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Tamilnadu Samacheer Kalvi 10th Social Science Solutions History Chapter 1 Outbreak of World War I and Its Aftermath

Samacheer Kalvi 10th Social Science Outbreak of World War I and Its Aftermath Text Book Back Questions and Answers

I. Choose the correct answer

Question 1.
What were the three major empires shattered by the end of First World War?
(a) Germany, Austria Hungary, and the Ottomans
(b) Germany, Austria-Hungary, and Russia
(c) Spain, Portugal and Italy
(d) Germany, Austria-Hungary, Italy
Answer:
(a) Germany, Austria Hungary, and the Ottomans

Question 2.
Where did the Ethiopian army defeat the Italian army?
(a) Delville
(b) Orange State
(c) Adowa
(d) Algiers
Answer:
(c) Adowa

Question 3.
Which country emerged as the strongest in East Asia towards the close of nineteenth century?
(a) China
(b) Japan
(c) Korea
(d) Mongolia
Answer:
(b) Japan

Question 4.
Who said “imperialism is the highest stage of capitalism”?
(a) Lenin
(b) Marx
(c) Sun Yat-sen
(d) Mao Tsetung
Answer:
(a) Lenin

Question 5.
What is the Battle of Marne remembered for?
(a) air warfare
(b) trench warfare
(c) submarine warfare
(d) ship warfare
Answer:
(b) trench warfare

Question 6.
Which country after the World War I took to a policy of isolation?
(a) Britain
(b) France
(c) Germany
(d) USA
Answer:
(a) Britain

Question 7.
To which country did the first Secretary General of League of Nations belongs?
(a) Britain
(b) France
(c) Dutch
(d) USA
Answer:
(a) Britain

Question 8.
Which country was expelled from the League of Nations for attacking Finland?
(a) Germany
(b) Russia
(c) Italy
(d) France
Answer:
(b) Russia

II. Fill in the blanks

1. Japan forced a war on China in the year ……………….
2. The new state of Albania was created according to the Treaty of ………………. signed in May 1913.
3. Japan entered into an alliance with England in the year ……………….
4. In the Balkans ………………. had mixed population.
5. In the battle of Tannenberg ………………. suffered heavy losses.
6. ………………. as Prime Minister represented France in Paris Peace Conference.
7. ………………. became Prime Minister leading a new coalition of liberals and moderate Socialists before Lenin established the Bolshevik government.
8. Locarno Treaty was signed in the year ………………..

Answers:

1. 1894
2. London
3. 1902
4. Macedonia
5. Russia
6. Clemenceau
7. Kerensky
8. 1925

III. Choose the correct statement

Question 1.
(i) Italy remained a neutral country when the World War broke out.
(ii) Italy was much disappointed over the peace settlement at Versailles.
(iii) The Treaty of Sevres was signed with Italy.
(iv) Italy was denied even small places such as Trieste, Istria and the south Tyrol.
(a) (i) and (ii) are correct
(b) (iii) is correct
(c) (iv) is correct
(d) (i), (iii) and (iv) are correct
Answer:
(a) (i) and (ii) are correct

Question 2.
(i) The Turkish Empire contained many non-Turkish people in the Balkans.
(ii) Turkey fought on the side of the central powers
(iii) Britain attacked Turkey and captured Constantinople
(iv) Turkey’s attempt to attack Suez Canal but were repulsed.
(a) (i) and (ii) are correct
(b) (i) and (Hi) are correct
(c) (iv) is correct
(d) (i), (ii) and (iv) are correct
Answer:
(d) (i), (ii) and (iv) are correct

Question 3.
Assertion (A): Germany and the United States were producing cheaper manufactured goods and capturing England’s markets.
Reason (R): Both the countries produced required raw material for their industries.
(a) Both A and R are correct
(b) A is right but R is not the correct reason
(c) Both A and R are wrong
(d) R is right but it has no relevance to A.
Answer:
(b) A is right but R is not the correct reason

Question 4.
Assertion (A): The first European attempts to carve out colonies in Africa resulted in bloody battles.
Reason (R): There was stiff resistance from the native population.
(a) Both A and R are correct
(b) A is right but R is not the correct reason
(c) Both A and R are wrong
(d) R is right but it has no relevance to A.
Answer:
(a) Both A and R are correct

IV. Match the following

Answers:
A. (iii)
B. (iv)
C. (ii)
D. (v)
E. (i)

V. Answer briefly

Question 1.
How do you assess the importance of Sino-Japanese War?
Answer:
Sino-Japanese war took place in the years 1894 – 1895. China was defeated in the war. Japan annexed the Liaotung peninsula with Port Arthur inspite of warning given by three great powers, Russia, Germany and France. By this Japan had proved that it was the strongest nation of the East – Asia.

Question 2.
Name the countries in the Triple Entente.
Answer:
Britain, France and Russia.

Question 3.
What were the three militant forms of nationalism in Europe?
Answer:
The three militant forms of nationalism were, England’s Jingoism, France’s Chauvinism and Germany’s Kultur.

Question 4.
What do you know of trench warfare?
Answer:
Trench warfare is a type of land warfare using occupied fighting lines consisting largely of military trenches, in which troops are well-protected from the enemy’s small arms fire and are substantially sheltered from artillery. It is a warfare in which opposing armed forces attack, counterattack, and defend from relatively permanent systems of trenches dug in the ground.

Question 5.
What was the role of Mustafa Kemal Pasha?
Answer:
When Britian attacked Turkey directly and tried to capture Constantinople, Turks put up a brave fight and Mustafa Kemal Pasha played a great role to win freedom for the country. He put an end to the sultanate and caliphate. He modernized it and changed it out for recognition.

Question 6.
Highlight the global influence of Russian Revolution?
Answer:
The Russian Revolution fired people’s imagination across the world. In many countries, communist parties were formed. The Russian communist government encouraged the colonies to fight for their freedom and gave all support to them. Debates over key issues, land reforms, social welfare, workers’ rights, and gender equality taking place in a global context.

Question 7.
List out any two causes for the failure of the League of Nations.
Answer:
League did not had the military power of its own , it could not enforce its decisions. Even though, it had world wide membership it become very much the center of European diplomacy.

VI. Answer all the questions given under each caption

Question 1.
Imperialism
(a) What do you know of monopoly capitalism?
(b) How did Japan emerge as an imperial power?
(c) Why did the industrial countries need colonies in the nineteenth century?
(d) What were the contrasts capitalism produced?
Answer:
(a) Capitalism based on the principle of free -trade without any control or regulation by the state is called monopoly Capitalism.
(b) Japan emerged as an imperial power by annexing the Liaotung peninsula with Port Arthur inspite of warning given by Russia, Germany and France.
(c) Because colonies acted as a market for surplus goods and vast supplies of raw materials.
(d) Capitalism produced extreme poverty and extreme wealth. Slum and skyscraper. Empire state and dependent exploited colony.

Question 2.
German Emperor

(a) What was the nature of Emperor Kaiser Wilhelm II of Germany?
Answer:
Emperor Kaiser Wilhelm II of Germany was ruthlessly assertive and aggressive. He proclaimed that Germany would be the leader of the world.

(b) What was the violent form of Germany called?
Answer:
It was called Germany’s Kultur.

(c) Why did Kaiser Wilhelm intervene in the Morocco affair?
Answer:
The British agreement with France over the latter’s interest in Morocco was consented by Germany. So Kaiser Wilhelm II of Germany intentionally recognised the independence of the Sultan and demanded an international conference to decide on the future of Morocco.

(d) What happened to Germany’s colonies in Africa?
Answer:
The German colonies in western and eastern Africa were attacked by the Allies. As these colonies were quite far off from Germany they could not receive any immediate help, and therefore had to surrender to the Allies.

Question 3.
Balkan Wars
(a) Why was Balkan League formed?
(b) What was the outcome of the first Balkan War?
(c) Who were defeated in this war?
(d) What was the name of the Treaty signed at the end of this second Balkan War?
Answer:
(a) To control Greece, Serbia, Bulgaria and Montenegro in succeeding Balkans from Turks, in March 1912 the Balkan League was formed.
(b) The Balkan League defeated the Turkish forces in the 1st Balkan war.
(c) Turkey and Bulgaria were defeated in this war.
(d) Treaty of Bucharest in August 1913.

VII. Answer the following in detail

Question 1.
Discuss the main causes of the First World War.
Answer:
The causes of the First World War are given below:

1. Formation of European alliances and counter alliances
2. Emergence of violent forms of nationalism in countries like England, France and Germany
3. Aggressive attitude of the German Emperor Kaiser Wilhelm II
4. Hostility of France towards Germany
5. Opportunity for imperial power politics in the Balkans
6. The Balkans wars
7. Immediate cause which included the assassination of Archduke Franz Ferdinand, nephew and heir to Franz Joseph, Emperor of Austria-Hungary, by Princip, a Bosnian Serb, on 28 June 1914.

Question 2.
Highlight the provisions of the Treaty of Versailles relating to Germany.
Answer:

1. All the central powers were directed to pay war indemnity especially Germany was to pay heavy amount for the losses suffered.
2. Germany had to pay 6,600 million pounds as per the Reparation Commission, but can be paid in installments.
3. The Germans should not have submarines and airforce, but can have a small navy and an army of one lakh men.
4. Austria and Germany separated and Austria was given independence.
5. All German colonies came under the mandated territories of League of nations.
6. Germany had to give up all her overseas possessions, rights and titles to the allies.
7. Germany surrendered Alsace-Lorraine to France.
8. She signed the Treaty of Brest-Litovsk with Russia and the treaty of Bucharest with Bulgaria.
9. Rhineland was to be occupied by the allies. East of Rhineland area was to be demilitarised.
10. Poland was recreated with a corridor to Baltic containing the port of Danzig of Germany.

Question 3.
Explain the course of the Russian Revolution under the leadership of Lenin.
Answer:

1. Lenin was in Switzerland when the revolution broke out in Russia. He wanted to continued revolution.
2. His slogan of “All power to the Soviets” soon won over the workers’ leaders. Devastated by war time shortages, the people were attracted by the slogan of ‘Bread, Peace and Land’.
3. In October Lenin persuaded the Bolshevik Central Committee to decide on immediate revolution. Trotsky prepared a detailed plan
4. On 7 November the key government buildings, including the Winter Palace, the Prime Minister’s headquarters, were seized by armed factory workers and revolutionary troops
5. On 8 November 1917a new Communist government was in office in Russia. Its head this time was Lenin. The Bolshevik Party was renamed the Russian Communist Party.

Question 4.
Estimate the work done by the League of Nations, pointing out the reasons for its failure?
Answer:

1. League of nations was formed in 1920 with the twin objective of avoiding war and to maintain peace in the world.
2. The main work done by the League was to solve the dispute arose between Sweden and Finland over the sovereignity of Aaland Island. It ruled that the island should go to Finland.
3. League solved the frontier dispute between Poland and Germany in upper Silesia.
4. When dispute arose between Greece and Bulgaria in 1925, Greece invaded Bulgaria and the League ordered a ceasefire.
5. League had been successful in signing the Locarno Treaty in 1925 by which Germany,France, Belgium, Great Britain and Italy mutually guaranteed peace in Western Europe.
6. The main reason for the failure of the League was Italy, Japan and Germany headed by dictators refused to be bound by the orders of the League and started violation and League rules.
7. When League condemned the violation, they withdrew their membership.
8. League did not had a military power of its own.
9. Though it had a world-wide membership, it became the center of European diplomacy.
10. The League remained a passive witness to events, issues and incidents of violations therefore finally dissolved in 1946.

VIII. Activity

Question 1.
Students can be taught to mark the places of battles and the capital cities of the countries that were engaged in the War.
Answer:
(a) Battles of I World war:
(i) Battle of Tannenberg
(ii) Battle of Marne
(iii) Battle of Gallipoli
(iv) Battle of Jutland
(v) Battle of Verdun
(vi) Battle of Passchendaele
(vii) Battle of Caporetto
(viii) Battle of Cambrai
(ix) Battle of the Somme.

(b) Capital cities of countries engaged in the IWW.
Central powers & Capital:
(i) Germany – Berlin
(ii) Austria – Vienna
(iii) Hungary – Budapest
(iv) Italy – Rome
(v) Ottoman Empire – Istanbul, Bursa, Edirne, Sogut
(vi) Bulgaria – Sofia
(vii) Tu rkey – An ka ra
Allies- Capital:
(i) Great Britain – London
(ii) France – Paris
(iii) Russia – Moscow
(iv) Italy – Rome
(v) United States – Washington D. C

Question 2.
An assignment or a project work on the role of Indian soldiers in different battle fields across the globe and the casualties they suffered during the War be attempted by the students.
Answer:
During the War, the Indian Army contributed a large number of divisions and independent brigades to the European, Mediterranean and the Middle East. The Indian Army fought against the German Empire in German East Africa and on the Western Front. Indian divisions were also sent to Egypt, Gallipoli and nearly 700,000 served in Mesopotamia against the Ottoman Empire. While some divisions were sent overseas others had to remain in India guarding the North West Frontier and on internal security and training duties.

In addition to the permanent divisions, the Indian Army also formed a number of independent brigades. As part of the Southern Army the Aden Brigade was stationed in the Aden Protectorate on the strategically important naval route from Europe to India, where there was limited fighting.

The Bannu Brigade, the Derajat Brigade and the Kohat Brigade were all part of the Northern Army and they were deployed along the North West Frontier. The South Persia Brigade was formed in 1915 at the start of the Persian Campaign to protect the Anglo- Persian oil installations in south Persia and the Persian Gulf.

On the outbreak of war, the Indian Army had 150,000 trained men and the Indian Government offered the services of two cavalry and two infantry divisions for service overseas. The force known as Indian Expeditionary Force A was attached to the British Expeditionary Force and the four divisions were formed into two army corps: an infantry Indian Corps and the Indian Cavalry Corps.

Indian Expeditionary Force B consisted of the 27th (Bangalore) Brigade from the 9th (Secunderabad) Division and an Imperial Service Infantry Brigade, a pioneer battalion, a mountain artillery battery and engineers were sent to Tanganyika with the task of invading German East Africa. Force C was formed from the Indian Army’s 29th Punjabis, together with half battalions from the Princely states of Jind, Bharatpur, Kapurthala and Rampur. The largest Indian Army force to serve abroad was the Indian Expeditionary Force D in Mesopotamia, under the command of Lieutenant-General Sir John Nixon.

Over one million Indian troops served overseas, of whom 62,000 died and another 67,000 were wounded. In total at least 74,187 Indian soldiers died during the War. Field-Marshal Sir Claude Auchinleck, Commander-in-Chief of the Indian Army from 1942, commented that the British “couldn’t have come through both wars [World War I and II] if they hadn’t had the Indian Army.”

IX. Map Work

Mark the following countries on the world map.

1. Great Britain
2. Germany
3. France
4. Italy
5. Morocco
6. Turkey
7. Serbia
8. Bosnia
9. Greece
10. Austria-Hungary
11. Bulgaria
12. Rumania

Timeline:

Samacheer Kalvi 10th Social Science Outbreak of World War I and Its Aftermath Additional Important Questions and Answers

I. Choose the correct answer

Question 1.
The Treaty of serves was signed with:
(a) Austria
(b) Hungary
(c) Turkey
(d) Bulgaria
Answer:
(c) Turkey

Question 2.
The policy of imperialism followed by the European countries from 1870-1945 was known as ……
(a) New imperialism
(b) Military imperialism
(c) Neo-imperialism
Answer:
(a) New imperialism

Question 3.
President Woodrow Wilson put forward ………….. points in the League of nations.
(a) 12
(b) 11
(c) 10
(d) 14
Answer:
(d) 14

Question 4.
With a modem army and navy, ….. had emerged as an advanced industrialised
power.
(a) Germany
(b) Japan
(c) Italy
Answer:
(b) Japan

Question 5.
Germany surrendered in:
(a) 1917
(b) 1918
(c) 1919
(d) 1916
Answer:
(b) 1918

Question 6.
The ‘Sphere of influence’ was adopted by the European countries in ……
(a) Japan
(b) China
(c) India
Answer:
(b) China

Question 7
………….. is the name of the parliament of Russia.
(a) Tsar
(b) Trotsky
(c) Duma
(d) Rasputin.
Answer:
(c) Duma

Question 8.
The word “Imperialism” is derived from ……
(a) Greek
(b) German
(c) Latin
Answer:
(c) Latin

Question 9.
Nicholas II abdicated from his throne on ……………. 1917.
(a) March 12
(b) March 15
(c) November 18
(d) October 14
Answer:
(b) March 15

Question 10.
The development of ……. speeded the movements of goods between colonies and other countries.
(a) Roadways
(b) Waterways
(c) Railways
Answer:
(c) Railways

II. Fill in the blanks

1. The biggest outcome of the first world war was the …………….
2. The Trust is an industrial organisation in the …………….
3. The Imperialist Prime Minister of South Africa was called …………….
4. Cartel means ……………. of enterprises in the same field of business.
5. The treaty of ……………. was signed after the Russo-Japanese war and Japan got back port Arthur.
6. The violent form of nationalism in Germany was called as …………….
7. France and Germany were old …………….
8. The enemity between and led to the outbreak of war in 1914.
9. The new state of Albania was created according to the treaty of ……………. signed in 1913.
10. Russia suffered heavy loses in the battle of …………….
11. Trench warfare was the style followed in the battle of …………….
12. Russia signed the treaty of ……………. with Germany.
13. Italy formally joined the allies in …………….
14. Battle of Jutland is a ……………. battle.
15. ……………. is the name of the American ship sunk by Germany.
16. ……………. was one of the principle in the fourteen points of Paris peace conference.
17. The war conditions led to the ……………. movement in India.
18. ……………. modernised Turkey and changed it out of all recognition.
19. £ is the symbol of …………….
20. The Bolshevik party was renamed as ……………. party.

Answers:

1. Russian Revolution
2. USA
3. Cecil Rhodes
4. Association
5. Portsmouth
6. Kultur
7. Rivals
8. Austria and Serbia
9. London
10. Tannenburg
11. Marne
12. Brest Litovsk
13. 1916
14. Naval
15. Lusitania
16. Self determination
17. Home Rule
18. Pound sterling
19. Kemal Pasha
20. Russian communist

III. Choose the correct statements.

Question 1.
(i) The Industrial achievements of Germany in the later half of the 19th Century gave her a dominating position in Europe.
(ii) When Germany came to the scene of exploitation, it became weak in its military power.
(iii) When there was nowhere else to expand, imperialist countries grab other’s possession.
(iv) Russia, Britain and France joined in the scramble for colonies.
(a) (i) and (ii) are correct
(b) (i) and (iii) are wrong
(c) (ii) and (iv) are wrong
(d) (i), (ii) and (iv) are correct
Answer:
(c) (ii) and (iv) are wrong

Question 2.
(i) The Central powers consisted of Germany, Austria-Hungary, Turkey and Bulgaria.
(ii) Italy strongly supported Germany.
(iii) In April 1916, Britain, France and Italy signed the Treaty of London.
(iv) Italy agreed to enter the war against the central powers in-return of this territory after the war.
(a) (i), (ii) and (iii) are correct
(b) (ii), (iii) and (iv) are correct
(c) (i) and (iii) are correct
(d) (i) and (iv) are correct
Answer:
(d) (i) and (iv) are correct

Question 3.
(i) Trenches are ditches dug by troops enabled soldiers.
(ii) It was done to protect themselves from enemy fire.
(iii) The battle of Jutland is a memorable one for Trench war fare.
(iv) Trench system used in the first world war consisted of six to seven trench lines running parallel to each other.
(a) (ii) and (iv) are correct
(b) (i) and (ii) are correct
(c) (i) and (iv) are correct
(d) (iii) and (iv) are correct
Answer:
(b) (i) and (ii) are correct

Question 4.
(i) The main provision of the Versailles treaty was that all central powers were directed to pay war indemnity.
(ii) All the German colonies became mandated territories under the League of nations.
(iii) The Saar coal mine was given to Bulgaria.
(iv) Northern Schleswig was given to France.
(a) (iii) and (iv) are correct
(b) (i) and (ii) are correct
(c) (i), (ii), (iv) are correct
(d) (ii) and (iv) are correct
Answer:
(b) (i) and (ii) are correct

Question 5.
(i) Triple Alliance was signed in 1882 between Germany, Austria-Hungary and Italy.
(ii) Entente cordiale was signed in 1906 between Britain and Russia.
(iii) Triple Entente was signed between Britain, France and Russia.
(iv) The Britain violation of Belgian neutrality forced German to enter the war.
(a) (i), (ii), (iv) are correct
(b) (iii) and (iv) are correct
(c) (i) and (iii) are correct
(d) (ii) and (iv) are correct
Answer:
(c) (i) and (iii) are correct

IV. Assertion and Reason

Question 1.
Assertion (A): Inspite of warning of the three great powers, Russia, Germany and France, Japan annexed the Liaotung Peninsula with Port Arthur.
Reason (R): Japan proved that it was the strongest nation of the East Asia.
(a) Both A and R are correct
(b) A is right but R is not the correct reason
(c) Both A and R are wrong
(d) R is right but it has no relevant to A
Answer:
(a) Both A and R are correct

Question 2.
Assertion (A): Two peace conferences were held at the Hague in Holland in 1899 and in 1907.
Reason (R): Lenin of Russia wanted to bring Universal peace and suggested these conferences.
(a) Both A and R are correct
(b) A is right but R is not the correct reason
(c) Both A and R are wrong
(d) R is right but it has no relevant to A
Answer:
(b) A is right but R is not the correct reason

Question 3.
Assertion (A): Italy formally joined with the allies fighting with Austria, initially sustained, but finally collapsed.
Reason (R): Germans came to Austria’s help.
(a) Both A and R are correct
(b) A is right but R is not the correct reason
(c) Both A and R are wrong
(d) R is right but it has no relevant to A
Answer:
(a) Both A and R are correct

Question 4.
Assertion (A): In Germany and Austria, women and children suffered from hunger and privation.
Reason (R): Aeroplanes were used for bombing targeted Civilian population.
(a) Both A and R are correct
(b) A is right but R is not the correct reason
(c) Both A and R are wrong
(d) R is right but it has no relevant to A
Answer:
(b) A is right but R is not the correct reason

Question 5.
Assertion (A): Marxists in Russia had the fortune of getting Lenin as their leader.
Reason (R): Tsar Nicholas li was under the strong influence of his wife Alexandra.
(a) Both A and R are correct
(b) A is right but R is not the correct reason
(c) Both A and R are wrong
(d) R is right but it has no relevant to A
Answer:
(b) A is right but R is not the correct reason

Question 6.
Assertion (A): The League of nations could apply the principle of collective security.
Reason (R): It was supported by Italy, Japan and Germany.
(a) Both A and R are correct
(b) A is right but R is not the correct reason
(c) Both A and R are wrong
(d) R is right but it has no relevant to A
Answer:
(c) Both A and R are wrong

V. Match the following

Question 1.
Match the Column I with Column II.

