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History-2000-Set I

Q1. Explain any one significant feature of the Regulating Act of 1773.
Ans. The Regulating Act introduced by the British Government in 1773 was the first act, which broke the monopoly of East India Company’s administrative control over India. This Act made changes in the constitution of the Court of Directors of the Company and subjected their actions to the supervision of the British Government.

Q2. Explain the nature of Tipu sultan’s relations with Britain. What, in your view, were the main reasons of his defeat?
Ans. The most important power that emerged in South India in 18th century was Mysore under Haider Ali and his son Tipu Sultan. Sultan Tipu ,(1782-1799A.D.) was a staunch enemy of British like his father. .He was a lover of freedom. Having rejected subsidiary alliance with the Britishers, in preference to lead a life of subordination, sacrificed his life while fighting the fourth Anglo-Mysore war in 1799 in Serigapatam.
As a statesman, Sultan, more than any other 18th century Indian ruler, recognized to the full extent the threat that the English posed to South India as well as to other Indian powers. With an objective of seeking help, Tipu sent his ambassadors to France, Turkey, Iran and Arab states. He organized his army on European style. He also made an effort to build a modern navy.
Though, Tipu sultan was recklessly brave and, as a commander, brilliant. He was, however, hasty in action and unstable in nature. He also lacked political foresight, which became the main cause of his defeat. According to Col.Wilkes, “In the estimation of character, Haider Ali rarely made error while Tipu was rarely right.”Instead of seeking help from the neighboring Indian states of Marathas and Nizams, he made efforts to seek help from distant countries of France, Turkey, and Iran. . As a general also his war strategies were weak. In preference to cavalry, he paid much attention towards infantry and fortification. Hence, the pace of his army was slow and his war strategy instead of becoming aggressive became defensive.

OR

Q Why did the Portuguese fail to expand in India? Explain.
Ans. In 1498, Vasco Da Gama of Portugal discovered a new sea route from Europe to India, which was to witness a new era in European trade relations with India. Under the viceroyalty of Alfonso d’ Albuquerque, who captured Goa in 1510A.D. , The Portuguese were the first to establish their domination over the entire Asian coast.

Inspite of their barbaric behavior, which included piracy, raids and mindless conversions of Indians to christianity, the Portuguese survived in India for a century because they enjoyed control over the high seas but in the latter half of the 16th century, Portuguese lost their trading monopoly to the English, Dutch and the French .The new European powers, with well equipped army and strong government support were easily able to evacuate small trading posts established by the Portuguese.

The incompetent successors of Albuquerque failed to preserve Portuguese empire in India.The raids and piracies conducted by them made them unpopular with Indian rulers who preferred the sophisticated and diplomatic behavior of the British and the French.
The discovery of Brazil diverted many Portuguese to this new trading venture with very few traders maintaining trade relations with India.

History-2000-Set II

Q1. Explain one significant feature of the Pitts India Act.(2marks)
Ans.The Pitts India Act was passed by the British Prime Minister ,William Pitt.in 1784 AD in order to remove the shortcomings of the Regulating act of 1773 and to improve the administration of the East India company. Through Pitts Act ,the powers of the governor-general were enhanced considerably .Also , the commercial arrangements of the company was in the hands of the directors . They could now dismiss British officials posted in India.

Q 2. Critically analyze the impact of the British policy of the Free trade in India in early 19th century.(5marks)
Ans.The commercial policy of Britain was largely influenced by its imperialistic regime in India. During the second half of the 18th century and early 19th century Britain underwent profound social and economic transformation due to the Industrial Revolution and the British industry developed and expanded rapidly on the basis of modern machines,factory system and capitalism .Britain had had also captured and monopolized many foreign markets.by means of colonialism. It now had a strong industrial class whose interests were exporting its manufactured goods to vast markets provided in form of the colonies.
Thus ,the government of Britain , in 19th century followed a policy of ‘free trade’ or unrestricted entry of British goods . The Indian handicrafts were now exposed to the fierce and unequal competition of machine made products of Britain and face extinction. India had to admit British goods free or at minimum tariff rates . The Indian handmade goods were unable to compete with much cheaper machine made foreign products.
The Indian products, which could still compete, with British products were subjected to heavy duty. The duties on some imports going as high as 400 percent which led to falling of Indian export market.
In short, the British commercial policy was guide by the needs of the British industry with the main aim of transforming India into a consumer of British manufactures and a supplier of raw material.

