Prasanna

Students can download 6th Social Science Term 1 Geography Chapter 2 Land and Oceans Questions and Answers, Notes, Samacheer Kalvi 6th 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 6th Social Science Geography Solutions Term 1 Chapter 2 Land and Oceans

Samacheer Kalvi 6th Social Science Land and Oceans Text Book Back Questions and Answers

A. Choose the correct answer

Question 1.
Which of the following is the smallest ocean on Earth?
(a) The Pacific Ocean
(b) The Indian Ocean
(c) The Atlantic Ocean
(d) The Arctic Ocean
Answer:
(d) The Arctic Ocean

Question 2.
The Malacca Strait connects
(a) The Pacific and Atlantic Oceans
(b) The Pacific and Southern Oceans
(c) The Pacific and Indian Oceans
(d) The Pacific and Arctic Oceans
Answer:
(c) The Pacific and Indian Oceans

Question 3.
Which of the following oceans is the busiest ocean?
(a) The Pacific Ocean
(b) The Atlantic Ocean
(c) The Indian Ocean
(d) The Arctic Ocean
Answer:
(b) The Atlantic Ocean

Question 4.
The frozen continent is
(a) North America
(b) Australia
(c) Antarctica
(d) Asia
Answer:
(c) Antarctica

Question 5.
A narrow strip of water that connects two large water bodies?
(a) A Strait
(b) An Isthmus
(c) An Island
(d) A Trench
Answer:

B. Fill in the blanks

1. The world’s largest continent is …………….
2. ……………. is the mineral-rich plateau in India.
3. The largest ocean is …………….
4. Deltas are ……………. order landforms ……………..
5. The Island continent is …………….

Answer:

1. Asia
2. Chotanagpur Plateau
3. The Pacific ocean
4. Third
5. Australia

C. Circle the odd one out

D. Match the following

Answer:
1. – b
2. – a
3. – d
4. – e
5. – c

E. (i) Consider the following statements

1. Plains are formed by rivers.
2. The ‘South Sandwich Trench’ is found in the Indian Ocean.
3. Plateaus have steep slopes.
Choose the correct answer using the codes given below.
(a) 1 and 3
(b) 2 and 3
(c) 1, 2 and 3
(d) 2 only
Answer:
(a) 1 and 3

(ii) Consider the following statements

Statement I : Mountains are second order landforms.
Statement II : The Mariana Trench is the deepest trench in the world.
Which of the statement(s) is/are true?
(a) I is true; II is wrong
(b) I is wrong; II is true
(c) Both the statements are true
(d) Statements I and II are wrong.
Answer:
(c) Both the statements are true

F. Answer in a word

Question 1.
Which is the highest plateau in the world?
Answer:
Tibetan Plateau.

Question 2.
Name a second-order landform.
Answer:
Mountains or Plateaus or Plains

Question 3.
Which ocean is named after a country?
Answer:
Indian Ocean.

Question 4.
Name the island located in the Arabian Sea.
Answer:
Lakshadweep islands

Question 5.
What is the deepest part of the ocean called?
Answer:
Trench

G. Answer in brief

Question 1.
What is a continent?
Answer:
The vast landmasses on Earth are called Continents.

Question 2.
Name the continents which surround the Atlantic Ocean.
Answer:
The Atlantic ocean is bounded by North America and South America in the West, and ( Europe and Africa in the East)

Question 3.
What are the oceans?
Answer:
Oceans are a vast expanse of water.

Question 4.
List out the names of continents according to their size
Answer:
From the largest to the smallest, they are Asia, Africa, North America, South America,  Antarctica, Europe, and Australia.

Question 5.
Name the oceans which surround North America and South America.
Answer:
North America: On the west by the Pacific Ocean, on the east by Atlantic ocean and on the north by Arctic ocean
South America: On the west by the Pacific Ocean, on the east by Atlantic ocean.

H. Distinguish between

Question 1.
A Mountain and a Plateau?
Answer:
Mountains

1. A landform that rises over 600 meters above its surroundings and has steep slopes is called a mountain.
2. Example: Himalayas

Plateaus

1. Plateaus are the elevated portions of the Earth that have flat surfaces bounded by steep slopes. The elevation of plateaus maybe a few hundred metres or several thousand metre.
2. Example: Chotanagpur Plateau

Question 2.
An ocean and a sea
Answer:

Ocean

1. Oceans are a vast expanse of water.
2. Eg. the Pacific Ocean

Sea

1. Seas are water bodies partially or fully enclosed by land.
2. Eg: Bay of Ben, Arabian Sea.

I. Answer the following questions in detail

Question 1.
Mention the classification of landforms.
Answer:
First-order landforms:

1. Continents and oceans are grouped as first-order landforms.
2. The vast landmasses on Earth are called Continents and huge water bodies are called Oceans.
3. There are seven continents in the world. They are Asia, Africa, North America, South America, Antarctica, Europe and Australia.
4. The five oceans are the Pacific, Atlantic, Indian, Southern, and Arctic Oceans.