Answer:
A. (iv)
B. (v)
C. (i)
D. (ii)
E. (iii)

Question 2.
Match the column I with column II.

Answer:
A. (iv)
B. (i)
C. (v)
D. (ii)
E. (iii)

VI. Answer the following questions briefly

Question 1.
What was the aim of the capitalist countries?
Answer:
The aim of the capitalistic countries was to produce more and more. The surplus wealth that was produced was used to build more factories, railways, steamship and other such undertakings.

Question 2.
What is colonialism?
Answer:
(i) Colonialism refers to the policy of acquiring and maintaining colonies especially for exploitation.
(ii) It also means that it is a relationship between an indigenous majority and a minority foreign invaders.

Question 3.
What was the immediate cause of the first world war?
Answer:
The nephew and heir to Franz Joseph, Emperor of Austria-Hungary. The Arch duke Franz Ferdinand was killed by Princip a Serbian of Bosnia. This was the immediate cause as Austria got help from Germany and Serbia got help from Russia. Thus the war began in 1914.

Question 4.
How did China became an International colony?
Answer:

1. The Boers were defeated by foreign powers.
2. When they reached Peking, the capital of China, Empress Dowager fled from the capital,
3. The U.S.A. and England formulated the Open Door Policy or Me Too Policy.
4. The Chinese territories were partitioned among the foreign powers for trade rights. Thus China became an international colony.

Question 5.
What do you understand by Paris peace conference?
Answer:
The Paris peace conference held in January 1919 two months after the signing of the armistice.
Woodrow Wilson of America and Lloyd George of Britain were the important personalities. On 28 June 1919, the peace treaty was signed in The Hall of Mirrors at Versailles.

Question 6.
What was the immediate cause of the First World War?
Answer:

1. In 1908, Austria annexed Bosnia and Herzegovina against the Congress of Berlin.
2. Austrian Prince Francis Ferdinand and his wife were assassinated at Sarajevo on June 28, 1914.
3. Austria sent an ultimatum to Serbia, but Serbia ignored it.
4. So Austria declared war on Serbia on 28th July 1914.

Question 7.
Write the slogans raised by Lenin that attracted soviet people.
Answer:
“All power to the soviets” and “Bread, Peace and Land” were the slogans raised by Lenin that attracted the soviet people who were devastated by war time shortages.

Question 8.
Write any two terms of the Treaty of Versailles.
Answer:

1. A huge war indemnity was imposed on Germany. Her army was reduced.
2. The overseas possessions of Germany were divided among the victorious nations.

Question 9.
Write any two objectives of the League.
Answer:
The two main objective of the League of Nations was (i) To avoid war and to maintain peace in the world, (ii) To promote international co-operation in economic and social affairs.

Question 10.
What do you mean by Russian Revolution?
Answer:
The fall of monarch in February 1917 and the events of October are known as the Russian Revolution.

Question 11.
What is Duma? Why did the Tsar dismiss the first Duma within 75 days of its election?
Answer:
An elective legislative assembly established in 1905 by Nicholas II in Russia is known as Duma. Because the Tsar did not want anyone to question his authority, so he dismissed the first Duma within 75 days.

VII. Answer all the questions given under each caption

1. Characteristics of Imperialism

(a) What led to concept of Imperialism?
Answer:
Capitalism inevitably led to the concept of Imperialism.

(b) What was Lenin idea on Imperialism?
Answer:
According to Lenin, imperialism is the highest stage of Capitalism.

(c) What were the purposes for which the colonies were made use of?
Answer:
The colonies served as a market for goods and also vast suppliers of raw materials like cotton, Rubber etc.

(d) What was the logic behind Imperialism apart from colonisation?
Answer:
The logic behind Imperialism apart from colonisation was, total militarisation and total war.

2. The ambition of Germany

(а) Who was the ruler of Germany during the First World War?
Answer:
Kaiser Wilhelm II.

(b) What did he believe?
Answer:
He believed that Germany alone was competent to rule the whole world.

(c) What could not be tolerated by him?
Answer:
He could not tolerate the British saying that the Sun never sets in the British Empire.

3. Naval Battles

(a) Name the Naval battle that took place in 1916?
Answer:
In 1916, the Naval battle had taken place in the North sea called as Battle of Jutland.

(b) Which country started the Sub-marine warfare thereafter?
Answer:
Germany started their Submarine warfare thereafter.

(c) Name the ship that bombarded Madras?
Answer:
The ship that bombarded Madras was the famous Emden ship.

(d) Name the American ship torpedoed by a German Submarine.
Answer:
Lusitania, an American ship was torpedoed by a German Submarine.

4. Course of the First World War

(a) Give the duration of the First World War.
Answer:
From July 28, 1914 to November 11, 1918.

(b) Who were called the Central Powers?
Answer:
The countries which were on the side of Germany were called the Central Powers.

(c) Who were called the Allies?
Answer:
The countries which were on the side of Britain were called as the Allies.

(d) What and all were used in war?
Answer:
Artillery, Tanks and submarines were used in the war.

5. Lenin

(a) Where was he born?
Answer:
Lenin was bom in 1870 near the middle Volga to educated parents.

(b) What was his belief?
Answer:
Lenin believed that the wav for freedom was through mass action.

(c) When and why was he arrested?
Answer:
He was arrested in 1895 and kept in Serbia for encouraging the ideas of Marxism to the factory workers in St. Petersburg.

(d) How did he form the Bolshevik party?
Answer:
Lenin gained the support of small majority called Bolshmstvo known as Bolsheviks which later became the Bolshevik party.

6. Results of the war

(a) How were the terms of the treaties drafted?
Answer:
Based upon the fourteen points of the American President Woodrow Wilson.

(b) What did Germany surrendered to France?
Answer:
Germany surrendered Alsace and Lorraine to Europe.

(c) Where was monarchy abolished?
Answer:
In Germany, Russia, Austria and Turkey.

(d) Name the new Republics.
Answer:
Czechoslovakia and Poland.

VIII. Answer the following in detail

Question 1.
Write a note on the structure and composition of its League of Nations.
Answer:

1. The covenant of the League of Nations was formed at the Paris peace conference after the first world war.
2. President of USA -Woodrow Wilson largely supported for this task to be accomplished.
3. The structure of the League consist of the Assembly, the council, the Secretariat, the permanent court of Justice and the International Labour organization.
4. Each member country was represented in the Assembly.
5. Each member country’ and had one vote and also possessed the right of veto.
6. Britain, France, Italy, Japan and United States were originally declared permanent members of the council.
7. The council was the executive of the League.
8. The staff of the secretariat was appointed by the Secretary General in consultation with the council.
9. The court of Justice consisted of fifteen Judges.
10. The International Labour organization comprised a Secretariat. The general conference will include four representatives from each country.
11. The first secretary general of League of Nations was Sir Eric Drummond from Britain.

Question 2.
What were the results of the first world war?
Answer:
The Paris Peace Conference:

1. The first world war came to an end by the Paris Peace Conference of 1919.
2. The city of Danzig was internationlized.
3. Lithuvania, Latvia and Estonia were granted independence.

The formation of the League of Nations:

1. The first world war brought untold miseries to people.
2. All the nations wanted a permanent body to maintain peace in the world. So the League of Nations was formed in 1920.
3. The victorious nations forced the defeated nations with unfair treaties. It sowed the seed for the second world war.

Question 3.
What was the impact of First world war on India?
Answer:

1. The first world war had multiple effects on the Indian economy, society and politics.
2. Indians had taken an active part in the war on the side of Britain, believing that they would reward Independence after the war.
3. But also, disappointment was rewarded to the Indians.
4. Indian soldiers asked to serve in Europe, Africa and West Asia.
5. India contributed £230 million in cash and over £125 million in loan towards war expenses.
6. India also sent war materials to the value of £ 250 million .
7. There were economic distress all over the country.
8. Towards the end of the war, India suffered under the world wide epidemic of influenza.
9. Home Rule Movement arose in India due to the war conditions.
10. The congress split of extremists and moderates reunited.
11. The Ottoman Empire under the Turkish Sultan was defeated in World war I and the territories shared between Britain and France.
12. This led to the formation of Khilafat Movement in India.

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Tamil Nadu Samacheer Kalvi 10th Science Model Question Paper 3 English Medium

General Instructions:

1. The question paper comprises of four parts
2. You are to attempt all the questions in each part. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II, III and IV are to be attempted separately.
4. Question numbers 1 to 12 in Part I are Multiple Choice Questions of one mark each.
   These are to be answered by writing the correct answer along with the corresponding option code.
5. Question numbers 13 to 22 in Part II are of two marks each. Any one question should be answered compulsorily.
6. Question numbers 23 to 32 in Part III are of four marks each. Any one question should be answered compulsorily.
7. Question numbers 33 to 35 in Part IV are of seven marks each. Draw diagrams wherever necessary.

Time: 3 Hours
Maximum Marks: 75

Part – I

(i) Answer all the questions. [12 × 1 = 12]
(ii) Choose the most suitable answer and write the code with the corresponding answer.

Question 1.
If the Earth shrinks to 50% of its real radius its mass remaining the same, the weight of a body on the Earth will ______.
(a) decrease by 50%
(b) increase by 50%
(c) decrease by 25%
(d) increase by 300%
Answer:
(c) decrease by 25%

Question 2.
The refractive index of four substances A, B, C and D are 1.31, 1.43, 1.33, 2.4 respectively. The speed of light is maximum in ______.
(a) A
(b)B
(c) C
(d) D
Answer:
(a) A

Question 3.
When a sound wave travels through air, the air particles ______.
(a) vibrate along the direction of the wave motion
(b) vibrate but not in any fixed direction
(c) vibrate perpendicular to the direction of the wave motion (id) do not vibrate
Answer:
(a) vibrate along the direction of the wave motion

Question 4.
Which of the following represents 1 amu?
(a) mass of a C-12 atom
(b) mass of hydrogen atom
(c) 1/12th of the mass of a C-12 atom
(d) mass of 0-16 atom
Answer:
(c) 1/12th of the mass of a C-12 atom

Question 5.
______ is a relative periodic property.
(a) atomic radii
(b) Ionic radii
(c) Electron affinity
(d) Electron negativity
Answer:
(b) Ionic radii

Question 6.
Which of the following is the universal solvent?
(a) Acetone
(b) Benzene
(c) Water
(d) Alcohol
Answer:
(c) Water

Question 7.
Root hairs are ______.
(a) cortial cell
(b) projection of epidermal cell
(c) unicellular
(d) both (b) and (c)
Answer:
(d) both (b) and (c)

Question 8.
Polyphagia is a condition seen in ______.
(a) Obesity
(b) Diabetes mellitus
(c) AIDS
(d) Cancer
Answer:
(b) Diabetes mellitus

Question 9.
9 : 3: 3 : 1 ratio is due to ______.
(a) Segregation
(b) Independent Assortment
(c) Crossing over
(d) Recessive factors
Answer:
(b) Independent Assortment

Question 10.
rDNA is a ______.
(a) vector DNA
(b) circular DNA
(c) recombinant of vector DNA
(d) satellite DNA
Answer:
(c) recombinant of vector DNA

Question 11.
Biogenesis was speculated by ______.
(a) Louis pasteur
(b) Darwin
(c) Lamark
(d) Oparin
Answer:
(a) Louis pasteur

Question 12.
Green house effect refers to ______.
(a) cooling of earth
(b) warming of earth
(c) cultivation of plants
(d) trapping of UV rays
Answer:
(b) warming of earth

Part – II

Answer any seven questions. (Q.No: 22 is compulsory) [7 × 2 = 14]

Question 13.
State Newton’s laws of motion.
Answer:
Every body continues to be in its state of rest or the state of uniform motion along a straight line unless it is acted upon by some external force.

Question 14.
Why are traffic signals red in colour?
Answer:

• Red light has the highest wavelength.
• It is scattered by atmospheric particles.
• So red Tight in able to travel the longest distance through fog, rain etc.

Question 15.
What is co-efficient of apparent expansion?
Answer:
Coefficient of apparent expansion is defined as the ratio of the apparent rise in the volume of the liquid per degree rise in temperature to its unit volume. The SI unit of coefficient of apparent expansion is K^-1.

Question 16.
Difference between atoms and molecules.
Answer:
Atom:

• An atom is the smallest particle of an element.
• Atom does not exist in free state except in a noble gas.
• Atoms does not have a chemical bond.

Molecules:

• A molecule is the smallest particle of an element or compound.
• Molecule exists in free state.
• Atoms in a molecule are held by chemical bonds.

Question 17.
Define Hydrated salt.
Answer:
The number of water molecules found in the crystalline substance or salts is called water of crystallization. Such salts are called hydrated salts.

Question 18.
What are synthetic auxins?
Answer:
Artificially synthesized auxins, that have the properties like auxins are called as synthetic auxins. Eg. 2,4-D (2, 4-Dichlorophenoxy Acetic acid)

Question 19.
Mention the Medicinal value of Leech.
Answer:

• They can be used to treat cardiovascular diseases.
• Biochemical substances derived from leech saliva are used for preparation of pharmaceutical drugs that can treat hypertension.

Question 20.
Define triple fusion.
Answer:
During double fertilization, one sperm fuses with the egg and forms a diploid zygote. The other sperm fuse with the secondary nucleus to form the primary endosperm, which is triploid in nature. This called triple fusion.

Question 21.
What are Analogous organs?
Answer:
The analogous organs look similar and perform similar functions but they have different origin and developmental pattern. E.g: The function of the wings of a bat, the wings of a bird and wings of an insect are similar, but their basic structures are different.

Question 22.
A current of 2A flows through a 12 V bulb then find resistance.
Answer:
Given: V = 12V;    I = 2A
V = IR
R = \(\frac{V}{I}=\frac{12}{2}\)
R = 6 Ω

Part – III

Answer any seven questions (Q.No: 32 is compulsory) [7 × 4 = 28]

Question 23.
Deduce the equation of a force using Newton’s second law of motion.
Answer:
“The force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force”.

Let, ‘m’ be the mass of a moving body, moving along a straight line with an initial speed ‘u’ After a time interval of ‘t’, the velocity of the body changes to ‘v’ due to the impact of an unbalanced external force F.
Initial momentum of the body P_i = mu
Final momentum of the body P_f = mv
Change in momentum Δp = P_f – P_i.
= mv – mu

By Newton’s second law of motion,
Force, F ∝ rate of change of momentum
F ∝ change in momentum / time
F ∝ \(\frac{m v-m u}{t}\)
F ∝ \(\frac{k m(v-u)}{t}\)
Here, k is the proportionality constant, k = 1 in all systems of units. Hence,
F = \(\frac{m(v-u)}{t}\)

Since, acceleration = change in velocity / time, a = (v – u)/t. Hence, we have
F = m x a
Force = mass x acceleration

• No external force is required to maintain the motion of a body moving with uniform velocity.
• When the net force acting on a body is not equal to zero, then definitely the velocity of the body will change.
• Thus, change in momentum takes place in the direction of the force. The change may take place either in magnitude or in direction or in both.

Question 24.
Differentiate the eye defects: Myopia and Hypermetropia.
Answer:
Myopia:

• Myopia, also known as short sightedness, occurs due to the lengthening of eye ball.
• With this defect, nearby objects can be seen clearly but distant objects cannot be seen clearly.
• The focal length of eye lens is reduced or the distance between eye lens and retina increases.
• The far point will not be infinity for such eyes and the far point has come closer.
• Due to this, the image of distant objects are formed before the retina.
• This defect can be corrected using a concave lens.

Hypermeteropia:

• Hypermeteropia, also known as long sightedness, occurs due to the shortening of eye ball.
• With this defect, distant objects can be seen clearly but nearby objects cannot be seen clearly.
• The focal length of eye lens is increased or the distance between eye lens and retina decreases.
• Hence, the near point will not be at 25 cm for such eyes and the near point has moved farther.
• Due to this, the image of nearby objects are formed behind the retina.
• This defect can be corrected using a convex lens.

Question 25.
(i) Define electric potential and potential difference.
Answer:
Electric Potential: The electric potential at a point is defined as the amount of work done in moving a unit positive charge from infinity to that point against the electric force.

Electric Potential Difference: The electric potential difference between two points is defined as the amount of work done in moving a unit positive charge from one point to another point against the electric force.

(ii) How does a fuse wire protect electrical appliances?
Answer:

1. The fuse wire is connected in series, in an electric circuit.
2. When a large current passes through the circuit, the fuse wire melts due to Joule’s heating effect and hence the circuit gets disconnected.
3. Therefore, the circuit and the electric appliances are saved from any damage.
4. The fuse wire is made up of a material whose melting point is relatively low.

Question 26.
Give the salient features of “Modern atomic theory”.
Answer:
The salient features of “Modem atomic theory” are,

• An atom is no longer indivisible.
• Atoms of the same element may have different atomic mass.
• Atoms of different elements may have same atomic masses.
• Atoms of one element can be transmuted into atoms of other elements. In other words, atom is no longer indestructible.
• Atoms may not always combine in a simple whole number ratio.
• Atom is the smallest particle that takes part in a chemical reaction.
• The mass of an atom can be converted into energy [E = mc²].

Question 27.
(i) How will you classify Hydrocarbons?
Answer:
Hydrocarbons are classified into three classes such as Alkanes, Alkenes and Alkynes.
(a) Alkenes:
These are hydrocarbons, which contain only single bonds. They are represented by the general formula C_nH_{2n + 2} (where n = 1,2, 3) Ex: Methane (CH₄)

(b) Alkenes:
The hydrocarbons, which contain one or more C = C bonds are called alkenes. These are unsaturated compounds. They are represented by the general formula C_nH_2n.
Ex: Ethylene (C₂H₄)

(c) Alkynes:
The hydrocarbons containing carbon to carbon triple bond are called alkynes. They have the general formula C_nH_{2n – 2} Ex: Acetylene (C₂H₂)

(ii) Write the characteristic of hydrocarbons.
Answer:

• Lower hydrocarbons are gases at room temperature E.g. methane, ethane are gases.
• Alkanes are least reactive when alkynes are most reactive due to presence triple bond.
• Alkanes are saturated whereas alkenes and alkynes are unsaturated.
• They are insoluble in water.

Question 28.
Which acts as a link between the nervous system and endocrine system?
Answer:
Hypothalamus, acts as a link between nervous system and endocrine system. It lies at the base of the thalamus. It controls involuntary functions like hunger, thirst, sleep, sweating, sexual desire, anger, fear, water balance, blood pressure etc. It acts as a thermo regulatory (temperature control) center of the body. It controls the secretion of hormones from anterior Pituitary gland.

Question 29.
(i) What are heart sounds? How are they produced?
(ii) What is Aneuploidy?
Answer:
(i) The rhythmic closure and opening of the valves causes heart sounds.
The first sound ‘LUBB’ is of longer duration and is produced by the closure of the tricuspid and bicuspid valves after the beginning of ventricular systole.
The second sound ‘DUPP’ is of a shorter duration and produced by the closure of semilunar valve at the end of ventricular systole.

(ii) Aneuploidy is the loss or gain of one or more chromosomes in a set. It is of three types. Monosomy (2n – 1), Trisomy (2n + 1)andNullisomy (2n – 2).

Question 30.
Discuss the importance of biotechnology in the field of medicine.
Answer:
Using genetic engineering techniques, medicinally important pharmaceutical products for the treatment of various diseases have been developed.

1. Insulin used in the treatment of diabetes.
2. Human growth hormone used for treating children with growth deficiencies.
3. Blood clotting factors are developed to treat haemophilia.
4. Development of vaccines against various diseases like Hepatitis B and rabies
5. Tissue plasminogen activator is used to dissolve blood clots and to prevent heart attack.

Question 31.
What are the phases of menstrual cycle? Indicate, the changes in the ovary and uterus.
Answer:
The four phases of the menstrual cycle are:

1. Menstrual or Destructive phase
2. Follicular or Proliferative phase
3. Ovulatory phase
4. Luteal or secretory phase

Events of menstrual cycle and changes in ovary and changes in uterus.

Question 32.
(i) Explain how the loss of heat (or transfer of heat) due to modes of transfer of heat is minimised in a thermos flask.
Answer:
Transfer of heat is thermos is minimised as under.
(1) By conduction:
As in conduction heat can transfer by contact of material medium. In thermos air is evacuated between the walls so heat transfer in stopped by conduction mode.

(2) By convection:
As convection mode also require material (fluid) medium and there is nothing between the walls of thermos so heat does not transfer by connection mode.