History-2000-Set III

Q.1. Explain any one feature of Charter Act of 1833.
Ans 1. The Charter Act of 1833 abolished the trading monopoly of the East India Company in India but the Indian territories, which it owned and the revenue of these territories was left with the company. Thus, this Act changed a trading company into a political power.

Q.2. How was the royotwary system different from the permanent settlement? Why was it introduced?
Ans. The ryotwari system was a system of revenue collection introduced by the Britishers in whom the government did not act through any intermediary or zamindar but maintained direct contact with the ‘ryot’ or the peasant. This system was introduced in Madras and Bombay.The rent collected in this system were so high that more often than not he was gripped in the clutches of the money lender.
Permanent settlement was different from ryotwary settlement as the zamindars were considered owners of the land which made the plight of the peasantry quite miserable as now they were left at the mercy of the zamindar. The British profited from this settlement as the zamindars now took special interest in land to increase the production as the land now belonged to them .
OR
Q. What were the changes introduced by Lord Cornwallis in the company’s administration in India? What was their impact?
Ans. Lord cornwallis became the governor general (1786-93) and commander –in chief of Indian army in India.He is better known in India because of the administrative and land reforms which he introduced. He increased the salaries of the servants so that they could resist temptations. He also made strict rules to control bribery and private trade. Cornwallis seperated the functions of the collectors and the district judge which were earlier merged. The collectors were to be responsible for the revenue collection and the district judges were to now supervise the work of judicial courts.
Lord Cornwallis introduced the system of permanent settlement in1793 A.D in Bihar and Bengal to increase the revenue of the company from Indian agriculture. According to this settlement, the peasant were made the owners of the land and had to give 10%to the government from the total production of the land. If any zamindar failed to fulfill these conditions he was ousted from the land and the English did not hesitate in putting his land on auction.
By conferring the ownership right of the land to the zamindars , Lord Cornwallis was able to create a class of staunch loyalist in form of these zamindars. Knowing that they had permanent hold over their land, the zamindars took special interest in its improvement and thus the company was able to make higher profits in form of the collection of the land revenue.

English(Core)-1997

SECTION A

Q 1. Read the following passage and answer the questions that follow it:
So great is our passion for doing things for ourselves, that we are becoming increasingly less dependent on specialized labor. NO one can plead ignorance of a subject any longer, for three are countless do-it yourself publications. Armed with the right tools and materials, newly-weds gaily embark on the task of decorating their own fireplaces, laying-out their own gardens, building garages and making furniture. Some really keen enthusiasts go so far as to make their own record players and a radio transmitters. Shops cater for the do-it yourself craze not only by running special advisory services for novices, but by offering consumers bits and pieces which they can assemble at home. Such things provide an excellent outlet for pent up creative energy, but unfortunately not all of us are born handymen.

Wives tend to believe that their husbands are infinitely resourceful and versatile. Even husbands who can hardly drive a nail in straight are supposed to be born electricians, carpenters, plumbers and mechanics. When lights fuse, furniture gets rickety, pipes get clogged, or vacuum cleaners fail to operate, wives automatically assume that their husbands will somehow put things right. The worst thing about the do-it yourself game is that sometimes husbands live under the delusion that they can do anything even when they have been repeatedly proved wrong. It is a question of pride s much as anything else.

English(Core)-1999

Q 1.Read the following passage carefully and answer the questions that follow:

People travelling long distances frequently have to decide whether they would prefer to go by land, sea or air. Hardly anyone can positively enjoy sitting in a train for more than a few hours. Train compartments soon get cramped and stuffy. It is almost impossible to take your mind off the journey. Reading is only a partial solution, for the monotonous rhythm of the wheels clicking on the rails soon lulls you to sleep. During the day, sleep comes in snatches. At night when you really wish to go to sleep, you rarely manage to do so. If you are lucky enough to get a couchette, you spend half the night staring at the small blue light in the ceiling, or fumbling to find your passport when you cross a frontier. Inevitably you arrive at your destination almost exhausted.

