in Latin squares – grids where each row and column contains each member of a set of numbers or objects once. Without this work, we might not have had sudoku. Carl Friedrich Gauss (1777-1855) Carl Friedrich Gauss (1777-1855). Photograph: Bettmann/CORBIS Known as the prince of mathematicians, Gauss made significant contributions to most fields of 19th century mathematics. An obsessive perfectionist, he didn't publish much of his work, preferring to rework and improve theorems first. His revolutionary discovery of non-Euclidean space (that it is mathematically consistent that parallel lines may diverge) was found in his notes after his death. During his analysis of astronomical data, he realised that measurement error produced a bell curve – and that shape is now known as a Gaussian distribution. Georg Cantor (1845-1918) Georg Ferdinand Cantor (1845-1918), German mathematician. Photograph: © Corbis Of all the great mathematicians, Cantor most perfectly fulfils the (Hollywood) stereotype that a genius for maths and mental illness are somehow inextricable. Cantor's most brilliant insight was to develop a way to talk about mathematical infinity. His set theory lead to the counter-intuitive discovery that some infinities were larger than others. The result was mind-blowing. Unfortunately he suffered mental breakdowns and was frequently hospitalised. He also became fixated on proving that the works of Shakespeare were in fact written by Francis Bacon.
  • 7. Paul Erdös (1913-1996) Paul Erdos (1913-96). Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel. He rarely published alone, preferring to collaborate – writing about 1,500 papers, with 511 collaborators, making him the second-most prolific mathematician after Euler. As a humorous tribute, an "Erdös number" is given to mathematicians according to their collaborative proximity to him: No 1 for those who have authored papers with him; No 2 for those who have authored with mathematicians with an Erdös No 1, and so on. ohn Horton Conway (b1937) John Horton Conway. The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles. In 1970, he came up with the rules for the Game of Life, a game in which you see how patterns of cells evolve in a grid. Early computer scientists adored playing Life, earning Conway star status. He has made important contributions to many branches of pure maths, such as group theory, number theory and geometry and, with collaborators, has also come up with wonderful-sounding concepts like surreal numbers, the grand antiprism and monstrous moonshine. Grigori Perelman (b1966) Russian mathematician Grigory Perelman. Photograph: © EPA/Corbis Perelman was awarded $1m last month for proving one of the most famous open questions in maths, the Poincaré Conjecture. But the Russian recluse has refused to accept the cash. He had already turned down maths' most prestigious honour, the Fields Medal in 2006. "If the proof is correct then no other recognition is needed," he reportedly said. The Poincaré Conjecture was first stated in 1904 by Henri Poincaré and concerns the behaviour of shapes in three dimensions. Perelman is currently unemployed and lives a frugal life with his mother in St Petersburg. Terry Tao (b1975) Terry Tao. Photograph: Reed Hutchinson/UCLA An Australian of Chinese heritage who lives in the US, Tao also won (and accepted) the Fields Medal in 2006. Together with Ben Green, he proved an amazing result about prime numbers – that you can find sequences of primes of any length in which every number in the sequence is a fixed distance apart. For example, the sequence 3, 7, 11 has three primes spaced 4 apart. The sequence 11, 17, 23, 29 has four primes that are 6 apart. While sequences like this of any length exist, no one has found one of more than 25 primes, since the primes by then are more than 18 digits long. Alex Bellos is the author of Alex's Adventures in Numberland