(3) By Radiation:
As Ag polish is coated opaque on inner and outer walls of thermos radiation obeys the laws of refraction and reflection so no refraction takes place through opaque wall. Reflection of outer radiation goes outside of innerwall goes inside. So the transfer of heat is minimised by polishing.

(ii) Briefly write any four characteristics of group in the periodic table.
Answer:

• The element present in a group have the same valency.
• The element present in a group have identical chemical properties.
• The physical properties of the elements in the group vary gradually.
• The atomic radii of the elements present in a group increases downwards

Part – IV

(1) Answer all the questions. [3 × 7 = 21]
(2) Each question carries seven marks.
(3) Draw diagram wherever necessary.

Question 33.
(a) (i) State Ohm’s law.
Answer:
According to Ohm’s law, at a constant temperature, the steady current ‘I’ flowing through a conductor is directly proportional to the potential difference ‘V’ between the two ends of the conductor.
I ∝ V.
∴V = IR

(ii) With the help of a circuit diagram derive the formula for the resultant resistance of three resistances connected in parallel.
Answer:
Resistors in Parallel:
A parallel circuit has two or more loops through which current can pass. If the circuit is disconnected in one of the loops, the current can still pass through the other loop(s). The wiring in a house consists of parallel circuits.

(i) Consider that three resistors R₁, R₂ and R₃ are connected across two common points A and B.
(ii) The potential difference across each resistance is the same and equal to the potential difference between A and B. This is measured using the voltmeter.
(iii) The current I arriving at A divides into three branches I₁, I₂ and I₃ passing through R₁, R₂ and R₃ respectively.
According to the Ohm’s law, we have,

The total current through the circuit is given by
I = I₁ + I₂ + I₃
Using equations (1), (2) and (3), we get

Let the effective resistance of the parallel combination of resistors be Rp. Then,
I = \(\frac{V}{R_{p}}\) …….(5)
Combining equations (4) and (5), we have

Thus,
(iv) When a number of resistors are connected in parallel, the sum of the reciprocals of the individual resistances is equal to the reciprocal of the effective or equivalent resistance.
(v) When ‘n’ resistors of equal resistances Rare connected in parallel, the equivalent resistance is \(\frac{R}{n}\)

Hence, R_p = \(\frac{R}{n}\)
(vi) The equivalent resistance in a parallel combination is less than the lowest of the individual resistances.

(OR)

(b) (i) A man is standing between two vertical walls 680 m apart. He claps his hands and hears two distinct echoes after 0.9 seconds and 1.1 second respectively. What is the speed of sound in the air?
Answer:
Given Data
d = 680 m
t₁ = 0.9 s
t₂ = 1.1 s
v = ?

(ii) An electric heater of resistance 5 Ω is connected to an electric source. If a current of 6 A flows through the heater, then find the amount of heat produced in 5 minutes.
Answer:
Given resistance R = 5 Ω, Current I = 6 A,
Time t = 5 minutes = 5 × 60 s = 300 s
Amount of heat produced, H = I²Rt
H = 6² × 5 × 300. Hence, H = 54000 J

Question 34.
(a) (i) Calculate the gram molecular mass of NH₃.
Answer:
Atomic mass of N = 14
H = 1
Gram molecular mass of NH₃ = (14 × 1) + (1 × 3)
= 14 + 3 = 17 g

(ii) Calculate the percent by mass of glucose in a solution made by dissolving 500 g of glucose in 50 g of water.
Answer:

(iii) Calculate the number of water molecule present in one drop of water which weights 0.18.
Answer:

Number of molecules = No. of moles x Avogadro number
= 0.01 × 6.023 × 10²³
= 0.06023 × 10²³
= 6.023 × 10²¹ molecules

(OR)

(b) (i) How does pH play an important role in everyday life?
Answer:

• The pH of blood is almost 7.4. Any increase or decrease in this value leads to diseases.
• Citrus fruits require slightly alkaline soil, while rice requires acidic soil and sugarcane requires neutral soil.
• If pH of rain water becomes less than 7, it becomes acid rain which is harmful in day-to-day life.
• pH changes cause tooth decay.
• During indigestion the stomach produces too much acid and this causes pain and irritation.

(ii) Classify the following compounds based on the pattern of carbon chain and give their structural formula: (i) Propane (ii) Benzene (iii) Cyclobutane (iv) Furan
Answer:
(i) Propane is open chain or a cyclic compound because it contains an open chain.
CH₃ – CH₃ – CH₃ [Propane]

(ii) Benzene is a carbocyclic compound because it contains carbon atoms cyclic ring of 6 atoms.

(iii) Cyclobutane is a carbocyclic compound.

(iv) Furan is a hetrocyclic compound because in the cyclic chain one atom is oxygen atom.

Question 35.
(a) (i) What is Scratch?
(ii) Differentiate between type 1 and type 2 diabetes mellitus
(iii) Why fossil fuels are to be conserved?
Answer:
(i) ‘Scratch’ is a software used to create animations, cartoons and games easily. Scratch, on the other hand, is a visual programming language.

(ii)
Type-1 Diabetes mellitus:

• People with type-1 diabetes do not produce Insulin in pancreas.
• Immune system destroys insulin producing beta cells in the pancreas.
• Cannot be controlled without taking insulin.
• Diagnosed in childhood
• Not associates with excess body weight

Type-2 Diabetes mellitus:

• People with type-2 diabetes do not respond to insulin.
• Type 2 diabetes are Insulin Resistant.
• Possible to treat initially without medication or treating with tablets.
• Diagonsed over 30 years old.
• Associated with excess body weight.

(iii) Formation of fossil fuels is a very slow process and takes very long period of time for renewal. Hence to be conserved.

[OR]

(b) (i) Write the dental formula of rabbit.
Answer:
(i) Dental formula is (I\(\frac{2}{1}\), C\(\frac{0}{0}\), PM\(\frac{3}{2}\), M\(\frac{3}{2}\)) in Rabbit, which is written as \(\frac{2033}{1023}\)
I – Incisors
PM – Premolar
C – Canines
M – Molars

(ii) With a neat labelled diagram explain the techniques involved in gene cloning.
Answer:
Gene cloning:

The carbon copy or more appropriately, a clone means to make a genetically exact copy of an organism.
In gene cloning, a gene or a piece of DNA fragment is inserted into a bacterial cell, where DNA will be multiplied (copied) as the cell divides.

Techniques involved in gene cloning:

• Isolation of desired DNA fragment by using restriction enzymes.
• Insertion of the DNA fragment into a suitable vector (plasmid) to make rDNA.
• Transfer of rDNA into bacterial host cell (Transformation).
• Selection and multiplication of recombinant host cell to get a clone.
• Expression of cloned gene in host cell.

Students can download Maths Chapter 6 Trigonometry Unit Exercise 6 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Unit Exercise 6

Question 1.
Prove that
(i) cot² A \(\left(\frac{\sec A-1}{1+\sin A}\right)\) + sec² A \(\left(\frac{\sin A-1}{1+\sec A}\right)\) = 0
(ii) \(\frac{\tan ^{2} \theta-1}{\tan ^{2} \theta+1}\) = 1 – 2 cos² θ
Answer:


Hence it is proved

= 1 – cos² θ
L.H.S = R.H.S
Hence it is proved.

Question 2.
Prove that
\(\left(\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}\right)^{2}=\left(\frac{1-\cos \theta}{1+\cos \theta}\right)\)
Answer:

LHS = RHS
Hence it is proved

Question 3.
If x sin² θ + y cos² θ = sin θ cos θ and x sin θ = y cos θ, then prove that x² + y² = 1.
Answer:
Given x sin² θ + y cos² θ = sin θ cos θ
x sin θ = y cos θ ……..(1)
x sin³ θ + y cos³ θ = sin θ cos θ
x sin θ (sin² θ) + y cos θ (cos² θ) = sin θ cos θ
x sin θ (sin² θ) + x sin θ (cos² θ) = sin θ cos θ
x sin θ (sin² θ + cos² θ) = sin θ cos θ
x sin θ = sin θ cos θ
x = cos θ
substitute x = cos θ in (1)
cos θ sin θ = y cos θ y = sin θ
L. H. S = x² + y² = cos² θ + sin² θ = 1
L.H. S = R.H.S
Hence it is proved.

Question 4.
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = ± \(\sqrt{a^{2}+b^{2}-c^{2}}\).
Answer:
Given a cos θ – b sin θ = c
Squaring on both sides
(a cos θ – b sin θ)² = c²
a² cos² θ + b² sin² θ – 2 ab cos θ sin θ = c²
a² (1 – sin² θ) + b² (1 – cos² θ) – 2 ab cos θ sin θ = c²
a² – a² sin² θ + b² – b² cos² θ – 2 ab cos θ sin θ = c²
– a² sin² θ – B² – cos² θ – 2 ab cos θ sin θ = – a² – b² + c²
a² sin² θ + b² cos² θ + 2 ab cos θ sin θ = a² + b² – c²
(a sin θ + b cos θ)² – a² + b² – c²
a sin θ + b cos θ = ± \(\sqrt{a^{2}+b^{2}-c^{2}}\)
Hence it is proved.

Question 5.
A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45° . The bird flies away horizontally in such away that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30° . Determine the speed at which the bird flies. (\(\sqrt { 3 }\) = 1.732)
Answer:

A is the initial position of the bird B is the final position of the bird Let the speed of the bird be “s”
Distance = speed × time
∴ AB = 2x
Let CD be x
∴ CE = x + 2s
In the ∆ CDA, tan 45° = \(\frac { AD }{ CD } \)
1 = \(\frac { 80 }{ x } \)
x = 80 ……..(1)
In the ∆ BCE
tan 30° = \(\frac { BE }{ CE } \)
\(\frac{1}{\sqrt{3}}\) = \(\frac { 80 }{ x+2s } \)
x + 2s = 80 \(\sqrt { 3 }\)
x = 80 \(\sqrt { 3 }\) – 2 s ………(2)
From (1) and (2) we get
80 \(\sqrt { 3 }\) – 2 s = 80
80 \(\sqrt { 3 }\) – 80 = 2 s ⇒ 80 (\(\sqrt { 3 }\) – 1) = 2 s
s = \(\frac{80(\sqrt{3}-1)}{2}\) = 40 (1.732 – 1) = 40 × 0.732 = 29.28
Speed of the flying bird = 29.28 m/sec

Question 6.
An aeroplane is flying parallel to the Earth’s surface at a speed of 175 m/sec and at a height of 600 m. The angle of elevation of the aeroplane from a point on the Earth’s surface is 37° at a given point. After what period of time does the angle of elevation increase to 53°? (tan 53° = 1.3270, tan 37° = 0.7536)
Answer:
Let C is the initial and D is the final position of the aeroplane.
Let the time taken by the aeroplane be “t”
∴ CD = 175 t (Distance = speed × time)

Let AB be x
∴ AE = x + 175 t
In the right ∆ ABC


∴ Time taken is 1. 97 seconds

Question 7.
A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away.
(i) How far is B to the North of A?
(ii) How far is B to the West of A?
(iii) How far is C to the North of B?
(iv) How far is C to the East of B?
(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)
Answer:

(i) To find the distance of B to the north of A
In ∆ ABB,

Distance of B to the North of A = 24. 58 km

(ii) Distance from B to the west of A is AB’
In ∆ ABB’
cos 55° = \(\frac{\mathrm{AB}^{\prime}}{\mathrm{AB}}\)
0.5736 = \(\frac{A B^{\prime}}{30}\)
∴ AB’ = 0.5736 × 30 = 17. 21 km
Distance of B to the West of A is 17. 21 km

(iii) Distance from C to the North of B is CD
In the right ∆ BCD, sin 42° = \(\frac { CD }{ BC } \)
0.6691 = \(\frac { BD }{ 32 } \)
∴ CD = 0.6691 × 32 = 21.41 km
Distance of C to the North B is 21. 41 km

(iv) The distance of C to the East of B is BD
In the right ∆ BDC, cos 42° = \(\frac { BD }{ BC } \)
0.7431 = \(\frac { BD }{ 32 } \)
∴ BD = 0.7431 × 32
= 23.78 km
Distance of C to the East of B is 23.78 km.

Question 8.
Two ships are sailing in the sea on either side of the lighthouse. The angles of depression of two ships as observed from the top of the lighthouse are 60° and 45° respectively. If the distance between the ships is 200 \(\left(\frac{\sqrt{3}+1}{\sqrt{3}}\right)\) meters, find the height of the lighthouse
Answer:
Let A and B the position of the first ship and the second ship
Distance = 200 \(\left(\frac{\sqrt{3}+1}{\sqrt{3}}\right)\) m
Let the height of the light house CD be “h”

In the right ∆ ACD, tan 60° = \(\frac { CD }{ AD } \)
\(\sqrt { 3 }\) = \(\frac { h }{ AD } \)
∴ AD = \(\frac{h}{\sqrt{3}}\) ……….(1)
In the right ∆ BCD
tan 45° = \(\frac { DC }{ BD } \)
1 = \(\frac { h }{ BD } \)
∴ BD = h
Distance between the two ships = AD + BD
200 (\(\frac{\sqrt{3}+1}{\sqrt{3}}\)) = \(\frac{h}{\sqrt{3}}\) + h ⇒ 200 (\(\sqrt { 3 }\) + 1) = h + \(\sqrt { 3 }\) h
200 (\(\sqrt { 3 }\) + 1) = h(1 + \(\sqrt { 3 }\)) ⇒ h = \(\frac{200(\sqrt{3}+1)}{(1+\sqrt{3})}\)
h = 200
Height of the light house = 200 m

Question 9.
A building and a statue are in opposite side of a street from each other 35 m apart. From a point on the roof of building the angle of elevation of the top of statue is 24° and the angle of depression of base of the statue is 34° . Find the height of the statue. (tan 24° = 0.4452, tan 34° = 0.6745)
Answer:
Let the height of the statue be “h” m
Let AD be x
∴ EC = h – x
In the right ∆ ABD,

tan 34° = \(\frac { AD }{ AB } \)
0.6745 = \(\frac { x }{ 35 } \)
∴ x = 0.6745 × 35 ⇒ x = 23.61 m
In the right ∆ DEC ⇒ tan 24° = \(\frac { EC }{ DE } \)
0.4452 = \(\frac { h-x }{ 35 } \) ⇒ h – x = 0.4452 × 35
h – 23.61 = 15. 58 ⇒ h = 15.58 + 23.61 = 39.19 m
Height of the statue = 39.19 m

Students can Download Samacheer Kalvi 10th English Model Question Paper 2 Pdf, Samacheer Kalvi 10th English Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamil Nadu Samacheer Kalvi 10th English Model Question Paper 2

General Instructions:

1. The question paper comprises of four parts.
2. You are to attempt all the sections in each part. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II, III and IV are to be attempted separately.
4. Question numbers I to 14 in Part I are Multiple Choice Questions of one mark each. These are to be answered by writing the correct answer along with the corresponding – option code.
5. Part II has got four sections. The questions are of two marks each. Question numbers 15 to 18 in Section I and Question numbers 19 to 22 in Section II are to be answered in about one or two sentences each. Question numbers 23 to 28 in Section III and IV are to be answered as directed.
6. Question numbers 29 to 45 in Part III are of five marks each and have been divided in five sections. These are to be answered as directed.
7.  Question numbers 46 and 47 in Part IV are of eight marks each. Question number 47 has four questions of two marks each. These are to be answered as directed.

Time: 2.30 Hours
Maximum Marks: 100

Part – I

Answer all the questions. [14 x 1= 14]
Choose the most suitable answer and write the code with the corresponding answer.
Choose the appropriate synonyms for the italicised words.

Question 1.
His parents circled around raising a proud cackle.
(a) babble
(b) screech
(c) walk
(d) tackle
Answer:
(a) babble

Question 2.
A reporter, a thin-faced, wispy man, came up to me.
(a) considerable
(b) significant
(c) substantial
(d) frail
Answer:
(d) frail

Question 3.
Nagen uncle’s tea shop stood next to a grocery shop.
(a) erected
(b) erased
(c) expunged
(d) severed
Answer:
(a) erected

Choose the appropriate antonym for the italicised words.

Question 4.
It is about a hurricane force of wind on land.
(a) farce
(b) vigour
(c) weakness
(d) potency
Answer:
(c) weakness

Question 5.
Unlike the developed world, India’s disabled are deprived by attitudinal barriers.
(a) developing
(b) industrialized
(c) established
(d) settled
Answer:
(a) developing

Question 6.
He was a frail man.
(a) weak
(b) feeble
(c) thin
(d) strong
Answer:
(d) strong

Question 7.
Choose the correct plural form of ‘Rhino’.
(a) rhinos
(b) rhinoes
(c) rhinoses
(d) rhinosses
Answer:
(b) rhinoes

Question 8.
Form a derivative by adding the right suffix to the word – ‘flame’.
(a) ity
(b) graphy
(c) able
(d) er
Answer:
(c) able

Question 9.
Choose the correct expansion of the abbreviation BCCI.
(a) Board of Chess Control in India
(b) Board of Cricket Collector in India
(c) Board of Cricket Control Institute
(d) Board of Control for Cricket in India
Answer:
(d) Board of Control for Cricket in India

Question 10.
Complete the following sentence with the most appropriate phrasal verb given below:
The advocate …………….. the case cleverly.
(a) dealt in
(b) dealt with
(c) dealt out
(d) dealt on
Answer:
(b) dealt with

Question 11.
Choose the suitable option to pair it with the word ‘mail to form a compound word.
(a) send
(b) box
(c) drop
(d) it
Answer:
(b) box

Question 12.
Fill in the blank with the most appropriate preposition given below:
He seized ………….. the opportunity to construct a solar panel for the school.
(a) seized with
(b) seized over
(c) upon
(d) seized on
Answer:
(c) upon

Question 13.
Complete the following sentence using the most appropriate tense form’of the verb given below:
Aditya’s father ……………….. the ancestral home and moved to Kolkata, where he had set up
his own business.
(a) has left
(b) had left
(c) is leaving
(d) were left
Answer:
(b) had left

Question 14.
Choose the most appropriate linker from the given four alternatives.
Promise me that you will phone me …………… reach home.
(a) before
(b) as soon as
(c) in case
(d) so that
Answer:
(b) as soon as

Part – II [10 x 2 = 20]

Section – I

Answer any THREE of the following questions in a sentence or two. [3 x 2 = 6]

Question 15.
How did the bird try to reach its parents without having to fly?
Answer:
The young bird trotted back and forth from one end of the ledge to the other with his long grey legs stepping daintily, trying to find some means of reaching his parents without having to fly.

Question 16.
What were the various things that tempted Franz to spend his day outdoors?
Answer:
The various things that tempted Franz to spend his day outdoors was simply because it was warm and bright outside. The birds were chirping at the edge of the woods and the Prussian soldiers were drilling in the open field, behind the sawmill. It was all much more tempting than the rule for participles.

Question 17.
What were the problems they faced during their training voyage? How was it a tutorial to them?
Answer:
As the boat was old, it had minor leaks and repairs. They also ran out of water and food soon. The trip was a tutorial for them on how to manage food, water and even electricity during the big voyage.

Question 18.
From the jeweller’s shop where did Aditya and his friend go? Why?
Answer:
From the jeweller’s shop Aditya went straight to Jogesh Kabiraj’s house where Mr. Sasanka Sanyal whom he met at Nagen uncle’s tea shop lived. Aditya wanted to meet Sasanka Sanyal.

Section – II

Read the following sets of poetic lines and answer any THREE of the following. [3 x 2 = 6]

Question 19.
“In the dim past, nor holding back in fear
From what the future veils; but with a whole
And happy heart, that pays its toll
To Youth and Age, and travels on with cheer.’’
(a) What does the poet mean by the phrase ‘in the dim past’?
(b) Is the poet afraid of future?
Answer:
(a) The poet means that the past was very dull and glum.
(b) No, the poet isn’t afraid of the future.

Question 20.
‘‘The worst thing is that if anyone stays Among them too long, he will learn their ways;”
(a) What is the worst thing that can happen if anyone stays with them?
(b) What are the ways of the Grumble family?
Answer:
(a) The worst thing that can happen if anyone stays with them is that they too will start complaining and become one with them.
(b) The ‘Grumble Family’ growl at anything and everything so much that they sometimes growl that they have nothing to grumble about.

Question 21.
“Not a crumb to be found On the snow-covered ground
(a) What couldn’t he find on the ground?
(b) Why was the ground covered with snow?
Answer:
(a) He couldn’t find even a single piece of bread on the ground.
(b) The ground was covered with snow because of the onset of winter season.

Question 22.
“ We were taken from the ore-bed and the mine,
We were melted in the furnace and the pit
We were cast and wrought and hammered to design,
We were cut and filed and tooled and gauged to fit”
(a) What metals are obtained from ores and mines?
(b) Mention a few machines which are hammered to design.
Answer:
(a) The metals obtained from ores are iron ores and minerals from mines.
(b) Pulley – Power lift, The Cutting Wedge, The Wheel and Axle are a few machines which are hammered to design.

Section – III

Answer any THREE of the following. [3 x 2 = 6]

Question 23.
Rewrite the following sentence to the other voice.
Cathy is not driving a car.
Answer:
A car is not being driven by Cathy.

Question 24.
Rewrite using indirect speech.
She asked me, “Could you help me with my luggage?”
Answer:
She asked me if I could help her with her luggage.

Question 25.
Punctuate the following.
i dont know what wed do without her we’d lose out on so many opportunities
Answer:
I don’t know what we’d do without her we’d lose out on so many opportunities.

Question 26.
Transform the following sentence into a simple sentence.
He must work hard otherwise, he will be suspended.
Answer:
He must work hard to avoid suspension.