Long car journeys are even less pleasant, for it is quite impossible even to read. On motor-ways you can at least travel fairly safely at high speeds, but more often than not, the greater part of the journey is spent on narrow, bumpy roads which are crowded with traffic . By comparison, trips by sea offer a great variety of civilized comforts. You can stretch your legs on the spacious decks, play games, swim, meet interesting people and enjoy good food-always assuming, of course, that the sea is calm. If it is not, and you are likely to get sea-sick, no form of transport could be worse. Even if you travel in ideal weather, sea-journeys take a long time. Relatively few people are prepared to sacrifice up to a third of their holidays for the pleasure of travelling on a ship.

Aeroplanes have the reputation of being dangerous and even hardened travellers are intimidated by them. They also have the grave disadvantage of being the most expensive form of transport. But nothing can match them for speed and comfort. Travelling at a height of 30,000 feet, far above the clouds, and at over 500 miles an hour is an exhilarating experience. You do not have to devise ways of taking your mind off the journey, for an aeroplane gets you to your destination rapidly. For a few hours, you settle back in a deep armchair to enjoy the flight. The real escapist can watch a free film show and sip a hot or cold drink on some services. But even when such refreshments are not available, there is plenty to keep you occupied. An aeroplane offers you an unusual breath taking view of the world. You soar effortlessly over high mountains and deep valleys. You really see the shape of the land. If the landscape is hidden from view, you can enjoy the extraordinary sight of unbroken clouds, plains that stretch out for miles before you, while the sun shines brilliantly in a clear sky. The journey is so smooth that there is nothing to prevent you from reading or sleeping. However you decide to spend your time, one thing is certain: you will arrive at your destination fresh and uncrumpled. You will not have to spend the next few days recovering from a long and arduous journey.

Maths-1996 -Set I

Q1) Using elementary row transformations, find the inverse of the matrix
A = 4 5
3 4

Ans1) Here
A =
4 5
3 4
and I =
1 0
0 1
Now A = IA
=>
4 5
3 4=1 0
0 1
A=> Applying R1 (1/4)R1
1 5/4
3 4=1/4 0
0 1
A=> Applying R2 R2 – 3R1
1 5/4
0 1/4
=
1/4 0
-3/4 1
A=> Applying R2 4R2
1 5/4
0 1=1/4 0
-3 4
A=> Applying R1 R1 – (5/4)R2
1 0
0 1
=
4 -5
-3 4
AA-1 = 4 -5
-3 4
Q2) For the matrices A and B, verify that (A, B)’ = A’B’ where
A = 1 2
3 4
B = 4 5
1 2
Ans2) Here
A = 1 2
3 4
B = 4 5
1 2= 6 9
16 23= 6 16
9 23
R.H.S. = B’A’ =4 1 1 3 = 6 16 = L.H.S.
5 2 2 4 9 23

Maths-1996 -Set II

Q2) Find the work done by the force = + 2 + , acting on a particle, if the particle is displaced from the point with position vector 2 + + to the point with position vector 3 + 2 + 4.
Ans2) Here = + 2 +
call A(2 + + ) and B(3 + 2 + 4)
… = – = (3 + 2 + 4) – (2 + + )
= + + 3
… work done = .
= ( + 2 + ) . ( + + 3)
= 1 . I + 2 . I + I . 3 = 6

Q4) For the matrices A and B, verify that (AB’ ) = A’B’ where
A = 1 3
2 4
B = 1 4
2 5