Question 27.
Rearrange the words in the correct order to make meaningful sentences.
(a) Sports / building / physical strength / necessary / are / for
(b) They / sportsmanship / cooperation / include / and
Answer:
(a) Sports are necessary for building physical strength.
(b) They include sportsmanship and cooperation.

Section – IV

Answer of the following. [1 x 2 = 2]

Question 28.
Guide an old lady from the bus stand to the nearby Government Hospital (GH). Here you find the road map. Write three instructions by way of helping her.
Answer:

• Go straight and take the first left cut.
• Walk a little distance, you will come across a pharmacy on to your right.
• Walk a little further, you’ll find the Government Hospital on the same side.

Part – III [10 x 5 = 50]

Section -I

Answer any TWO of the following in utmost 10 lines. [2 x 5 = 10]

Question 29.
Bring out the character of the grandfather and the mother in the lesson, ‘The Night the Ghost got in’.
Answer:
The narrator’s grandfather is an oldtimer of the Union army of the Civil War, which terminated about fifty-two years ago. His bedroom is in the attic. When the police come to the house to search for the burglar, the grandfather thinks that they are militaries who are abandoning because they are losing to the South. The grandfather calls them “cowardly dog” and “lily- livered cattle” and then fetches a policeman’s holster and shoots a man with his own gun.

The police retreat, terrified of the irrational old man but at the breakfast table the next morning, Grandfather seems impeccably conscious of the previous night’s situation, asking why so many police had been “tarryhootin” around the house. On the contraryj the narrator’s mother, Mrs Thurber is a highly excitable woman, scatter brained yet practical at times. Hearing a sound in her house and suspecting a burglar, she thinks of the clever plan of alerting Mrs and Mr.

Bodwell the neighbours by throwing a shoe through his closed window. After he goes to alert the police, she considers throwing the matching shoe, a thrill and fanciful act. She is surprised to hear that Grandfather has shot a policeman, not because of the courageous ferocity of the act, but because the cop was such a nice-looking young man.
“Great powers don’t get angry
Nor do they act in haste”

Question 30.
How do we use technology in our day to day lives?
Answer:
Technology is growing day after day and we all depend on technology. Today we have various developing technologies that impact our lives in different ways. As the world keeps on developing, technology will change. Keeping oneself updated is very important in this modem world. It has totally transformed the life of an individual.

A Refrigerator is programmed to replenish food when the vegetables or milk or eggs are over. Ink cartridges too self-order replacements when it is empty. Technology helps one to manage entertainment and home appliances by voice commands or swapping the finger. When you are bored watching a programme on TV, you can just inform your smart TV your desire to view your social feed. Technology helps you to watch programmes understanding your mood swings.

When caught in traffic, technology permits your kettle to prepare tea for you to sip it hot the moment you reach home. Technology also automates all water and energy management systems. Therefore, accepting it and learning how to use technology in whatever we do is highly important and recommended.
“We are changing the world with Technology.”

Question 31.
Give a brief character sketch of Sasanka Sanyal.
Answer:
Sasanka Sanyal was a wise and intelligent student. Perhaps luck never favoured him. He may have been a book-worm. However, he was overpowered by his friends because of his innocence. Hence, Aditya Narayan Chowdhury exploits him and takes away his Silver medal that he had received for Poetry Recitation. He had a wonderful memory power and could recall every single incident of his past. He remembered Aditya when he saw him in Nagen’s Tea Cabin and confirmed his memory seeing his mole on the right cheek.

He was rude in his behaviour towards Aditya as he did not want to suppress his feelings and vented out his anger on him. He was remorse after the death of his family members. He whiled away his time at Nagen’s shop yet never gave up his self-respect and paid for the cup of coffee and biscuits if in case he had. Financially, he wasn’t comfortable since he couldn’t afford even a spectacle because of his partial deformity in his eye-sight.
“Self-respect permeates every aspect of your life.”

Question 32.
How was the last lesson different from earlier lessons?
Answer:
The last lesson was different from earlier lessons in numerous ways. It revealed the love and respect of the teacher and students for their mother tongue. Even the teacher was unusually kind and did not scold children. M. Hamel taught very patiently, with utmost dedication and sincerity. It seemed as if he wanted to give all that he knew before going away.

He was dressed at his best and his ‘iron ruler’ was not used even to rap it on the desk. The last lesson was attended by villagers with deep remorse to show their love and respect for their mother tongue and also to M. Hamel. The students listened very carefully and everybody was absolutely quiet. Franz regretted for not learning his lesson. The last lesson was indeed emotional. It stirred patriotic feelings and awakened the villagers to the importance of their mother tongue.
“The bird of love flies on two wings-
Faith and Dedicated Service.”

Section – II

Answer any TWO of the following in utmost 10 lines. [2 x 5 = 10]

Question 33.
In what way do we dispossess, betray and condemn ourselves by hating our brothers and taking up arms against them?
Answer:
By hating our brothers and taking up arms against them, we ‘dispossess’ ourselves as we rob ourselves of their love. When we hate them, they too react destructively and stop loving us. Mutually, we deprive each other of the noble emotion of love. We deceive ourselves as our hatred leads to wars, and wars cause widespread death and devastation.

This leads to the piling up of waste that pollutes our own mother earth. The dust and smoke from war obstruct the air that we breathe. So, hatred of fellow beings, in fact, leads to betrayal of our own selves. Further, this earns us condemnation as we disrupt the purity of the elements of nature. We threaten our own existence by ruining the systems that sustain us. Hence, hating our brothers and taking up arms against them does more damage to us.
“The universal brotherhood of man is our most precious possession.”

Question 34.
What qualities have made women powerful?
Answer:
The woman is made powerful due to her multifaceted personality. Today’s women are empowered, brave, strong and resolute. They love to explore and venture into new horizons. They are persistent and work tirelessly to prove what they are capable of. Her inner beauty, her supremacy and strength makes her all-powerful. She exhibits her power by showcasing her fearless nature. She is the symbol of strength as she is strong in her faith and beliefs.

She is seen as all-powerful because of her determined nature. She may sigh, cry and moan but is strong in her hope and firm in her trust. She is a lioness, brave and daring and one dare not muddle with her. If anyone is a mischief maker, she will not spare them. The woman should be feared cautiously since she would thaw or saw you for your deeds against her.
“A Woman believes in being strong, even when things seem to go wrong.”

Question 35.
Read the following stanza and answer the questions given below.
“The weather is always too hot or cold;
Summer and winter alike they scold.
Nothing goes right with the folks you meet Down on that gloomy Complaining Street. ”
(i) Pick out the rhyming words from the above lines?
(li) Write the rhyme scheme of the poem.
(iii) Give another rhyming word for cold and street.
(iv) Name the poem and the poet.
Answer:
(i) The rhyming words are ‘cold and scold’ as well as ‘meet and street’.
(ii) The rhyme scheme for the above are, ‘aabb’ pattern. .
(iii) COLD – bold; STREET – treat
(iv) The Grumble family by Lucy Maud Montgomery is the name of the poem and the poet respectively.

Question 36.
Paraphrase the following stanza.
It is the human earth that we defile.
Our hells of fire and dust outrage the innocence
Of air that is everywhere our own,
Remember, no men are foreign, and no countries strange.
Answer:
The poet again retells us in that people are contaminating this earth by their deeds. The fatal weapons emit fire and ashes that spread all over and pollute the environment. War is futile as it spoils the very earth for which we take up arms against each other. We should protect our atmosphere and keep in mind that this universe is the creation of God and we all are one. It is, therefore, imperative not to consider any human being as foreign and any country as strange.

Section – III

Answer any ONE of the following: [1 x 5 = 5]

Question 37.
Rearrange the following sentences in coherent order.
(i) The moon is six hundred times nearer than Mars, and yet our correspondence service is in regular operation with Mars.
(ii) ‘Aren’t you getting some result from the moon, at any rate?’
(iii) As soon as he awoke, Francis Bennett switched on his phonotelephote.
(iv) He questioned one of the ten astronomical reporters.
(v) Later, he went on into the reporters’ room.
Answer:
Rearranged number sequence: (iii), (v), (iv), (ii), (i)
(iii) As soon as he awoke, Francis Bennett switched on his phonotelephote.
(v) Later, he went on into the reporters’ room. .
(iv) He questioned one of the ten astronomical reporters.
(ii) ‘Aren’t you getting some result from the moon, at any rate?’
(i) The moon is six hundred times nearer than Mars, and yet our correspondence service is in regular operation with Mars.

Question 38.
Read the following passage and answer the questions that follow.
Answer:
I was just thirty-seven when my Uncle Philip died. A week before that event he sent for me; and here let me say that I had never set eyes on him. He hated my mother, but I do not know why. She told me long before his last illness that I need expect nothing from my father’s brother. He was an inventor, an able and ingenious mechanical engineer, and had much money by his improvement in turbine-wheels.

He was a bachelor; lived alone, cooked his own meals, and collected precious stones, especially rubies and pearls. From the time he made his first money he had this mania. As he grew richer, the desire to possess rare and costly gems became stronger. When he bought a new stone, he carried it in his pocket for a month and now and then took it out and looked at it. Then it was added to the collection in his safe at the trust company.

Questions.
(i) How old was the narrator when his uncle died?
(ii) What did the narrator’s mother tell him about his uncle?
(iii) What was Uncle Philip’s mania?
(iv) When did Uncle Philip call for his nephew to meet him?
(v) What was the profession of Uncle Philip?
Answer:
(i) The narrator was 37 years old when his uncle died.
(ii) The narrator’s mother told that he need expect nothing from his uncle.
(iii) Uncle Philip had the mania of collecting precious stones, especially rubies and pearls.
(iv) Uncle Philip called the narrator one week before he died.
(v) Uncle Philip was a ingenious mechanical engineer.

Section – IV

Answer any FOUR of the following. [4 x 5 = 20]

Question 39.
Prepare an attractive advertisement using the hints given below.
Singapore and Australia tours – free travel for child or discount.
Answer:

Question 40.
You are Kirubakaran / Suganthi. You are interested in doing a short term course in Computer Programming during your summer vacation. Write a letter to the Director, Computer World, Sector-22, Kanchipuram, enquiring about the duration of such a course and the terms and conditions for admission.
Answer:
Kirubakaran / Suganthi
119, 2nd main road
Kanchipuram
10 May 20XX
The Director
Computer World
Sector-22
Kanchipuram
Sir,
Sub: Short term Course in Computer Programming
Kindly refer to your advertisement in Daily Thanthi dated 8th May 20XX regarding the above mentioned course. I have just passed the A.I. CBSE examination of XII Class with science stream. I am interested in doing a short term course in computer programming during my summer vacation. However, before joining the course, I would like to know the following
details:
(a) Duration of the course and fees
(b) Mode of payment: lump sum/installments
(c) Whether a diploma/certificate is issued
(d) Recognition and its validity
(e) Timings of classes and other relevant information
(f) Individual time on computer

In case you have-some printed material for information kindly send it to me. A self addressed and duly stamped envelope is enclosed for the purpose. An early response will enable me to join your course immediately.

Yours faithfully
Kirubakaran / Suganthi

Address on the envelope
To
The Director
Computer World
Sector-22
Kanchipuram

Question 41.
Write a notice for the school notice-board inviting volunteers for an N.S.S. Camp. You are Sashilatha/Sashikumar the Group leader of S.D. Sr. Sec. School, Vellore.
Answer:

S.D. SR. SEC. School, Vellore 2 July 2020 Notice N.S.S. CAMP An N.S.S. camp of our unit will be held from 15th Aug. to 30th Aug. at village Vallimalai. Projects include Adult Literacy, Tree Plantation, Cleanliness Campaign and Health Awareness. Volunteers should give their names to the undersigned by 7th July 2020 Sashilatha/Sashikumar Group Leader N.S.S.

Question 42.
Look at the following picture and express your views on it in about five sentences.

Answer:
Civic sense is not common. A motorist should not cross the dividing concrete wall. He jeopardizes his own life and those who are likely to drive or walk on the road. If each motorist follows rules as per his convenience, there will be total chaos on the road. Let us respect road rules. Let us cross roads only in places where it is allowed.

Question 43.
Make notes or write a summary of the following passage.
Economics has become one of the important branches of social sciences. It is of great practical value in our daily life. In pure sciences, we study the subject to arrive at the truth. But an economist is a social scientist. He studies the subject not only to know the truth for its own sake, but to find out a way for many economic and social problems of the society. “Knowledge for knowledge’s sake” is not the goal of an economist.

Economics must be fruit bearing. Of course, an economist has no ready made answer for immediate problems. But he can help the government in making broad economic policies. According to J.M. Keynes, “the theory of economics does not furnish a body of settled conclusions immediately applicable to policy. It is a method, rather than doctrine, an apparatus of the mind, a technique of thinking, which helps its possessor to draw correct conclusions”.

Most of the problem of the modern state are economic in nature. So economists play an important role in the affairs of the state. During World War II, the German economy was damaged heavily. There was inflation, shortage of goods and mass unemployment. But the German economy recovered quickly by following the advice of an economist Ludwig Erhard. The German recovery is considered an economic miracle. Similarly, J.M. Keynes had great influence on the economic policies of the American government when it was in great economic trouble during the 1930s. In economics, we study about things like prices, rent, wages, interest, profits and taxation. All these affect every person in one way or the other. It has been rightly said, “you cannot be in any real sense a citizen, unless you are also in some degree an economist.”

Notes
Title: Importance of Economics

• one of the important branches of social sciences – economics
• Economist find out a way for many economical and social problems
• helps the government in making broad economic policies.
• During World War II heavy damage to German economy
• recovered by the economist Ludwig Erhard, – considered a miracle.
• American economic trouble – economist J.M. Keynes.
• we study things like prices, rent, wages, interest, profits and taxatidn
• Economic affects every individual

Summary

Title: Importance of Economics
Rough Draft

Economics one of the important branches of social sciences. An economist not only studies, but find out a way for more many economic and social problems of the society. He can help the government in making broad-ecopomic policies. During World War II, the heavy damage of German economy was recovered by the economist Ludwig Erhard, which is considered a miracle. Similarly in 1930, American government economic trouble was set right by the economist J.M. Keynes. In economics, we study about thmgsTiko-pirices, rent, wages,interest, profits and taxation.

Fair Draft:
Title: Importance of Economics

Economics is one of the important branches of social sciences. An economist find out solutions for many economic and social problems of the society. He can help the government in making broad economic policies. During World War II, the heavy damage of German economy was recovered by the economist Ludwig Erhard, which is considered a miracle. In 1930, American government’s economic trouble was set right by the economist J.M. Keynes. A citizen must be an economist to some degree.
No. of words: 79

Question 44.
Identify and correct the errors in the following sentences.
(a) The workers formed an union for their welfare.
(b) He did not listen to his father’s advises.
(c) Mohan is one of the best student in his class.
(d) Though his mother tongue is Tamil but he always speaks in English.
(e) If he had known of your arrival, he would come to receive you.
Answer:
(a) The workers formed a union for their welfare.
(b) He did not listen to his father’s advice.
(c) Mohan is one of the best students in his class.
(id) Though his mother tongue is Tamil, he always speaks in English.
(.e) If he had known of your arrival, he would have come to receive you.

Section – V

Quote from memory. [1 x 5 = 5]

Question 45.
Not hurrying …………… that pays its toll.
Answer:
Not hurrying to, nor turning from the goal;
Not mourning for the things that disappear
In the dim past, nor holding back in fear
From what the future veils; but with a whole
And happy heart, that pays its toll

Part – IV

Question 46.
Write a paragraph of about 150 words by developing the following hints. [2 x 8 = 16]

(a) Men and Women created equal – man differentiates jobs – Mulan takes a stand – takes a stand – frail father – comfort and pride – responsibilities – martial art, Kung Fu inborn traits head of the family – times of crisis – rises to situations – powers of a woman – knowledge, experience – gender equality far and wide.
Answer:
The Story of Mulan portrays the legendary Chinese warrior Hua Mulan. This old Chinese folktale is about the story of the young Chinese maiden who learns that her wizened, old and frail father is to be called up into the army in order to fight the invading Huns by the Chinese Emperor. When the Huns invade China, one man from every family is called to arms. She hears of the order that every family must send one man to the army while washing clothes. Mulan’s father, who is frail and aged decides to fight for his country though it is clear that he will not survive an enemy encounter.

He decides to go to war but is prevented by her daughter with her outrageous decision. Knowing her father’s frail state, she decides to disguise herself and join in his place without second thoughts. In the army, Mulan proves to be a brave soldier who is later put in charge of other soldiers. Her battles goes so well that more soldiers are added. After a few years, Mulan becomes the General of the entire army. Suddenly, bad fever swept through the army. Many soldiers including Mulan become a prey. The arrival of the doctor brings to light the hidden truth.

Many soldiers disprove such a thought, though some soldiers see the winning chances. Just then a soldier announces the surprise attack by the enemies. With no time to debate, the soldiers spring to action at the command of the General who hears this from inside her tent. She gets dressed and though not strong, she stands tall. She instructs the soldiers to attack knowing very well her strategic planning that all her soldiers acknowledge and win the battle. It was such a big victory that the enemy gave up, at last. The war was over, and China was saved! The Emperor forgives Mulan and was glad that Mulan had ended the long war.

He wanted Mulan to stay with him in the palace and be an advisor but as She chose to go to her family, the emperor gave her six horses and six fine swords so that her people will know that he thinks of her.

[OR]

(b) Elucidate, ‘With the crown, there cometh wisdom’ by developing the following hints. Saying – the crown of snow – elders – shapes our society – age – experiences to be intelligent – Theoretical knowledge – superficial – impact – wisdom-incomparable – learns from mistakes – elders optimistic – different challenges – survivors.
Answer:
In the saying “With the crown of snow, there cometh wisdom” – the crown of snow is pertaining to the eiders. It underlines the importance of the elders in shaping our society. The word, “there cometh wisdom” explains that as we get old our everyday experiences makes us to be intelligent. Theoretical knowledge is always superficial.

The impact is made only by experienced persons. The wisdom one gets from experience can never be compared to one who is learned theoretically. A person learns from Mistakes. Elders are generally optimistic and are ready to learn from their mistakes. They also remember it for their lifetime and never repeat them. The elders who have faced different challenges in life and had survived them braving all storm serve as our guiding path because their varied experiences teach us to become wise. They are wise enough to know what is right from wrong.

Question 47.
Read the following passage and answer the questions given below:
Environmentalist are worried at the speed with which fossil fuel is burnt and also at the disappearance of forests. The trees cut are not replaced. This changes the temperature pattern of the atmosphere. In a way much heat is released in the atmosphere, the larger part of that being Carbon Dioxide. ‘The green house effect’ occurs. This is the initial stages of global warming.

The ill effects of accumulated Carbon Dioxide can be minimized by trees and ample vegetation as they absorb it by photosynthesis and make Carbohydrates. Therefore, a well stocked ecosystem exercises. Considerable beneficial effects on human environment by moderating the climate, regulating the water supplies, purifying the air and helping in abating noise.

The most important environmental factors are micro – climate soil characteristics, moisture availability and interaction of animals and insects. Micro – climate is governed by solar radiation, rainfall, wind, humidity and air on the soil temperature. Soil temperature is also influenced by the forests.

Questions.
(a) What are the two reasons which make the environmentalists worried?
(b) How does “green house effect” occur?
(c) How can trees counter the ill effects of carbon dioxide?
(d) What are the factors that govern the micro – climate?
Answer:
(a) The two reasons which make the environmentalists worried are the speed with which fossil fuel is burnt and the disappearance of forests as a result.
(b) ‘The green house effect’ occurs because the trees cut are not replaced. This changes the temperature pattern of the atmosphere releasing much heat in the atmosphere.
(c) The ill effects of accumulated Carbon dioxide can be minimized by trees through their absorbing it by photosynthesis and making Carbohydrates.
(d) The factors that govern the micro – climate are solar radiation, rainfall, wind, humidity and air on the soil temperature which is also influenced by the forests.

[OR]

Read the following poem and answer the questions given below:
Bigot
The bigot insults his own religion When he slays a man of another faith.
Conduct the judges, not in the light of reason;
In the temple, he raises the blood-stained banner And worships the devil in the name of God.
All that is shameful and barbarous through the Ages,
Has found a shelter in their temples—
Those they turn into prisons;
O’ I hear the trumpet call of Destruction!
The time comes with her great broom Sweeping all refuse away.
That which should make man free,
They turn into fetters;
That which should unite, they turn into a sword;
That which should bring love From the fountain of the Eternal,
They turn into a prison
And with its waves, they flood the world.
They try to cross the river In a bark riddled with holes;
And yet, in their anguish, whom do they blame Oh Lord, breaking false religion,
Save the blind!
Break, O break
The altar that is drowned in blood.
Let your thunder strike Into the prison of false religion,
And bring to this unhappy land The light of knowledge

Questions.
(a) Who is a bigot?
(b) What does the word ‘Refuse’ refer to?
(c) What do the followers of false religion do?
(d) What is meant by the phrase ‘the fountain of the Eternal’?
Answer:
(a) A bigot is a human being who is narrow-minded in his religious views. In general he is an extremist.
(b) The word ‘Refuse’ refers to all the infirmities such a dirt and filth found in false religions.
(c) The followers of false religion turn religion into prison, fetters and swords to destroy one another.
(d) The phrase ‘the fountain of the Eternal’ means God Almighty who is everlasting.

Students can download 10th Social Science History Chapter 7 Anti-Colonial Movements and the British of Nationalism Questions and Answers, Notes, Samacheer Kalvi 10th Social Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Social Science Solutions History Chapter 7 Anti-Colonial Movements and the British of Nationalism

Samacheer Kalvi 10th Social Science Anti-Colonial Movements and the British of Nationalism Text Book Back Questions and Answers

I. Choose the correct answer

Question 1.
Which one of the following was launched by Haji Shariatullah in 1818 in East Bengal?
(a) Wahhabi Rebellion
(b) Farazi Movement
(c) Tribal uprising
(d) Kol Revolt
Answer:
(b) Farazi Movement

Question 2.
‘Who declared that “Land belongs to God” and collecting rent or tax on it was against divine law?
(a) Titu Mir
(b) Sidhu
(c) Dudu Mian
(d) Shariatullah
Answer:
(c) Dudu Mian

Question 3.
Who were driven out of their homeland during the process of creation of Zamins under Permanent Settlement?
(a) Santhals
(b) Titu Mir
(c) Munda
(d) Kol
Answer:
(a) Santhals

Question 4.
Find out the militant nationalist from the following.
(a) Dadabhai Naoroji
(b) Justice Govind Ranade
(c) Bipin Chandra Pal
(d) Romesh Chandra
Answer:
(c) Bipin Chandra Pal

Question 5.
When did the Partition of Bengal come into effect?
(a) 19 June 1905
(b) 18 July 1906
(c) 19 August 1907
(d) 16 October 1905
Answer:
(a) 19 June 1905

Question 6.
What was the context in which the Chotanagpur Tenancy Act was passed?
(a) Kol Revolt
(b) Indigo Revolt
(c) Munda Rebellion
(d) Deccan Riots
Answer:
(c) Munda Rebellion

Question 7.
Who set up the first Home Rule League in April 1916?
(a) Annie Basant
(b) Bipin Chandra Pal
(c) Lala Lajpat Rai
(d) Tilak
Answer:
(d) Tilak

Question 8.
Who drew the attention of the British to the suffering of Indigo cultivation through his play Nil darpanl
(a) Dina Bandhu Mitra
(b) Romesh Chandra Dutt
(c) Dadabhai Naoroji
(d) Birsa Munda
Answer:
(a) Dina Bandhu Mitra

II. Fill in the blanks

1. In 1757, Robert Clive was financially supported by ……………….. the moneylenders of Bengal.
2. ……………….. was an anti-imperial and anti-landlord movement which originated in and around 1827.
3. The major tribal revolt which took place in Chotanagpur region was ………………..
4. The ……………….. Act, restricted the entry of non-tribal people into the tribal land.
5. Around 1854 activities of social banditry were led by ………………..
6. The British Commander of Kanpur killed by the rebels during the 1857 Rebellion was ………………..
7. Chota Nagpur Act was passed in the year ………………..
8. W.C. Bannerjee was elected the president of Indian National Congress in the year ………………..

Answers:

1. Jagat Seth
2. The Wahhabi rebellion
3. Kol revolt
4. Chota Nagpur Tenancy
5. Birsingh
6. Major General Hugh Wheeler
7. 1908
8. 1885

III. Choose the correct statement

Question 1.
(i) The Company received ₹ 22.5 million from Mir Jafar and invested it to propel the industrial revolution in Britain.
(ii) Kols organized an insurrection in 1831-1832, which was directed against government officers and moneylenders.
(iii) In 1855, two Santhal brothers, Sidhu and Kanu, ledtheSanthal Rebellion.
(iv) In 1879, an Act was passed to regulate the territories occupied by the Santhals.
(a) (i), (ii) and (iii) are correct
(b) (ii) and (iii) are correct
(c) (iii) and (iv) are correct
(d) (i) and (iv) are correct
Answer:
(a) (i), (ii) and (iii) are correct

Question 2.
(i) Dudu Mian laid emphasis on the egalitarian nature of Islam and declared that “Land belongs to God”.
(ii) According to the Doctrine of Lapse, new territories under the corrupt Indian rulers were to be annexed.
(iii) The British officials after the suppression of 1857 Revolt were given power to judge and take the lives of Indians without due process of law.
(iv) One of the causes of the failure of the Revolt of 1857 was many of the Indjan princes and zamindars remained loyal to the British.
(a) (ii), (iii) and (iv) are correct
(b) (i), (ii) and (iv) are correct
(c) (i), (iii) and are correct
(d) (i), (ii) and (iii) are correct
Answer:
(c) (i), (iii) and are correct

Question 3.
(i) One of the most significant contributions of the early Indian Nationalists was the formulation of an economic critique of colonialism.
(ii) The early Congress leaders stated that religious exploitation in India was the primary reason for the growing poverty.
(iii) One of the goals of the moderate Congress leaders was to achieve Swaraj or self-rule.
(iv) The objective of the Partition of Bengal was to curtail the Bengali influence and weaken the nationalist movement.
(a) (i) and (iii) are correct
(b) (i), (iii), and (iv) are correct
(c) (ii) and (iii) are correct
(d) (iii) and (iv) are correct
Answer:
(b) (i), (iii), and (iv) are correct

Question 4.
Assertion (A): Under colonial rule, for the first time in Indian history, government claimed a direct proprietary right over forests.
Reason (R): Planters used intimidation and violence to compel farmers to grow indigo.
(a) Both A and R are correct, but R is not the correct explanation of A
(b) Both A and R are wrong
(c) Both A and R are correct and R is the correct explanation of A
(d) A is wrong and R is correct.
Answer:
(b) Both A and R are wrong

Question 5.
Assertion (A): The Revolt of 1857 was brutally suppressed by the British army.
Reason (R): The failure of the rebellion was due to the absence of Central authority.
(a) Both A and R are wrong
(b) A is wrong and R is correct
(c) Both A and R are correct and R is the correct explanation of A
(d) Both A and R are correct, but R is not the correct explanation of A
Answer:
(c) Both A and R are correct and R is the correct explanation of A

IV. Match the following

Answer:
A. (iii)
B. (iv)
C. (i)
D. (v)
E. (ii)

V. Answer the following questions briefly

Question 1.
How are the peasant uprisings in British India classified?
Answer:
There were nearly a hundred peasant uprisings during British rule. They can be classified into the following categories –

• Restorative rebellions
• Religious movements
• Social Banditry
• Mass insurrection

Question 2.
Write about the Kanpur Massacre of 1857.
Answer:

1. The seige of Kanpur was an important episode in the 1857 Rebellion.
2. The rebel forces under Nana Sahib besieged the Company forces and civilians in Kanpur.
3. They were unprepared for the extended besiege.
4. It forced them to surrender to the rebel forces under Nana Sahib, in return for a safe passage to Allahabad.
5. The boats in which they were proceeding were burned and most of them were killed including Major General Hugh Wheeler the British Commander of Kanpur.

Question 3.
Name the territories annexed by the British under the Doctrine of Lapse.
Answer:
Satara, Sambalpur, parts of Punjab, Jhansi and Nagpur.

Question 4.
What do you mean by drain of wealth?
Answer:
India was economically subjugated and transformed into a supplier of raw materials. It became a market to dump English manufactures and for the investment of British Capital. So the colonial economy was a continuous transfer of resources from India to Britain without any favourable returns back to India. This is referred as “the drain of wealth”.

Question 5.
Explain the concept of constructive swadeshi?
Answer:
Under Constructive Swadeshi, the self-defeating modest approach of moderates was rejected and self-help was focused on through swadeshi industries, national schools, arbitration courts and constructive programmes in the village. It was totally non-political in nature.

Question 6.
Highlight the objectives of Home Rule Movement.
Answer:
Objectives of the Home Rule Movement:

1. To attain self Government within the British empire by constitutional means.
2. To obtain the status of dominion a political position.
3. To use non-violence constitutional methods to achieve their goals.

Question 7.
Summarise the essence of Lucknow Pact.
Answer:
In the Lucknow Pact that took place in 1916, the Congress Party and the Muslim League agreed that there should be self-government in India as soon as possible. In return of this gesture from the Muslim League, the congress leadership accepted the concept of separate electorate for Muslims. This created a new sense of enthusiasm among the people.

VI. Answer all the questions under each caption

Question 1.
Deccan riots

(a) When and where did the first recorded incident of rioting against the moneylenders in the Deccan appear?
Answer:
In May 1875 in Supa, a village near Poona the first recorded incident of rioting against the moneylenders in the Deccan appeared.

(b) What was the right given to moneylenders under a new law of the British?
Answer:
Under the new law of the British the moneylenders were given the right to attach the mortgaged land of the defaulters auction it off.

(c) What did it result in?
Answer:
It resulted in the transfer of land from the cultivators to the non-cultivating classes.

(d) Against whom was the violence directed in the Deccan riots.
Answer:
In the Deccan riots violence was directed against the Gujarat money lenders.

Question 2.
The Revolt of 1857
(a) Who assaulted his officer, an incident that led to the outbreak of 1857 Revolt?
Answer:
Mangal Pandey assaulted his officer.

(b) Who was proclaimed the Shahenshah-e-Hindustan in Delhi?
Answer:
The Mughal Emperor Bahadur Shah II was proclaimed the Shahenshah-e-Hindustan in Delhi.

(c) Who was the correspondent of London Times to report on the brutality of the 1857 revolt?
Answer:
The correspondent’s name was William Howard Russell.

(d) What did the Queen’s proclamation say on matters relating to religion?
Answer:
The Queen proclaimed to the Indian people that the British government would not interfere in traditional institutions and religious matters.

Question 3.
Indian National Congress

(a) What were the techniques adopted by the Congress to get its grievances redressed ?
Answer:
The congress to get its grievances redressed adopted the techniques by way of appeals petitions and delegations.

(b) What do you know of Lal-Bal-Pal triumvirate?
Answer:
Lala Lajpat Rai of Punjab, Bal Gangadara Tilak of Maharashtra and Bipin Chandra Pal of Bengal called as Lai – Bal – Pal.
Lai – Bal – Pal triumvirate were the prominent Congress leaders of militiant nationalists.

(c) Where was the first session of Indian National Congress held?
Answer:
The first session of Indian National Congress was held at Bombay.

(d) How did the British respond to the Swadeshi Movement?
Answer:
The British brutally crushed the Swadeshi Movement. Revolutionaries were hanged. Press was crushed and prominent leaders were arrested and imprisoned for long terms.

VII. Answer in detail

Question 1.
Discuss the causes and consequences of the Revolt of 1857?
Answer:
The Great Rebellion of 1857 is a unique example of resistance to the British authorities, in India. There were several reasons that triggered the Revolt:
(i) The annexation policy of British India created dissatisfaction among the native rulers. The British claimed themselves as paramount, exercising supreme authority. New territories were annexed on the grounds that the native rulers were corrupt, and inept.

(ii) The British annexed several territories such as Satara, Sambalpur, parts of Punjab, Jhansi and Nagpur through the Doctrine of Lapse. This also angered many Indian rulers.

(iii) Indian sepoys were upset with discrimination in salary’ and promotion. They were paid much less than their European counterparts. They felt humiliated and racially abused by their seniors.

Consequences:
(i) India was pronounced as one of the many crown colonies to be directly governed by the Parliament. This resulted in the transfer of power from the East India company to the British crown.

(ii) Queen Victoria proclaimed to the Indian people that the British government would not interfere in traditional institutions and religious matters. It was promised that Indians would be absorbed in government services.

(iii) There came significant changes in the Indian army. The number of Indians was reduced.
Indians were restrained from holding important ranks and position.

(iv) It was also decided that instead of recruiting soldiers from Rajputs, Brahmins and North Indian Muslims, more soldiers would be recruited from the Gorkhas, Sikhs and Pathans.

Question 2.
How did the people of Bengal respond to the Partition of Bengal (1905)?
Answer:

1. In 1899 Lord Curzon was appointed as the Viceroy of India.
2. Curzon resorted to repressive measures to undermine the idea of local Government, autonomy of higher educational Institutions and gag the press.
3. The idea of partition was planned to suppress the political activities against the British rule in Bengal by creating a Hindu-Muslim divide.
4. It was openly stated that the main notion of partition was to curtail Bengali mfluence and to weaken the nationalist movement.
5. Bengal was Partitioned into two units Bengali Hindus (West Bengal) and Muslims (East Bengal).
6. Partition of Bengal in 1905 led to widespread protests all across India, starting a new phase of the Indian National movement.
7. The partition instead of dividing, united the people of Bengal.
8. People marched on the streets of Calcutta in thousands singing Bande mataram.
9. The partition led to the Boycott of the British goods and Swadeshi movement.

Question 3.
Attempt a narrative account of how Tilak and Annie Besant by launching Home Rule Movement sustained the Indian freedom struggle after 1916?
Answer:
(i) The Indian National Movement was revived and also radicalised during the Home Rule , League Movement that lasted from 1915 to 1918. It was led by Lokamanya Tilak and Annie Besant.

(ii) The objective of the Home Rule Movement was to attain self-government within the British Empire.

(iii) Tilak set up the first Home Rule League in April 1916. In September 1916, after repeated demands of her followers, Annie Besant decided to start the Home Rule League without the support of the Congress. Both the Leagues worked independently.

(iv) The Home Rule Leagues were utilised to carry extensive propaganda through press, speeches, public meetings, lectures, discussions and touring in favour of self government.

(v) Both the leagues succeeded in enrolling young people in large numbers and extending the movement to the rural areas.

VIII. Activity

Question 1.
Identify the Acts passed in British India from 1858 to 1919, with a brief note on each.
Answer:
Government of India Act (1858):

1. It was passed to end the rule of the East India Company and transfer the power to the British Crown.
2. The British Governor General Post was designated as viceroy of India, who became the representative of the British Monarch.

Indian Council Act – 1892:

1. The British Parliament introduced various amendments to the composition and functions of legislative council, increased the number of additional members to be represented both in central and provinces.
2. The members were given the right to ask questions on budget.
3. This Act laid the foundation of parliamentary system in India.
4. It is a landmark in the constitutional development.

Indian Council Act of 1909:

1. Popularly known as Minto – Morley Reforms.
2. This Act directly introduced the elective principle to membership in the imperial and local legislative councils.
3. It increased the involvement of Indians limitedly in the British Governance.

Montagu – Chelmsford Reform (1919):

1. The British Parliament passed this Act to expand participation of Indians in the division of executive branch of each provincial Government in to authoritarian and popularly responsible section for the provinces of British India.
2. Embodied reforms recommended in the report of the secretary of state of India.
3. This Act promised gradual progress of India towards self – Government.

Dy Archy (1919):

1. This Act introduced dual Government for the provinces of British India. One is accountable and the other one non accountable.
2. It marked the 1st introduction of democratic principle into the executive branch of British administration.
3. It was the association of Indians with the legislation work.
4. Introduced Port – folio system.

Question 2.
Mark the important centres of 1857 Revolt on an outline map.
Answer:

Question 3.
Prepare an album with pictures of frontline leaders of all the anti-colonial struggles launched against the British.
Answer:
Pictures of Moderates

Tribal Rebellion and other movement

Samacheer Kalvi 10th Social Science Anti-Colonial Movements and the British of Nationalism Additional Important Questions and Answers

I. Choose the correct answer

Question 1.
The Nawab of Bengal ……………….. was defeated by the East India company at the Battle of Plassey.
(a) Shuja-ud-daullah
(b) Siraj-ud-daullah
(c) Mirjafar
(d) Mir Kasim
Answer:
(b) Siraj-ud-daullah

Question 2.
Indian Historians describes the revolt of 1857 as ……………….
(a) Sepoy mutiny
(b) First war of Indian Independence
(c) Military revolt
Answer:
(b) First war of Indian Independence

Question 3.
The collective farming of the tribals of Ranchi was known as:
(a) Jhum
(b) Bethbegari
(c) Khunkatti
(d) Ryotwari
Answer:
(c) Khunkatti

Question 4.
The peasants had to pay heavy …………….
(a) land taxes
(b) tariffs
(c) service taxes
Answer:
(a) land taxes

Question 5.
The ……………….. had leased out to moneylenders the job of revenue collection.
(a) Raja of Chota Nagpur
(b) European officers
(c) Nawab of Bengal
(d) Birsaite Raj
Answer:
(a) Raja of Chota Nagpur

Question 6.
The sepoys broke into open revolt at …………..
(a) Meerut
(b) Kanpur
(c) Barrackpore
Answer:
(a) Meerut

Question 7.
On ……………….. a band of sepoys from Meerut marched to the Red Fort in Delhi.
(a) 1^st May 1858
(b) 11^th May 1852
(c) 11^th May 1857
(d) 19^th September 1916
Answer:
(c) 11^th May 1857

Question 8.
After the  1857 revolt the Governor-General of India was designated as …………….
(a) Viceroy of India
(b) Ruler of India
(c) Minister of India
Answer:
(a) Viceroy of India

Question 9.
……………….. led the Revolt at Bareilly.
(a) Bahadur Shah – II
(b) Khan Bahadur
(c) Nana Sahib
(d) Kunwar Singh
Answer:
(b) Khan Bahadur

Question 10.
Rani Lakshmi Bai led the revolt at …………….
(a) Kanpur
(b) Central India
(c) Lucknow
Answer:
(b) Central India

Question 11.
The play “Nil Darpan” by ……………….. did much to draw attention in India and Europe to the plight of the indigo growers.
(a) Dina Bandhu mitra
(b) Bankim Chandra Chatterjee
(c) Lockmanya Tilak
(d) Ranajit Guha
Answer:
(a) Dina Bandhu mitra

Question 12.
In 1858, the Royal Durbar was held at …………..
(a) Meerut
(b) Allahabad
(c) Delhi
Answer:
(b) Allahabad

Question 13.
The Madras Native Association was formed in the year:
(a) 1806
(b) 1852
(c) 1884
(d) 1852
Answer:
(b) 1852

Question 14.
Which one was not a trading company?
(a) The Portuguese
(b) The French
(c) The Japanese
Answer:
(c) The Japanese

Question 15.
……………….. lent his services to facilitate the formation of Indian National Congress.
(a) A.O.Hume
(b) W.C.Baneijee
(c) Mrs. Annie Besant
(d) V.O.Chidambarampillai
Answer:
(a) A.O.Hume

II. Fill in the blanks

1. The ………………….. helped to unite the Congress party after the Surat split.
2. The ………………….. movement enhanced to participation of masses in Nationalist Politics.
3. The British mainly responded to political activities of nationalists by repression and …………………..
4. The Indian National Movement was revived and ………………….. during the Home Rule movement.
5. ………………….. launched the Swadeshi Steam Navigation Company in Tuticorin.
6. One of the common goals of the extremist leaders was to achieve …………………..
7. For ………………….. Swaraj was the attainment of complete autonomy and total freedom from foreign rule.
8. ………………….. decided to started the Home Rule League without the support of the Congress.
9. The Home Rule Movement in India borrowed much of its principles from the …………………..
10. In the ………………….. session of Indian National Congress (1916) decided to admit the militant faction in to the party.
11. Pherozeshah Metha and Gokhale two main voices of opposition against militant faction had died in …………………..
12. Bengal was officially partitioned on ………………….. by Lord Curzon.
13. The official declaration of partition of Bengal was observed as a day of …………………..
14. In a divided Bengal Curzen made the Bengali speaking people to a …………………..
15. In the year 1899 ………………….. was appointed as the viceroy of India.
16. Early Indian Nationalists advocated …………………..
17. The formation of the ………………….. in 1885 was intended to establish an All India Organisation.
18. The early leaders felt that ………………….. was the main obstacle to the India’s Economic Development.
19. One of the key demand of the Indian National Congress was creation of ………………….. at provincial and central level.
20. ………………….. played a significant role in propagating the ideas of Nationalism.
21. Under British rule peasants were forced to pay revenue directly to the …………………..
22. Vicious cycle of debt forced the peasants to abandon ………………….. in 1875.
23. The British planters forced the cultivators to grow ………………….. rather than food crops.
24. ………………….. was appointed by the British Parliament to look into the Indian affairs after 1857 revolt.
25. In November 1858 the power to govern India was transferred from ………………….. to the British Crown.
26. The ………………….. was an important episode in the rebellion of 1857.
27. The Kingdom of Jhansi was annexed under …………………..
28. De throning of many Indian rulers affected the livelihood of ………………….. due to lose of patronage.
29. ………………….. of the people against the British took the form of a people’s revolt.
30. Thousands of weavers were thrown out of employment due to the dumping of …………………..
31. By the beginning of June 1857 except ………………….. and ………………….. British Rule in North India had disappeared because of the mutineers.
32. The precursor to the revolt was the introduction of new ………………….. of the Enfiled Rifles.
33. The ………………….. claimed themselves as paramount power.
34. The ………………….. was the first major revolt of armed forces accompanied by civilian rebellion.
35. In the 1890’s ………………….. offered resistance against the alienation of tribal people from their land.
36. The ………………….. prompted the British to formulate a policy on Tribal land.
37. The Munda people were forcefully recruited as ………………….. to work on plantations.
38. The Munda rebellion movement received an impetus when ………………….. declared himself as the messenger of God.
39. The disillusionment with ………………….. aggravated the miseries of Munda people.
40. One of the prominent tribal rebellion in Ranchi was known as …………………..
41. After the battle of ………………….. the British adopted a policy of territorial expansion.
42. The British ………………….. was rapidly mechanized with the money received by the company from Mir Jafar.
43. India was led to the path of because of Britsh manufactured goods.
44. ………………….. was forced to create a market for the products from Britain.
45. The plunder of India by the ………………….. continued for nearly 190 years.
46. There were nearly a hundred ………………….. during the British rule.
47. The leaders of ………………….. movements were looked upon by their people as heroes of their cause.
48. The ………………….. are usually leaderless and spontaneous uprising.
49. The subletting of land by the zamindars increased the ………………….. on the peasants.
50. Wahhabi Rebellion originated in 1827 in and around ………………….. of Bengal.