Ans4) Here
A =
1 3
2 4
B =
1 4
2 5
L.H.S. =
7 19
10 28= 7 10
18 28
R.H.S. = B’A’ =
1 2
4 5
1 2
3 4
=
7 10
18 28= L.H.S
Q7) Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 3 or by 4?
Ans7) Let P(3), P(4), P(3 and 4), P(3 or 4) respectively denote the Probs of the sum of the no.s on the two faces be divisible by 3, 4, 3 and 4, 3 or 4 then
P(3) = 12/16 = 1/3
… the favourable Pairs are
(1, 2); (1, 5); (2, 1); (2, 4); (3, 3); (3, 6); (4, 2); (4, 5); (5, 1); (5, 4); (6, 3); (6, 6)
P(4) = 9/36 = 1/4
… the favourable Pairs are
(1, 3); (2, 2); (2, 6); (3, 1); (3, 5); (4, 4); (5, 3); (6, 2); (6, 6)
P(3 and 4) = 1/36
(only one pair, (6, 6) is common)
P(3 or 4) = P(3) + P(4) – P(AB)
= 1/3 + 1/4 – 1/36 = (12 + 9 – 1)/36 = 5/9

Maths-1997 -Set I

Q1) Find from first principle the derivative of (x2 + 1)/x w.r.t. x
Ans1) Let y = (x2 + 1)/x = x + 1/x – (i)
Let x be a small incremental in the value of x and y be the corresponding incremental in the value of y, then
y + y = x + x + 1/(x + x) – (ii)
Now (ii) – (i)
=> y = x + 1/(x + x) – 1/x
y = x – x/(x(x + x)) => y/x = 1 – 1/(x(x + x))

… dy/dx =

y/x
=
(1 – 1/(x(x + x))

= 1 – 1/x2
= (x2 – 1)/x2

Q2) Evaluate :
1 – cos 5x
1 – cos 6x

Ans2)
1 – cos 5x =
1 – cos 6x 2sin2 (5x/2)
2sin2 (3x)
(5/2)2[sin (5x/2)/(5x/2)]2
32 [sin 3x/3x]2 = 25/36

Q3) Using differentials, find the approximate value of 29
Ans3) To find 29
Let x = 27 and x = 2 then x + x = 27 + 2 = 29
Taking y = x1/3, we get dy/dx = 1/3 x-2/3
Also y + y = (x + x)1/3 = 291/3
where y = x1/3 = 271/3 = 3
… 3 + y = 291/3
Again y = dydx x = 1/3 x-2/3 . 2 = 2/3(27)-2/3 = 2/27
291/3 = 3 + y = 3 + (2/27) = 83/27

Maths-1997 -Set II

Q1) In a group there are 2 men and 3 women 3 person are selected at random from this group. Find the probability that 1 man and 2 women or 2 men and 1 woman are selected.
Ans1) Given Men (2) and women (3)
To be selected : 3 Person
Total no. of cases = 5C3
Now P(1 M and 2 W or 2 M and 1 W) = P(1 M and 2 W) + P(2 M and 1 W)
= (2C1 . 3C2)/5C3 + (2C2 . 3C1)/5C3 = (2 . 3)/10 + (1 . 3)/10 = 9/10

Q6) Evaluate :
xtan x
1 – cos 2x

Ans6)
xtan x =
1 – cos 2x xsin x
cos x . 2sin2 x
x =
sin x 1 = 1 .1/2 = 1/2
2cos x

Q9) Evaluate
/2 sin x dx
0 1 + cos2 x

Ans9) Let I =
/2 sin x dx
0 1 + cos2 x

Put cos x = t => sin x dx = -dt
Also x = 0 => t = 1 and x = /2 => t = 0
… I = 0 -dt = – [tan-1 t]10 = -[0 - /4] = /4
1 1 + t2

Maths-1997 -Set III

15) Evaluate
/3 sec x tan x dx
0 1 + sec2 x

Ans15)
/3 sec x tan x dx
0 1 + sec2 x

Put sec x = t
sec x tan xdx = dt
Now when x = /3 => t = 2
x = 0 => t = 1
2 dt = tan-1 (t)
1 1 + t2 2
1

tan-1 (2) – tan-1 (1)
= tan-1 (2) – /4

Q24) Prove that
b+c c+a a+b
q+r r+p p+q
y+z z+x x+y = 2 a b c
p q r
x y z

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