Answer:

1. Home Ruler Movement
2. Swadeshi
3. Reconciliation
4. Radicaliszed
5. V.O.Chidambaranar
6. Swaraj or Self Rule
7. Tilak
8. Mrs. Annie Besant
9. Irish Home Rule Movement
10. Lucknow session
11. 1915
12. 16^th October 1905
13. Mourning
14. Linguistic minority
15. Lord Curzon
16. Industrialisation
17. Indian National Congress
18. Colonialism
19. Legislative councils
20. Print media
21. Government
22. agriculture
23. Indigo plant
24. Secretary of State
25. English East India Company
26. Seige of Kanpur
27. Doctrine of Lapse
28. Artisans and handicrafts persons
29. Collective anger
30. British manufacture
31. Punjab and Bengal
32. greased cartridges
33. British
34. Great Rebellion of 1857
35. Tribal chiefs
36. Munda rebellion
37. Indentured labourers
38. Birsa Munda
39. Christian missionaries
40. Ulugalan rebellion
41. Plassey
42. Textile industry
43. De. industrialisation
44. India
45. East India company
46. Peasant uprisings
47. Social banditry
48. Mass insurrection
49. Tax burden
50. Barasat

III. Choose the correct statement

Question 1.
(i) The urban elite of India was busy responding to the western ideas through socio – religious reform movements.
(ii) The traditional elite and peasantry wanted to restore pre – colonial order by revolts.
(iii) The practice of letting out and subletting of land complicated the industrial relations.
(iv) Changes introduced in the land tenures significantly altered the agrarian relations.
(a) (i), (ii) and (iv) are correct
(b) (i), (ii) and (iii) are correct
(c) (i), (iii) and (iv) are correct
(d) (ii), (iii) and (iv) are correct
Answer:
(a) (i), (ii) and (iv) are correct

Question 2.
(i) The commercialisation of forest led to the disintegration of the traditional tribal system.
(ii) The usury and forcible eviction of tribals from their land led to the resentment of kols.
(iii) The pushed out santhals were forced to rely on the moneylenders for their subsistence.
(iv) Santhals felt secured under the British.
(a) (i), (ii) and (iv) are correct
(b) (i), (iii) and (iv) are correct
(c) (i), (ii)-and(iii) are correct
(d) (ii), (iii) and (iv) are correct
Answer:
(c) (i), (ii)-and(iii) are correct

Question 3.
(i) The British annexed more territories through two major policies.
(ii) Indian sepoys accepted the new dress code and overseas service.
(iii) Before loading into Enfiled Rifle the cartridges had to be bitten off.
(iv) The Indian Sepoys felt humiliated and racially abused by their seniors.
(a) (i) and (iii) are correct
(b) (i), (ii) and (iii) are correct
(c) (i), (ii) and (iv) are correct
(d) (i), (iii) and (iv) are correct
Answer:
(d) (i), (iii) and (iv) are correct

Question 4.
Assertion (A): The mutiny was equally supported by an aggrieved rural society of North India.
Reason (R): Sepoys working in British army were infact peasants in uniform.
(a) Both A and R are wrong.
(b) Both A and R are correct and R is the correct explanation of A.
(c) A is correct R is wrong.
(d) Both A and R are correct but R is the not the correct explanation of A.
Answer:
(b) Both A and R are correct and R is the correct explanation of A.

Question 5.
Assertion (A): India extended its support to the British in world war I. Reason (R): Hoping for the attainment of self – Government after the war.
(a) A is correct R is wrong.
(b) Both A and R are wrong.
(c) Both A and R are correct but R is not the correct explanation of A.
(d) Both A and R are correct and R is the correct explanation of A.
Answer:
(d) Both A and R are correct and R is the correct explanation of A.

IV. Match the following

Question 1.
Match the Column I with Column II.

Answer:
A. (iii)
B. (v)
C. (iv)
D. (i)
E. (ii)

Question 2.
Match the Column I with Column II.

Answer:
A. (ii)
B. (v)
C. (iv)
D. (i)
E. (ii)

Question 3.
Match the Column I with Column II.

Answer:
A. (ii)
B. (v)
C. (i)
D. (iii)
E. (vi)
F. (vii)

V. Answer the following question briefly

Question 1.
What caused huge loss of revenue in Bengal?
Answer:
Aurangzeb’s farman had granted the company only the right to trade duty free. But the officials of the company, who were carrying on private trade on side also stopped paying duty. This caused a huge loss of revenue for Bengal.

Question 2.
Mention some of the issues of peasants that added to the sense of resentment against the British.
Answer:

1. The concept of private property rights in land.
2. Rigorous collection of land revenue.
3. Encroachment of tribal land by non-tribal people.
4. Interference of Christian Missionaries in the socio – religious life of the local people.

Were some of the issues of resentment against the British.

Question 3.
Why did the Battle of Plassey become famous?
Answer:
It was the first major victory the company won in India.

Question 4.
What were the reasons for Tribal upraising?
Answer:

1. Under colonial rule the Government claimed a direct proprietary right over forests.
2. The commercialisation of forests led to the disintegration of the traditional tribal system.
3. It encouraged the incursion of tribal areas by non-tribal people such as contractors, moneylenders traders, land grabbers.
4. This led to the wide spread loss of adivasi land and their displacement from their traditional habitats. So Tribal resistance arose.

Question 5.
What were the grievances of the company regarding the Nawabs of Bengal?
Answer:
The company declared that the unjust demands of the local officials were ruining the trade of the company. Trade could flourish only if the duties were removed. It was also convinced to expand trade, it had to enlarge its settlements, buy up villages and rebuild its forts.

Question 6.
Name the early leaders who criticized about colonial economy.
Answer:
Dadabhai Naoroji, Justice Ranade and Romesh Chandra Dutt strongly criticised about the colonial economy.

They clearly stated that the prosperity of the British lay in the economic and political subjugation of India.

They concluded that the colonialism was the main obstacle to the India’s economic development.

Question 7.
Which battle did Robert Clive fight in 1757 and against whom?
Answer:
In 1757, he fought the Battle of Plassey against Siraj-ud-daulah.

VI. Answer all the questions under each caption

Question 1.
Political causes for the Revolt of 1857.

(a) Who introduced subsidiary Alliance?
Answer:
Lord Wellesley introduced subsidiary Alliance.

(b) Name the policy introduced by Lord Balhousie.
Answer:
Lord Dalhousie introduced the policy of “Doctrine of Lapse”.

(c) What was the order issued by the British against the Mughal emperor?
Answer:
The British Government had ordered that the Mughal emperor had to give up their ancestral palace and Red fort.

(d) Why did Nana Saheb develop a grudge against the British.
Answer:
The British stopped the pension to Nana Saheb. So he developed a grudge against the British.

Question 2.
Great Rebellion of 1857

(a) What was the biggest challenge witnessed by the British in 1857?
Answer:
The Great Rebellion by the Sepoys and the civilians.

(b) What was witnessed by both sides during the revolt?
Answer:
Unprecedented violence

(c) What were the causes of the revolt?
Answer:

1. Annexation policy of the British in India.
2. Insensitivity of the British to Indian cultural sentiments.

(d) What was the people’s opinion on the new regulations of the British.
Answer:
There was always a suspicion among the people regarding British new regulations intention.

Question 3.
Wahhabi Rebellion in Barasat

(a) Who led the Wahhabi Rebellion? Write a few lines about him.
Answer:
Titu Mir, an Islamic preacher led this rebellion. He was deeply influenced by the Wahhabi teachings. He became an important figure among the predominantly Muslim peasantry oppressed under the zamindari system.

(b) How did this movement acquire an anti-Hindu complexion?
Answer:
The majority of zamindars were Hindus. Thus, the movement acquired an anti-Hindu complexion.

(c) what happened on 6 November 1831?
Answer:
On 6 November 1831, the first major attack was made in the town of Pumea. Titu Mir immediately declared freedom from British Rule.

(d) How did the British respond to this rebellion?
Answer:
The British sent a large number of Troops to Narkelberia. Titu Mir along with his soldiers were killed in the staiggle.

Question 4.
Peasant and Tribal Resistance

(a) What was the nature of the resistance against the British rule emerged in rural India?
Answer:
More aggressive response emerged in rural India.

(b) Who revolted against the British in rural areas?
Answer:
Traditional elite and peasants along with tribals revolted.

(c) What did they seek for?
Answer:
They sought for the restoration of the Pre-colonial order and not the removal of the British.

(d) What was the outlook of the tribals on British?
Answer:
The tribal people started looking at the British as invaders and encroachers.

VII. Answer in detail

Question 1.
Enumerate the cause for the failure of the Great Revolt of 1857.
Answer:
Administrative changes:

1. Disunity among the Indians was the first and the foremost cause.
2. A large number of rulers of the Indian states and the big zamindars did not join the movement,
3. The rulers of the Indian states, who did not support the movement, remained neutral.
4. The educated Indians did not support the movement.
5. The telegraph and postal communication proved very helpful to the British for proper military actions and sending their reinforcements at the earliest time.
6. The rebellious soldiers were short of modem weapons and other materials of war.
7. The rebellious soldiers had to fight with traditional weapons which were no match to modem weapons possessed by the British forces.
8. The revolt was not extended beyond North.
9. The Indian leaders like Nana Saheb, Tantia Tope, Rani Lakshmi Bai where no match to the British generals.
10. The revolt broke out prematurely and the preparations for the revolt remained incomplete.
11. The organization and the planning of the rebels was very poor.
12. The Indian leaders were brave and selfless but they lacked unity of command and discipline.
13. The revolutionaries had no common idea.
14. The Muslims wanted to revive Mughal rule and the Hindus wanted to receive the Peshwa Raj.
15. The British diplomacy of Divide and Rule prevented most of the Indian mlers to join together for a common cause.

Question 2.
What was the objective of the partition of Bengal (1905) and what was its result?
Answer:

1. The main objective of partition of Bengal was to divide the Hindu – Muslim unity and to influence and weaken the nationalist movement.
2. Bengal was partitioned into two administrative units.
3. Reduced the Bengali – speaking people to a linguistic minority in a divided Bengal.
4. Curzon assured Muslims that in the new province of East Bengal Muslim would enjoy a unity.

Result:

1. Curzon thought the partition would divide the Bengali people on religious line.
2. Instead the partition united the people of Bengal.
3. The growth of the vernacular newspapers played a vital role in building a sense of proud Bengali identity.
4. The day Bengal was officially partitioned (16th Oct 1905) was declared as a day of mourning.
5. Thousands of people took bath in Ganga and marched on the streets of Calcutta singing Bande Mataram.

Question 3.
Throw light on the Farazi Movement.
OR
Highlight the different phases of the Farazi Movement under Haji Shariatullah and his son Dudu Mia.
Answer:
Farazi Movement under Haji Shariatullah:
The Farazi Movement was launched by Haji Shariatullah in 1818, in the parts of eastern Bengal. The movement advocated the participants to keep themselves away from conflict with the zamindars and subsequently with the British, who favoured the zamindars to suppress the peasant uprising.

Farazi Movement under Dudu Mian:
After the death of Shariatullah in 1839, the movement was led by his son Dudu Mian. He called upon the peasant not to pay tax. The movement became popular on a simple doctrine that land and all wealth should be equally enjoyed by the common mass. Dudu Mian laid emphasis on the egalitarian nature of religion and declared that “Land belongs to God’’ and collecting rent or levying taxes on it was therefore against the divine law. The movement spread far and wide and was joined by a huge number of peasants. There were violent crashes throughout 1840s and 1850s with the zamidars and planters. The movement continued to resist even after the death of Dudu Mian in 1862.

Question 4.
What were the main objectives and key demands of Indian National Congress?
Answer:
The main objectives of Indian National Congress were to develop and consolidate the sentiments of national unity and loyalty to Britain.

Some of the key demands were:

1. Creation of legislative councils at provincial and central level.
2. Reducing military expenditure.
3. Holding civil services exams in India as well as in England.
4. Promotion of Indian industries and an end to unfair tariffs and an end to unfair tariffs and excise duties.
5. Extension of trial by jury.
6. Increasing the number of elected members in the legislative council.
7. Police reforms
8. Reduction of Home charges.
9. Reconsideration of forest laws.
10. Separating Judicial and executive functions.

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Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.1

Question 1.
Prove the following identities.
(i) cot θ + tan θ = sec θ cosec θ
(ii) tan⁴ θ + tan² θ = sec⁴ θ – sec² θ
Answer:
(i) L. H. S = cot θ + tan θ
= \(\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta}\)
= \(\frac{\cos ^{2} \theta+\sin ^{2} \theta}{\sin \theta \cos \theta}\)
[cos² θ + sin² θ = 1]
= \(\frac{1}{\sin \theta \cos \theta}\)
= sec θ . cosec θ = R. H. S
∴ cot θ + tan θ = sec θ cosec θ

(ii) tan⁴ θ + tan² θ = sec⁴ θ – sec² θ
L.H.S = tan⁴ θ + tan² θ
= tan² θ (tan² θ + 1)
= tan² θ sec² θ
R.H.S = sec⁴ θ – sec² θ
= sec² θ (sec² θ – 1)
= sec² θ tan² θ
L.H.S = R.H.S
∴ tan⁴ θ + tan² θ = sec⁴ θ – sec² θ

Question 2.
Prove the following identities.
(i) \(\frac{1-\tan ^{2} \theta}{\cot ^{2} \theta-1}\) = tan² θ
(ii) \(\frac{\cos \theta}{1+\sin \theta}\) = sec θ – tan θ
Answer:
(i) \(\frac{1-\tan ^{2} \theta}{\cot ^{2} \theta-1}\) = tan² θ

(ii) \(\frac{\cos \theta}{1+\sin \theta}\) = sec θ – tan θ

Aliter:
L.H.S = \(\frac{\cos \theta}{1-\sin \theta}\)
[conjugate (1 – sin θ)]

Question 3.
Prove the following identities.

Solution:

Question 4.
Prove the following identities.
(i) sec⁶ θ = tan⁶ θ + 3 tan² θ sec² θ + 1
(ii) (sin θ + sec θ)² + (cos θ + cosec θ)² = 1 + (sec θ + cosec θ)²
Answer:
(i) sec⁶ θ = tan⁶ θ + 3 tan² θ sec² θ + 1
L.H.S = sec⁶ θ
= (sec² θ)³ = (1 + tan² θ)³
= 1 + (tan² θ)³ + 3 (1) (tan² θ) (1 + tan² θ) [(a + b)³ = a³ + b³ + 3 ab (a + b)]
= 1 + tan⁶ θ + 3 tan² θ(1 + tan² θ)
= 1 + tan⁶ θ + 3 tan² θ (sec² θ)
= 1 + tan⁶ θ + 3 tan² θ sec² θ
= tan⁶ θ + 3 tan² θ sec² θ + 1
L.H.S = R.H.S

(ii) (sin θ + sec θ)² + (cos θ + cosec θ)² = 1 + (sec θ + cosec θ)²
L.H.S = (sin θ + sec θ)² + (cos θ + cosec θ)²]
= [sin² θ + sec² θ + 2 sin θ sec θ + cos² θ + cosec² θ + 2 cos θ cosec θ]
= (sin² θ + cos² θ) + (sec² θ + cosec² θ) + 2 (sin θ sec θ + cos θ cosec θ)

= 1 + sec² θ + cosec² θ + 2 sec θ cosec θ
= 1 + (sec θ + cosec θ)²
L.H.S = R.H.S
∴ (sin θ + sec θ)² + (cos θ + cosec θ)² = 1 + (sec θ + cosec θ)²

Question 5.
Prove the following identities.
(i) sec⁴ θ (1 – sin⁴ θ) – 2 tan² θ = 1
(ii) \(\frac{\cot \theta-\cos \theta}{\cot \theta+\cos \theta}=\frac{\csc \theta-1}{\csc \theta+1}\)
Answer:
(i) L.H.S = sec⁴ θ (1 – sin⁴ θ) – 2 tan² θ

L.H.S = R.H.S
∴ sec⁴ θ (1 – sin⁴ θ) – 2 tan² θ = 1

(ii) \(\frac{\cot \theta-\cos \theta}{\cot \theta+\cos \theta}=\frac{\csc \theta-1}{\csc \theta+1}\)

Question 6.
Prove the following identities.


Answer:

Question 7.
(i) If sin θ + cos θ = \(\sqrt { 3 }\), then prove that tan θ + cot θ = 1.
(ii) If \(\sqrt { 3 }\) sin θ – cos θ = θ, then show that tan 3θ = \(\frac{3 \tan \theta-\tan ^{3} \theta}{1-3 \tan ^{2} \theta}\)
Answer:
sin θ + cos θ = \(\sqrt { 3 }\) (squaring on both sides)
(sin θ + cos θ)² = (\(\sqrt { 3 }\))²
sin² θ + cos² θ + 2 sin θ cos θ = 3
1 + 2 sin θ cos θ = 3
2 sin θ cos θ = 3 – 1
2 sin θ cos θ = 2
∴ sin θ cos θ = 1
L.H.S = tan θ + cot θ

L.H.S = R.H.S ⇒ tan θ + cot θ = 1

(ii) If \(\sqrt { 3 }\) sin θ – cos θ = 0
To prove tan 3θ = \(\frac{3 \tan \theta-\tan ^{3} \theta}{1-3 \tan ^{2} \theta}\)
\(\sqrt { 3 }\) sin θ – cos θ = 0
\(\sqrt { 3 }\) sin θ = cos θ
\(\frac{\sin \theta}{\cos \theta}=\frac{1}{\sqrt{3}}\)
tan θ = tan 30°
θ = 30°
L.H.S = tan 3θ°
= tan3 (30°)
= tan 90°
= undefined (∝)

∴ tan 3θ = \(\frac{3 \tan \theta-\tan ^{3} \theta}{1-3 \tan ^{2} \theta}\)

Question 8.
(i) If \(\frac{\cos \alpha}{\cos \beta}=m\) and \(\frac{\cos \alpha}{\cos \beta}=n\) then prove that (m2 + n2) cos2 β = n2
(ii) If cot θ + tan θ = x and sec θ – sec θ – cos θ = y, then prove that (x2y)2/3 – (xy2)2/3 = 1
Answer:
(i) L.H.S = (m² + n²) cos² β

L.H.S = R.H.S ⇒ ∴ (m² + n²) cos² β = n²

(ii) Given cot θ + tan θ = x sec θ – cos θ = y
x = cot θ + tan θ
x = \(\frac{1}{\tan \theta}\) + tan θ
= \(\frac{1+\tan ^{2} \theta}{\tan \theta}\) = \(\frac{\sec ^{2} \theta}{\tan \theta}\)

y = sec θ – cos θ
= \(\frac{1}{\cos \theta}-\cos \theta=\frac{1-\cos ^{2} \theta}{\cos \theta}\)
y = \(\frac{\sin ^{2} \theta}{\cos \theta}\)

Question 9.
(i) If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q (p² – 1) = 2 p
(ii) If sin θ (1 + sin² θ) = cos² θ, then prove that cos⁶ θ – 4 cos⁴ θ + 8 cos² θ = 4
Answer:
(i) p = sin θ + cos θ
p² = (sin θ + cos θ)²
= sin² θ + cos² θ + 2 sin θ cos θ = 1 + 2 sin θ cos θ
q = sec θ + cosec θ
= \(\frac{1}{\cos \theta}+\frac{1}{\sin \theta}=\frac{\sin \theta+\cos \theta}{\sin \theta \cos \theta}\)
L.H.S = q(p² – 1)

(ii) sin θ (1 + sin² θ) = cos² θ
sin θ (1 + 1 – cos² θ) = cos² θ
sin θ (2 – cos² θ) = cos² θ
Squaring on both sides,
sin² θ (2 – cos² θ)² = cos⁴ θ
(1 – cos² θ) (4 + cos⁴ θ – 4 cos² θ) = cos⁴ θ
4 cos⁴ θ – 4 cos² θ – cos⁶ θ + 4 cos⁴ θ = cos⁴ θ
4 + 5 cos⁴ θ – 8 cos² θ – cos⁶ θ = cos⁴ θ
– cos⁶ θ + 5 cos⁴ θ – cos⁴ θ – 8 cos² θ = -4
– cos⁶ θ + 4 cos⁴ θ – 8 cos² θ = -4
cos⁶ θ – 4 cos⁴ θ + 8 cos² θ = 4
Hence it is proved

Question 10.
If \(\frac{\cos \theta}{1+\sin \theta}\) = \(\frac { 1 }{ a } \), then prove that \(\frac{a^{2}-1}{a^{2}+1}\) = sin θ
Answer:

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Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 5 Coordinate Geometry Additional Questions

I. Multiple Choice Questions

Question 1.
If the three points (-3, 7), (a, 1), (-3, 2) are collinear then the value of “a” is
(1) 0
(2) -1
(3) -3
(4) 1
Answer:
(3) -3
Hint:
Since the three points are collinear
Area of a ∆ = 0

-3 + 2a – 21 – (7a – 3 – 6) = 0 ⇒ 2a – 24 – 7a + 9 = 0
– 5a – 15 = 0 ⇒ – 5(a + 3) = 0
a + 3 = 0 ⇒ a = -3

Question 2.
If A (5, 5), B (-5, 1), C (10, 7) lie in a straight line, then the area of ∆ ABC is …………….
(1) \(\frac { 13 }{ 2 } \) sq.units
(2) 9 sq.units
(3) 25 sq.units
(4) 0
Answer:
(4) 0
Hint:
Area of the ∆^le

Question 3.
In a rectangle ABCD, area of ∆ ABC is \(\frac { 31 }{ 2 } \) sq. units. Then the area of rectangle is ……………
(1) 62 sq. units
(2) 31 sq. units
(3) 60 sq. units
(4) 30 sq. units
Answer:
(2) 31 sq. units
Hint:
In a rectangle area of ∆ ABC and area of ∆ ACD are equal.
Area of rectangle ABCD = 2 × \(\frac { 31 }{ 2 } \) = 31 sq.units

Question 4.
If the points (k, 2k), (3k, 3k) and (3,1) are collinear, then k is ……………..
(1) \(\frac { 1 }{ 3 } \)
(2) – \(\frac { 1 }{ 3 } \)
(3) \(\frac { 2 }{ 3 } \)
(4) – \(\frac { 2 }{ 3 } \)
Answer:
(2) – \(\frac { 1 }{ 3 } \)
Hint:
Since the three points are collinear. Area of a ∆ = 0

3k² + 3k + 6k – (6k² + 9k + k) = 0 ⇒ 3k² + 9k – 6k² – 10k = 0
-3 k² – k = 0 ⇒ -k(3k + 1) = 0
3k + 1 = 0 ⇒ 3 k = -1 ⇒ k = – \(\frac { 1 }{ 3 } \)

Question 5.
If the area of the triangle formed by the points (x, 2x), (-2, 6) and (3, 1) is 5 square units then x = ………….
(1) 2
(2) \(\frac { 3 }{ 5 } \)
(3) 3
(4) 5
Answer:
(1) 2
Hint:
Area of the triangle = 5 sq. units

6x – 2 + 6x – (-4x + 18 + x) = 10 ⇒ 12x – 2 – (-3x + 18) = 10
12x – 2 + 3x – 18 = 10
15x – 20 = 10 ⇒ 15x = 10 + 20 = 30
x = \(\frac { 30 }{ 15 } \) = 2

Question 6.
The slope of a line parallel to y-axis is equal to …………..
(1) 0
(2) -1
(3) 1
(4) not defined
Answer:
(4) not defined

Question 7.
In a rectangle PQRS, the slope of PQ = \(\frac { 5 }{ 6 } \) then the slope of RS is ………..
(1) \(\frac { -5 }{ 6 } \)
(2) \(\frac { 6 }{ 5 } \)
(3) \(\frac { -6 }{ 5 } \)
(4) \(\frac { 5 }{ 6 } \)
Answer:
\(\frac { 5 }{ 6 } \)
Hint:
In a rectangle opposite sides are parallel.
∴ Slope of the line RS is \(\frac { 5 }{ 6 } \).

Question 8.
The y – intercept of the line y = 2x is ………
(1) 1
(2) 2
(3) \(\frac { 1 }{ 2 } \)
(4) 0
Answer:
(4) 0

Question 9.
The straight line given by the equation y = 5 is …………..
(1) Parallel to x – axis
(2) Parallel to y – axis
(3) Passes through the origin
(4) None of these
Answer:
(1) Parallel to x – axis

Question 10.
The x – intercept of the line 2x – 3y + 5 = 0 is ………….
(1) \(\frac { 5 }{ 2 } \)
(2) \(\frac { -5 }{ 2 } \)
(3) \(\frac { 2 }{ 5 } \)
(4) \(\frac { -2 }{ 5 } \)
Answer:
(2) \(\frac { -5 }{ 2 } \)
Hint:
2x – 3y + 5 = 0 ⇒ 2x – 3y = – 5

Question 11.
The lines 3x – 5y + 1 = 0 and 5x + ky + 2 = 0 are perpendicular if the value of k is ………..
(1) -5
(2) 3
(3) -3
(4) 5
Answer:
(2) 3
Hint:
Slope of the first line (m₁) = \(\frac { -3 }{ -5 } \) = \(\frac { 3 }{ 5 } \)
Slope of the second line (m₂) = \(\frac { -5 }{ k } \)
Since the two lines are perpendicular.
m₁ × m₂ = -1
\(\frac { 3 }{ 5 } \) × \(\frac { -5 }{ k } \) = -1 ⇒ \(\frac { -3 }{ k } \) = -1
-k = -3 ⇒ The value of k = 3

Question 12.
If x – y = 3 and x + 2y = 6 are the diameters of a circle then the centre is at the point ………..
(1) (0, 0)
(2) (1, 2)
(3) (1, -1)
(4) (4, 1)
Answer:
(4) (4, 1)
Hint:
Centre of the circle is the intersection of the two diameters.

Centre of the circle is (4, 1)

Question 13.
The line 4x + 3y – 12 = 0 meets the x-axis at the point ……….
(1) (4, 0)
(2) (3, 0)
(3) (-3, 0)
Answer:
(2) (3,0)
Hint:
4x + 3y – 12 = 0 meet the x-axis the value of y = 0
4x- 12 = 0 ⇒ 4x = 12
x = \(\frac { 12 }{ 4 } \) = 3 ⇒ The point is (3, 0)

Question 14.
The equation of a straight line passing through the point (2, -7) and parallel to x-axis is ……………….
(1) x = 2
(2) x = -7
(3) y = -7
(4) y = 2
Answer:
(3) y = -7
Hint:
Equation of a line parallel to x-axis is y = -7

Question 15.
The equation of a straight line having slope 3 and y intercept – 4 is ………………
(1) 3x – y – 4 = 0
(2) 3x + y – 4 = 0
(3) 3x – y + 4 = 0
(4) 3x – y + 4 = 0
Answer:
(1) 3x – y – 4 = 0
Hint. The equation of a line is y = mx + c
y = 3 (x) + (-4) ⇒ y = 3x – 4
3x – y – 4 = 0

II. Answer the following questions:

Question 1.
If the points (3, – 4) (1, 6) and (- 2, 3) are the vertices of a triangle, find its area.
Answer:
Let the vertices A (3, – 4), B (1, 6) and C (- 2, 3)

Area of ∆ ABC = \(\frac { 1 }{ 2 } \) [x₁y₂ + x₂y₃ + x₃y₁, – (x₂y₁ + x₃y₂ + x₁y₃)]

Area of a ∆ = 18 sq. units

Question 2.
If the area of the triangle formed by the points (1,2) (2,3) and (a, 4) is 8 sq. units, find a.
Answer:
Area of a triangle = 8 sq. units.

\(\frac { 1 }{ 2 } \) [x₁y₂ + x₂y₃ + x₃y₁ – (x₂y₁ + x₃y₂ + x₁y₃)] = 8.
\(\frac { 1 }{ 2 } \) [3 + 8 + 2a – (4 + 3a + 4)] = 8
11 + 2a – 8 – 3a= 16 ⇒ – a + 3 = 16
– a = 16 – 3 ⇒ a = -13
The value of a = -13

Question 3.
If the points A (2, 5), B (4, 6) and C (8, a) are collinear find the value of “a” using slope concept.
Answer:
Since the three points are collineal
Slope of a line = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Slope of AB = Slope of BC
\(\frac { 6-5 }{ 4-2 } \) = \(\frac { a-6 }{ 8-4 } \) ⇒ \(\frac { 1 }{ 2 } \) = \(\frac { a-6 }{ 4 } \) ⇒ 2a – 12 = 4 ⇒ 2a = 16
a = \(\frac { 16 }{ 2 } \) = 8 ⇒ The value of a = 8

Question 4.
If the points (x,y) is collinear with the points (a, 0) and (0, b) then prove that \(\frac { x }{ a } \) + \(\frac { y }{ b } \) = 1
Answer:
Let A (x, y), B (a, 0), C(0, b)
Since the three points are collinear
Slope of AB = Slope of BC
Slope of a line = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
\(\frac { 0-y }{ a-x } \) = \(\frac { b-0 }{ 0-a } \)
\(\frac { -y }{ a-x } \) = \(\frac { b }{ -a } \)
ay = b (a – x)
ay = ba – bx
ay + bx = ab
Divided by ab
\(\frac { ay }{ ab } \) + \(\frac { bx }{ ab } \) = \(\frac { ab }{ ab } \)
\(\frac { y }{ b } \) + \(\frac { x }{ a } \) = 1 ⇒ \(\frac { x }{ a } \) + \(\frac { y }{ b } \) = 1

Question 5.
A straight line passes through (1, 2) and has the equation y – 2x – k = 0. Find k.
Answer:
The given line is y – 2x – k = 0
It passes through (1,2)
(2) -2 (1) -k = 0 ⇒ 2 – 2 – k = 0
0 – k = 0 ⇒ k = 0
The value of k = 0

Question 6.
If a line passes through the mid point of AB where A is (3, 0) and B is (5, 4) and makes an angle 60° with x – axis find its equation.
Answer:

Slope of a line = tan 60°
= \(\sqrt { 3 }\)
Equation of a line is y – y₁ = m (x – x₁)
y – 2 = \(\sqrt { 3 }\) (x – 4)
y – 2 = \(\sqrt { 3 }\) x – 4 \(\sqrt { 3 }\)
\(\sqrt { 3x }\) – y + 2 – 4\(\sqrt { 3 }\) = 0

Question 7.
Find the equation of the line through (3, 2) and perpendicular to the line joining (4, 5) and (1,2)
Answer:
Slope of a line = \(\frac { 2-5 }{ 1-4 } \) ⇒ \(\frac { -3 }{ -3 } \) = 1
Slope of the line perpendicular to it is – 1
Equation of the line joining -1 and (3, 2) is
y – y₁ = m (x – x₁) ⇒ y – 2 = -1(x – 3)
y – 2 = -x + 3 ⇒ x + y – 5 = 0

Question 8.
P and Q trisect the line segment joining the points (2, 1) and (5, – 8). If the point P lies on 2x – y + k = 0, then find the value of k.
Answer:

A line divides internally in the ratio 1 : 2
A line divide internally in the ratio l : m

The point P = (\(\frac { 5+4 }{ 3 } \),\(\frac { -8+2 }{ 3 } \))
= (\(\frac { 9 }{ 3 } \),\(\frac { -6 }{ 3 } \)) = (3, -2)
The given line 2x – y + k = 0 passes through the point (3,-2)
2 (3) – (- 2) + k = 0
6 + 2 + k = 0
8 + k = 0
k = – 8
The value of k = – 8

Question 9.
The line 4x + 3y – 12 = 0 intersect the X, Y – axis at A and B respectively. Fine the area of ∆AOB.
Answer:
The equation of the line AB is 4x + 3y – 12 = 0

4x + 3y = 12
\(\frac { 4x }{ 12 } \) + \(\frac { 3y }{ 12 } \) = 1 ⇒ \(\frac { x }{ 3 } \) + \(\frac { y }{ 4 } \) = 1
The point A is (3, 0) (it intersect the X – axis)
and B is (0, 4) (it intersect the Y – axis)
Area of ∆ AOB = \(\frac { 1 }{ 2 } \) [x₁y₂ + x₂y₃ + x₃y₁ (x₂y₁ + x₃y₂ + x₁y₃)]

Question 10.
Find the equation of the line passing through (4, 5) and making equal intercept in the axes.
Answer:
Let the equal intercept on the axes be a, a.
Equation of the line is \(\frac { x }{ a } \) + \(\frac { y }{ a } \) = 1 (Given equal intercepts)
The line passes through (4, 5)
\(\frac { 4 }{ a } \) + \(\frac { 5 }{ a } \) = 1 ⇒ \(\frac { 9 }{ a } \) = 1 ⇒ a = 9
The equation of the line is \(\frac { x }{ 9 } \) + \(\frac { y }{ 9 } \) = 1
Multiply by 9
x + y – 9 = 0

Question 11.
Find the equation of the line passing through (2, – 1) and whose intercepts on the axes are equal in magnitude but opposite in sign.
Answer:
Let the x – intercept be “a” and y intercept be = “-a”
The equation of the line is
\(\frac { x }{ a } \) + \(\frac { y }{ -a } \) = 1 (y – intercept is – a)
\(\frac { x }{ a } \) – \(\frac { y }{ a } \) = 1
It passes through (2, -1)
\(\frac { 2 }{ a } \) – \(\frac { (-1) }{ a } \) = 1
\(\frac { 2 }{ a } \) + \(\frac { 1 }{ a } \) = 1 ⇒ \(\frac { 3 }{ a } \) = 1
a = 3
The equation of the line is
\(\frac { x }{ a } \) + \(\frac { y }{ b } \) = 1
\(\frac { x }{ 3 } \) + \(\frac { y }{ -3 } \) = 1 ⇒ \(\frac { x }{ 3 } \) – \(\frac { y }{ 3 } \) = 1
x – y = 3
The equation is x – y – 3 = 0

Question 12.
The straight line cuts the coordinate axes at A and B. If the mid point of AB is (3,2) then find the equation of AB.
Answer:
Let the point A be (a, 0) and B be (0, b)


The point A (6, 0) and B (0, 4)
Equation of the line AB is

III. Answer the following questions

Question 1.
If the coordinates of two points A and B are (3, 4) and (5, – 2) respectively. Find the ‘ coordinates of any point “c”, if AC = BC and Area of triangle ABC = 10 sq. units.
Answer:
Let the coordinates C be (a, 6) then AC = BC
AC² = BC²
(a – 3)² + (b – 4)² = (a – 5)² + (b + 2)²
a² + 9 – 6a + b² + 16 – 8b = a² + 25 – 10a + b² + 4 – 4b
a² + b² + 25 – 6a – 86 = a² + b² + 29 – 10a + 4b

25 – 6a – 8b = 29 – 10a + 46
4a – 12b = 4 ⇒ a – 3b = 1 ………… (1)
Area of ∆ ABC = 10 sq. units
\(\frac { 1 }{ 2 } \) [x₁y₂ + x₂y₃ + x₃y₁ – (x₂y₁ + x₃y₂ + x₁y₃)] = 10

-6 + 5b + 4a – (20 – 2a + 3b) = 20
-6 + 5b + 4a – 20 + 2a – 3b = 20
6a + 2b – 26 = 20 ⇒ 6a + 2b = 46

Substitute the value of a = 7 in (2)
3 (7) + b = 23 ⇒ b = 23 – 21 = 2
The coordinate C is (7, 2)

Question 2.
The four vertices of a Quadrilateral are (1,2) (- 5,6) (7, – 4) and (k, – 2) taken in order. If the area of the Quadrilateral is 9 sq. units, find the value of k.
Answer:
Let A (1, 2) B (- 5, 6) C (7, – 4) and D (k, – 2)
Area of the
Quadrilateral ABCD = \(\frac { 1 }{ 2 } \)[(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) – (x₂y₁ + x₃y₂ + x₄y₃ + x₁y₄)]

Area of the Quadrilateral ABCD = 3k – 9
Given area of a Quadrilateral is 9 sq. units.
3k – 9 = 9 ⇒ 3k = 18 ⇒ k = \(\frac { 18 }{ 3 } \) = 6
The value of k = 6

Question 3.
Find the area of a triangles whose three sides are having the equations x + y = 2, x – y = 0 and x + 2y – 6 = 0.
Answer:
Find the three vertices of the triangles by solving their equation.
To find vertices A


Substitute the value of y = 4 in (1)
x + 4 = 2 ⇒ x = 2 – 4 = -2
The vertices A is (- 2, 4)
To find vertices B

Substitute the value of x = 1 in (1)
1 + y = 2 ⇒ y = 2 – 1 = 1
The vertices B is (1, 1)
To find vertices C

y = \(\frac { 6 }{ 3 } \) = 2
Substitute the value y = 2 in (3)
x – 2 = 0 ⇒ x = 2
The vertices C is (2, 2)

Area of the ∆ BC = 3 sq. units

Question 4.
Verify the Median of a triangle divides into two triangles of equal areas whose vertices are A (4, – 6), B (3, – 2) and C (5, 2)
Answer:

Let D be the mid point of AC .
Mid point of AC = (\(\frac { 5+4 }{ 2 } \),\(\frac { 2-6 }{ 2 } \)) = (\(\frac { 9 }{ 2 } \),-2)
Area of the triangle = \(\frac { 1 }{ 2 } \) [x₁y₂ + x₂y₃ + x₃y₁ – (x₂y₁ + x₃y₂ + x₁y₃)]

Area of ∆ ADB = Area of ∆ BDC
A median divides the triangle of equal areas.

Question 5.
Find the area of the ∆ ABC with A (1, – 4) and the mid points of sides through A being (2,-1) and (0,-1)
Answer:
Let the coordinates of B and C are (a, b) and (c, d) respectively.
Sides through A are AB and AC

Mid point of AB = (\(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\))
(2, -1) = (\(\frac { 1+a }{ 2 } \),\(\frac { -4+b }{ 2 } \))
\(\frac { 1+a }{ 2 } \) = 2
1 + a = 4
a = 4 – 1
= 3
The point B is (3,2)
\(\frac { -4+b }{ 2 } \) = -1
-4 + b = -2
b = -2 + 4
= 2
Mid point of AC = (\(\frac { 1+c }{ 2 } \),\(\frac { -4+d }{ 2 } \))
(0,-1) = (\(\frac { 1+c }{ 2 } \),\(\frac { -4+d }{ 2 } \))
\(\frac { 1+c }{ 2 } \) = 0
1 + c = 0
c = 0 – 1
= – 1
The point C is (-1,2)
\(\frac { -4+d }{ 2 } \) = -1
– 4 + d = -2
d = – 2 + 4
= 2
Thus the coordinates of the vertices of ∆ ABC are A (1, – 4) B (3, 2) and C (- 1, 2)
Area of ∆ ABC = \(\frac { 1 }{ 2 } \) [x₁y₂ + x₂y₃ + x₃y₁ – (x₂y₁ + x₃y₂ + x₁y₃)]

Area of ∆ ABC = 12 sq. units

Question 6.
Find the equation of the straight lines passing through (- 3, 10) whose sum of the intercepts is 8.
Answer:
Let the “x” intercept be “a” and y intercept be “b”
Sum of the intercepts = 8
a + b = 8 ⇒ b = 8 – a
Equation of a line is \(\frac { x }{ a } \) + \(\frac { y }{ b } \) = 1 ⇒ \(\frac { x }{ a } \) + \(\frac { y }{ 8-a } \) = 1
It passes through (-3,10)
\(\frac { -3 }{ a } \) + \(\frac { 10 }{ 8-a } \) = 1
\(\frac { -3(8-a)+10a }{ a(8-a) } \) = 1
-24 + 3a + 10a = 8a – a²
-24 + 13a = 8a – a²
a² + 5a – 24 = 0 ⇒ (a + 8) (a – 3) = 0
a + 8 = 0 (or) a – 3 = 0 ⇒ a = -8 (or) a = 3
The equation of a line is a
a = -8
\(\frac { x }{ -8 } \) + \(\frac { y }{ 8+8 } \) = 1
\(\frac { x }{ -8 } \) + \(\frac { y }{ 16 } \) = 1
-2x + y = 16
2x – y + 16 = 0
a = 3
\(\frac { x }{ 3 } \) + \(\frac { y }{ 5 } \) = 1
5x + 3y = 15
5x + 3y – 15 = 0
The equation of the lines are 2x – y + 16 = 0 (or) 5x + 3y – 15 = 0.

Question 7.
If (5, – 3), (- 5, 3), (6, 6) are the mid points of the sides of a triangle, find the equation of the sides.
Answer:
Since D, E, F are the mid points of ∆ ABC
EF || AB, FD || BC and DE || AC
Slope of a line = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Slope of EF = \(\frac { 6-3 }{ 6+5 } \) = \(\frac { 3 }{ 11 } \)
Since EF || AB; Slope of AB = \(\frac { 3 }{ 11 } \)
Equation of AB is
y – y₁ = m (x – x₁)
y + 3 = \(\frac { 3 }{ 11 } \) (x – 5)
3x – 15 = 11y + 33
3x – 11y – 15 – 33 = 0
3x – 11y – 48 = 0
Slope of DE = Slope of AC
Slope of DE = \(\frac { 3+3 }{ -5-5 } \) = \(\frac { 6 }{ -10 } \) = –\(\frac { 6 }{ 10 } \) = –\(\frac { 3 }{ 5 } \)
Slope of AC = – \(\frac { 3 }{ 5 } \)
Equation of AC is
y – y₁ = m (x – x₁)

y – 6 = – \(\frac { 3 }{ 5 } \) (x – 6) ⇒ 5y – 30 = -3x + 18
3x + 5y – 30 – 18 = 0 ⇒ 3x + 5y – 48 = 0
Slope of DF = Slope of BC
Slope of DF = \(\frac { 6+3 }{ 6-5 } \) = \(\frac { 9 }{ 1 } \) = 9
Slope of BC = 9
Equation of the line BC is
y – y₁ = m(x – x₁)
y – 3 = 9 (x + 5) ⇒ 9x + 45 = y – 3
9x – y + 45 + 3 = 0 ⇒ 9x – y + 48 = 0
Equation of the sides are
3x – 11y – 48 = 0 ; 9x – y + 48 = 0 and 3x + 5y – 48 = 0

Question 8.
Find the equation of the straight line passing through the point of intersection of the lines 5x – 8y + 23 = 0 and 7x + 6y – 71 = 0 and is perpendicular to the line joining the points (5,1) and (-2, 2)
Answer:

Substitute the value of x in (1)
5 (5) – 8y = – 23 ⇒ 25 – 8y = – 23
-8y = – 23 – 25 ⇒ -8y = – 48
y = \(\frac { 48 }{ 8 } \) = 6
The point of intersection is (5,6)
Slope of a line = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Slope of the line joining the points (5,1) and (-2,2) = \(\frac { 2-1 }{ -2-5 } \)
= \(\frac { 1 }{ -7 } \) = – \(\frac { 1 }{ 7 } \)
Slope of the perpendicular line is = 7
Equation of a line is
y – y₁ = m(x – x₁) ⇒ y – 6 = 7 (x – 5)
y – 6 = 7x – 35 ⇒ -7x + y – 6 + 35 = 0
7x – y – 29 = 0

Question 9.
Find the equation of the line passing through the point of intersection of 4x – y – 3 = 0 and x + y – 2 = 0 and perpendicular to 2x – 5y + 3 = 0.
Answer:

x = \(\frac { 5 }{ 5 } \) = 1
Substitute the value of x = 1 in (2)
1 + y = 2
y = 2 – 1 = 1
The point of intersection is (1, 1)
Any line perpendicular to 2x – 5y + 3 = 0 is
5x + 2y + k = 0
It passes through (1,1)
5(1) + 2(1) + k = 0 ⇒ 5 + 2 + k = 0
7 + k = 0 ⇒ k = -7
The line is 5x + 2y – 7 = 0

Question 10.
Find the equation of the line through the point of intersection of the lines 2x + y – 5 = 0 and x + y – 3 = 0 and bisecting the line segment joining the points (3, – 2) and (- 5, 6).
Answer:

x = 2
Substitute the value of x = 2 in (2)
2 + y = 3
y = 3 – 2 = 1
The point of intersection is (2, 1)
Mid point of the line joining the points (3,-2) and (-5,6)

Mid point of the line
Equation of the line joining the points (2, 1) and (-1,2) is

x – 2 = -3 (y – 1)
x – 2 = -3y + 3
x + 3y – 5 = 0
The equation of the line is x + 3y – 5 = 0

Students can download Maths Chapter 6 Trigonometry Ex 6.4 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.4

Question 1.
From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. Find the height of the second tree, (\(\sqrt { 3 }\) = 1.732)
Answer:
Let the height of the second tree be “h”
ED = (h – 13) m
Let AB = x m
In the right ∆ ABC, tan 30° = \(\frac { BC }{ AB } \)
\(\frac{1}{\sqrt{3}}\) = \(\frac { 13 }{ x } \)
x = 13 \(\sqrt { 3 }\) ……..(1)

In the right ∆ CED, tan 45° = \(\frac { DE }{ EC } \)
1 = \(\frac { h-13 }{ x } \)
x = h – 13 ……..(2)
From (1) and (2) we get
h – 13 = 13 \(\sqrt { 3 }\) ⇒ h = 13 \(\sqrt { 3 }\) + 13
= 13 × 1.732 + 13
= 22.52 + 13 = 35.52 m
∴ Height of the second tree = 35.52 m

Question 2.
A man is standing on the deck of a ship, which is 40 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30° . Calculate the distance of the hill from the ship and the height of the hill. (\(\sqrt { 3 }\) = 1.732)
Answer:
Let the height of the hill BE be “h” m and the distance of the hill from the ship be “x” m
In the right ∆ ABD
tan 30° = \(\frac { AD }{ DB } \)
\(\frac{1}{\sqrt{3}}=\frac{40}{x}\)
x = 40 \(\sqrt { 3 }\) ……..(1)
In the right ∆ CDE
tan 60° = \(\frac { CE }{ DC } \)
\(\sqrt { 3 }\) = \(\frac { h-40 }{ x } \)
x = \(\frac{h-40}{\sqrt{3}}\) ……..(2)

From (1) and (2) we get
\(\frac{h-40}{\sqrt{3}}\) = 40\(\sqrt { 3 }\)
h – 40 = 40 × 3
h = 120 + 40 = 160 m
Height of the hill = 160 m
Distance of the hill from the ship = 40 × \(\sqrt { 3 }\) = 40 × 1.732 = 69.28 m

Question 3.
If the angle of elevation of a cloud from a point ‘h’ metres above a lake is θ1 and the angle of depression of its reflection in the lake is θ2. Prove that the height that the cloud is located from the ground is \(\frac{h\left(\tan \theta_{1}+\tan \theta_{2}\right)}{\tan \theta_{2}-\tan \theta_{1}}\)
Answer:
Let P be the cloud and Q be its reflection.
Let A be the point of observation such that AB = h
Let the height of the cloud be x. (PS = x)
PR = x – h and QR = x + h

Let AR = y
In the right ∆ ARP, tan θ₁ = \(\frac { PR }{ AR } \)
tan θ₁ = \(\frac { x-h }{ y } \) ………(1)
In the ∆ AQR,
tan θ₂ = \(\frac { QR }{ AR } \)
tan θ₂ = \(\frac { x+h }{ y } \) ……….(2)
Add (1) and (2)

Question 4.
The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30° . If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiations control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms.
Answer:
Let the height of the cell phone tower be “h” m
AD is the height of the apartment; AD = 50 m
Let AB be “x”
In the right triangle ABC
tan 60° = \(\frac { BC }{ AB } \)
\(\sqrt { 3 }\) = \(\frac { h }{ x } \)

x = \(\frac{h}{\sqrt{3}}\) …….(1)
In the right triangle ABD, tan 30° = \(\frac { AD }{ AB } \)
\(\frac{1}{\sqrt{3}}\) = \(\frac { 50 }{ x } \)
x = 50 \(\sqrt { 3 }\) ……(2)
From (1) and (2) We get
\(\frac{h}{\sqrt{3}}\) = 50 \(\sqrt { 3 }\)
h = 50\(\sqrt { 3 }\) × \(\sqrt { 3 }\) = 50 × 3 = 150
Height of the cell phone tower is 150 m.
Yes, the cell phone tower meets the radiation norms.

Question 5.
The angles of elevation and depression of the top and bottom of a lamp post from the top of a 66 m high apartment are 60° and 30° respectively. Find
(i) The height of the lamp post.
(ii) The difference between height of the lamp post and the apartment.
(iii) The distance between the lamp post and the apartment. (\(\sqrt { 3 }\) = 1.732)
Answer:
(i) Let the height of the lamp post AE be “h” m
DE = h – 66
Let AB be “x”
In the right ∆ ABC, tan 30° = \(\frac { BC }{ AB } \)
\(\frac{1}{\sqrt{3}}=\frac{66}{x}\)
x = 66 \(\sqrt { 3 }\) ……(1)

In the right ∆ CDE, tan 60° = \(\frac { DE }{ DC } \)
\(\sqrt { 3 }\) = \(\frac { h-66 }{ x } \) ⇒ \(\sqrt { 3 }\) x = h – 66
x = \(\frac{h-66}{\sqrt{3}}\) ………….(2)
From (1) and (2) we get
\(\frac{h-66}{\sqrt{3}}\) = 66 \(\sqrt { 3 }\)
h – 66 = 66 \(\sqrt { 3 }\) × \(\sqrt { 3 }\) = 66 × 3
h – 66 = 198 ⇒ h = 198 + 66
h = 264 m
(i) the height of the lamp post = 264 m
(ii) Difference of the height of lamp post and apartment = 264 – 66
= 198 m
(ii) Distance between the lamp post and the apartment = 66 \(\sqrt { 3 }\) m
= 66 × 1.732 = 114.31 m

Question 6.
Three villagers A, B and C can see each other across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30°. Calculate:
(i) the vertical height between A and B.
(ii) the vertical height between B and C. (tan 20° = 0 .3640, \(\sqrt { 3 }\) = 1. 732)
Answer:
Let AD is the vertical height between A and B
In the right ∆ ABD

tan 20° = \(\frac { AD }{ BD } \)
0.3640 = \(\frac { AD }{ 8 } \)
AD = 0.3640 × 8 = 2.912 km
∴ AD = 2.91 km
CE is the vertical height between C and B
In the right ∆ BCE, tan 30° = \(\frac { CE }{ BE } \)
\(\frac{1}{\sqrt{3}}=\frac{C E}{12} \Rightarrow \sqrt{3} C E=12\)
CE = \(\frac{12}{\sqrt{3}}=\frac{12 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}=\frac{12 \times \sqrt{3}}{3}\)
= 4 \(\sqrt { 3 }\) = 4 × 1.732 = 6.928
= 6.93 km
(i) The vertical height between A and B = 2.91 km
(ii) The vertical height between B and C = 6.93 km

Students can download Maths Chapter 6 Trigonometry Ex 6.3 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.3

Question 1.
From the top of a rock 50 \(\sqrt { 3 }\) m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock.
Answer:
Let the distance of the car from the rock is “x” m

In the right ∆ ABC, tan 30° = \(\frac { AB }{ BC } \)
\(\frac{1}{\sqrt{3}}=\frac{50 \sqrt{3}}{x}\)
x = 50 \(\sqrt { 3 }\) × \(\sqrt { 3 }\) = 50 × 3
= 150 m
∴ Distance of the car from the rock = 150 m

Question 2.
The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.
Answer:
Let the height of the first building AD be “x” m
∴ EC = 120 – x
In the right ∆ CDE,
tan 45° = \(\frac { CE }{ CD } \)

1 = \(\frac { 120-x }{ 70 } \) ⇒ 70 = 120 – x
x = 50 cm
∴ The height of the first building is 50 m

Question 3.
From the top of the tower 60 m high the anles of depression the top and bottom of a vertical lamp post are observed be 38° and 60° respectively
Find the height of the lamp post. (tan 38° = 0.7813,\(\sqrt { 3 }\) = 1.732)
Answer:
Let the height of the lamp post be “h”
The height of the tower (BC) = 60 m
∴ EC = 60 – h
Let AB be x
In the right ∆ ABC,

tan 60° = \(\frac { BC }{ AB } \)
\(\sqrt { 3 }\) = \(\frac { 60 }{ x } \)
x = \(\frac{60}{\sqrt{3}}\) ……..(1)
In the right ∆ DEC, tan 38° = \(\frac { EC }{ DE } \)
0.7813 = \(\frac { 60-h }{ x } \)
x = \(\frac { 60-h }{ 0.7813 } \) …….(2)
From (1) and (2) we get
\(\frac{60}{\sqrt{3}}\) = \(\frac { 60-h }{ 0.7813 } \)
60 × 0.7813 = 60 \(\sqrt { 3 }\) – \(\sqrt { 3 }\) h
\(\sqrt { 3 }\) h = 60 \(\sqrt { 3 }\) – 46.88
= 60 × 1.732 – 46.88
= 103.92 – 46.88
1.732 h = 57.04 ⇒ h = \(\frac { 57.04 }{ 1.732 } \)
h = \(\frac { 570440 }{ 1732 } \) = 32.93 m
∴ Height of the lamp post = 32.93 m

Question 4.
An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are
60° and 30° respectively. Find the distance between the two boats. (\(\sqrt { 3 }\) = 1.732)
Answer:
C and D are the position of the two boats.
Let the distance between the two boats be “x”
Let BC = y
∴ BD = (x + y)

In the right ∆ ABC, tan 30° = \(\frac { AB }{ BD } \)
\(\frac{1}{\sqrt{3}}\) = \(\frac { 1800 }{ x+y } \)
x + y = 1800 \(\sqrt { 3 }\)
y = 1800 \(\sqrt { 3 }\) – x ……(1)
In the right ∆ ABC, tan 60° = \(\frac { AB }{ BC } \)
\(\sqrt { 3 }\) = \(\frac { 1800 }{ y } \)
y = \(\frac{1800}{\sqrt{3}}\) ……….(2)
From (1) and (2) we get
\(\frac{1800}{\sqrt{3}}\) = 1800 \(\sqrt { 3 }\) – x
1800 = 1800 × 3 – \(\sqrt { 3 }\)x
\(\sqrt { 3 }\)x = 5400 – 1800
x = \(\frac{3600}{\sqrt{3}}=\frac{3600 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}=\frac{3600 \times \sqrt{3}}{3}\)
= 1200 × 1.732 = 2078.4 m
Distance between the two boats = 2078.4 m

Question 5.
From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it are observed to be 30° and 60°. If the height of the lighthouse is h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is \(\frac{4 h}{\sqrt{3}}\) m.
Answer:
A and C be the position of two ships.
Let AB be x and BC be y. Distance between the two ships is x + y

In the right ∆ ABD, tan 60° = \(\frac { BD }{ AB } \)
\(\sqrt { 3 }\) = \(\frac { h }{ x } \)
x = \(\frac{h}{\sqrt{3}}\) ……(1)
In the right ∆ BCD,
tan 30° = \(\frac { BD }{ BC } \)
\(\frac{1}{\sqrt{3}}\) = \(\frac { h }{ y } \)
y = \(\sqrt { 3 }\) h
Distance between the two ships (x + y) = \(\frac{h}{\sqrt{3}}+\sqrt{3} h\)
= \(\frac{h+3 h}{\sqrt{3}}=\frac{4 h}{\sqrt{3}}\)
Hence it is verified

Question 6.
A lift in a building of height 90 feet with transparent glass walls is descending from the top of the building. At the top of the building, the angle of depression to a fountain in the garden is 60°. Two minutes later, the angle of depression reduces to 30°. If the fountain is 30 \(\sqrt { 3 }\) feet from the entrance of the lift, find the speed of the lift which is descending.
Answer:
Let the speed of the lift is “x” feet / minute
Distance AB = 2 x feet (speed × time)
BC = (90 – 2x)
In the right ∆ BCD,

tan 30° = \(\frac { BC }{ DC } \)
\(\frac{1}{\sqrt{3}}=\frac{90-2 x}{30 \sqrt{3}}\)
\(\sqrt { 3 }\) (90 – 2x) = 30\(\sqrt { 3 }\)
(90 – 2x) = \(\frac{30 \sqrt{3}}{\sqrt{3}}\) ⇒ (90 – 2x) = 30
2x = 60
x = \(\frac { 60 }{ 2 } \) = 30
x = 30 feet/minute
Speed of the lift = 30 feet / minute (or) [ \(\frac { 30 }{ 60 } \) second) 0.5 feet / second

Students can download Maths Chapter 6 Trigonometry Ex 6.2 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.2

Question 1.
Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of a tower of height 10 \(\sqrt { 3 }\) m.
Answer:
Height of the tower (AC) = 10 \(\sqrt { 3 }\) m
Distance between the base of the tower and point of observation (AB) = 30 m
Let the angle of elevation ∠ABC be θ
In the right ∆ ABC, tan θ = \(\frac { AC }{ AB } \)
= \(\frac{10 \sqrt{3}}{30}=\frac{\sqrt{3}}{3}\)

tan θ = \(\frac{1}{\sqrt{3}}\) = tan 30°
∴ Angle of inclination is 30°

Question 2.
A road is flanked on either side by continuous rows of houses of height 4\(\sqrt { 3 }\) m with no space in between them. A pedestrian is standing on the median of the road facing a row house. The angle of elevation from the pedestrian to the top of the house is 30° . Find the width of the road.
Answer:
Let the mid point of the road AB is “P” (PA = PB)
Height of the home = 4\(\sqrt { 3 }\) m
Let the distance between the pedestrian and the house be “x”
In the right ∆ APD, tan 30° = \(\frac { AD }{ AP } \)

\(\frac{1}{\sqrt{3}}=\frac{4 \sqrt{3}}{x}\)
x = 4 \(\sqrt { 3 }\) × \(\sqrt { 3 }\) = 12 m
∴ Width of the road = PA + PB
= 12 + 12
= 24 m

Question 3.
To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and if he is 5 m away from the wall, what is the height of the window? (\(\sqrt { 3 }\) = 1.732)
Answer:
Let the height of the window FE be “h” m
Let FC be “x” m
∴ EC = (h + x) m

In the right ∆ CDF, tan 45° = \(\frac { CE }{ CD } \)
1 = \(\frac { x }{ 5 } \) ⇒ x = 5
In the right ∆ CDE, tan 60° = \(\frac { CE }{ CD } \)
\(\sqrt { 3 }\) = \(\frac { x+h }{ 5 } \) ⇒ x + h = 5\(\sqrt { 3 }\)
5 + h = 5 \(\sqrt { 3 }\) (substitute the value of x)
h = 5 \(\sqrt { 3 }\) – 5 = 5 × 1.732 – 5 = 8. 66 – 5 = 3.66
∴ Height of the window = 3.66 m

Question 4.
A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 40° . Find the height of the pedestal.
(tan 40° = 0.8391, \(\sqrt { 3 }\) = 1.732)
Answer:
Height of the statue = 1.6 m
Let the height of the pedestal be “h”
AD = H + 1.6m
Let AB be x
In the right ∆ ABD, tan 60° = \(\frac { AD }{ AB } \)
\(\sqrt { 3 }\) = \(\frac { h+1.6 }{ x } \)
x = \(\frac{h+1.6}{\sqrt{3}}\) ……..(1)

In the right ∆ ABC, tan 40° = \(\frac { AC }{ AB } \)
0.8391 = \(\frac { h }{ x } \)
x = \(\frac { h }{ 0.8391 } \)
Substitute the value of x in (1)
\(\frac{h}{0.8391}=\frac{h+1.6}{\sqrt{3}}\)
(h + 1.6) 0.8391 = \(\sqrt { 3 }\) h
0.8391 h + 1.34 = 1.732 h
1.34 = 1.732 h – 0.8391 h
1.34 = 0.89 h
h = \(\frac { 1.34 }{ 0.89 } \) = \(\frac { 134 }{ 89 } \) = 1.5 m
Height of the pedestal = 1.5 m

Question 5.
A Flag pole ‘h’ metres is on the top of the hemispherical dome of radius ‘r’ metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30° . Find (i) the height of the pole (ii) radius of the dome. (\(\sqrt { 3 }\) = 1.732)

Answer:
Height of the Flag pole (ED) = h m
AF and AD is the radius of the semi circle (r)
AC = (r + 7)
AB = (r + 7 + 5)
= (r + 12)
In the right ∆ ABD, tan 30° = \(\frac { AD }{ AB } \)

\(\frac{1}{\sqrt{3}}=\frac{r}{r+12}\)
\(\sqrt { 3 }\) r = r + 12
\(\sqrt { 3 }\) r – r = 12 ⇒ r (\(\sqrt { 3 }\) – 1) = 12
r[1.732 – 1] = 12 ⇒ 0.732 r = 12
r = \(\frac { 12 }{ 0.732 } \) ⇒ = 16.39 m
In the right ∆ ACE, tan 45° = \(\frac { AE }{ AC } \)
1 + \(\frac { r+h }{ r+7 } \)
r + 7 = r + h
∴ h = 7 m
Height of the pole (h) = 7 m
Radius of the dome (r) = 16.39 m

Question 6.
The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
Answer:
Let the height of the electric pole AD be “h” m
EC = 15 – h m
Let AB be “x”

In the right ∆ ABC, tan 60° = \(\frac { BC }{ AB } \)
\(\sqrt { 3 }\) = \(\frac { 15 }{ x } \)
x = \(=\frac{15}{\sqrt{3}}=\frac{15 \times \sqrt{3}}{3}\)
= 5\(\sqrt { 3 }\)
In the right ∆ CDE, tan 30° = \(\frac { EC }{ DE } \)
\(\frac{1}{\sqrt{3}}=\frac{15-h}{x}\) ………….(1)
Substitute the value of x = 5 \(\sqrt { 3 }\) in (1)
\(\frac{1}{\sqrt{3}}=\frac{15-h}{5 \sqrt{3}} \Rightarrow \sqrt{3}(15-h)=5 \sqrt{3}\)
(15 – h) = \(\frac{5 \sqrt{3}}{\sqrt{3}}\) ⇒ 15 – h = 5
h = 15 – 5 = 10
∴ Height of the electric pole = 10 m

Question 7.
A vertical pole fixed to the ground is divided in the ratio 1:9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 25 m away from the base of the pole, what is the height of the pole?
Answer:
Let the first part of the pole be “x” and the second part be “9x”
∴ height of the pole (AC) = x + 9x = 10x
Given ∠CDB = ∠BDA
∴ BD is the angle bisector of ∠ADC
By angle bisector theorem

\(\frac { AB }{ BC } \) = \(\frac { AD }{ DC } \)
\(\frac { 9x }{ x } \) = \(\frac { AD }{ 25 } \) ⇒ AD = 9 × 25 = 225
In the right ∆ ACD
AD² = AC² + CD²
(225)² = (10x)² + 25²
50625 = 100x² + 625
∴ 100x² = 50625 – 625 = 50000
x² = \(\frac { 50000 }{ 100 } \) = 500
x = \(\sqrt { 500 }\) = \(\sqrt{5 \times 100}=10 \sqrt{5}\)
∴ AC = 10 × 10\(\sqrt { 5 }\) = 100 \(\sqrt { 5 }\) (AC = 10x)
∴ Height of the pole = 100 \(\sqrt { 5 }\) m

Question 8.
A traveler approaches a mountain on highway. He measures the angle of elevation to the peak at each milestone. At two consecutive milestones the angles measured are 4° and 8°. What is the height of the peak if the distance between consecutive milestones is 1 mile, (tan 4° = 0.0699, tan 8° = 0.1405)
Answer:
Let the height of the peak be “h” mile. Let AD be x mile.
∴ AB = (x + 1) mile.
In the right ∆ ADC, tan 8° = \(\frac { AC }{ AC } \)

0.1405 = \(\frac { h }{ x } \)
x = \(\frac { h }{ 0.1405 } \) ………..(1)
In ∆ ABC, tan 4° = \(\frac { AC }{ AB } \)
0.0699 = \(\frac { h }{ x+1 } \) ⇒ (x + 1) 0.0699 = h
0.0699x + 0.0699 = h
0.0699 x = h – 0.0699
x = \(\frac { h-0.0699 }{ 0.0699 } \) ………(2)
Equation (1) and (2) we get,
\(\frac { h-0.0699 }{ 0.0699 } \) = \(\frac { h }{ 0.1405 } \)
0.0699 h = 0.1405 (h – 0.0699)
0.0699 h = 0.1405 h – 0.0098
0.0098 = 0.1405 h – 0.0699 h
0.0098 = 0.0706 h
h = \(\frac { 0.0098 }{ 0.0706 } \) = \(\frac { 98 }{ 706 } \) = 0.1388
= 0.14 mile (approximately)
Height of the peak = 0.14 mile