Second-order landforms:

1. Mountains, Plateaus, and Plains are grouped as second-order landforms.
2. A landform that rises 600 meters above its surroundings and has steep slopes is called a mountain. Example:
3. The Himalayas, the Rocky Mountains, and the Andes.
4. Plateaus are the elevated portions of the Earth that have flat surfaces bounded by steep slopes. Example:
5. Tibetan plateau and Deccan plateau.
6. Plains are flat and relatively low-lying lands. These plains are used extensively for agriculture. Example: Indo – Gangetic plain.

Third-order landforms:

1. Third-order landforms are formed on mountains, plateaus, and plains mainly by erosional and depositional activities of rivers, glaciers, winds, and waves.
2. Example: Valleys, beaches, and sand dunes.

Question 2.
Write a note on plateaus.
Answer:
Ocean:

• An ocean is a vast expanse of water.
• Oceans are very deep.
• Example: The Pacific Ocean

Sea:

• A sea is a water body partially or fully enclosed by land.
• Seas are not so deep as oceans
• Example: The Arabian sea

Question 3.
Plains are highly populated. Give reasons.
Answer:

1. Plains are flat and relatively low-lying lands.
2. Plains are formed by rivers and their tributaries and distributaries.
3. Plains are used extensively for agriculture due to the availability of water and fertile soil.
4. Plains are most suitable for human inhabitation. Hence, they are highly populated.

Question 4.
Give the important features of the Pacific Ocean,
Answer:

1. The Pacific Ocean is the largest and deepest ocean on Earth.
2. It covers about one-third of the Earth’s total area.
3. It is bounded by Asia and Australia in its west and North America and South America in its east.
4. On its apex is the Bering Strait. It connects the Pacific Ocean with the Arctic Ocean.
5. The deepest point Mariana Trench is located in the Pacific Ocean.
6. A chain of volcanoes is located around the Pacific Ocean.

Question 5.
Write above the importance of oceans.
Answer:

1. Oceans are the first order landform.
2. 71% of the earth’s surface is covered with water.
3. Oceans influence man in various ways, from the climate he experiences to the food he eats.
4. Oceans are a major source of salt, valuable minerals, petroleum, pearls, and diamonds.
5. Ocean currents affect the climate of neighbouring areas.
6. Ocean trade plays an important role in the world economy.
7. Ocean currents can be converted into electricity.

J. Picture Study

Question 1.
Name the landform.
Answer:
Sand dune

Question 2.
What order of a landform is this?
Answer:
Third-order landform

Question 3.
By which activity of river is this landform formed?
Answer:
Deposition

K. (i) Activity (Activity to be done by students)

Trip to the nearby area to appreciate the physical features of any kind of landform.
Conduct a quiz on landforms and oceans.

(ii) Activity

Question 1.
Give examples for the following using an Atlas.
Answer:

1. Bay: Hudson Bay, Bay of Bengal, Bay of Biscay
2. Gulf: the Persian Gulf, Gulf of Kutch, Gulf of Mannar
3. Island: Srilanka, Australia, Maldives
4. Straits: Palk strait, Bering strait, Magellan strait

Question 2.
Map reading (with the help of an atlas)
Answer:

1. A sea in the east of India – Bay of Bengal
2. Continents in the west of Atlantic Ocean – North America, South America
3. Continents in the south of Arctic Ocean – Europe, Asia
4. A strait between India and Sri Lanka – Palk strait
5. Oceans which surround Australia – Indian ocean, Pacific ocean
6. Find out the Isthmusses – Isthmus of Panama, Isthmus of Avalon, Isthmus of La Dune

Samacheer Kalvi 6th Social Science Land and Oceans Additional Important Questions and Answers

I. Choose the correct answer

Question 1.
International Mountain Day is ……………..
(a) June 15
(b) April 11
(c) November 11
(d) December 11
Answer:
(d) December 11

Question 2.
Andes mountain is located in
(a) North America
(b) South America
(c) Asia
(d) Europe
Answer:
(b) South Amei leaf

Question 3.
The highest plateau in the world is …………….
(a) Ladakh plateau
(b) Tibetan plateau
(c) Deccan plateau
(d) Chotanagpur plateau
Answer:
(b) Tibetan plateau

Question 4.
The International Mountain Day is
(a) December 10th
(b) December 11th
(c) December 12th
(d) December 13th
Answer:
(b) December 11th

Question 5.
It connects the Pacific Ocean with the Arctic ocean.
(a) Bering strait
(b) Magellan strait
(c) Gibraltar strait
(d) Palk strait
Answer:
(a) Bering strait

II. Fill in the blanks

1. The sea around Pangea is called ……………….
2. The smallest continent is ……………….
3. The smallest ocean is ……………….
4. ………………. is called the Roof of the world
5. The deepest point in the Indian ocean is ……………….

Answer:

1. Panthalasa
2. Australia
3. Arctic ocean
4. Tibetan Plateau
5. Java trench

III. Answer in brief

Question 1.
What is an Isthmus?
Answer:
A narrow strip of land which connects two large landmasses or separates two large water bodies is called an Isthmus.

Question 2.
What are the Second-order landforms?
Answer:
The Second-order landforms are categorised as mountains, plateaus, and plains.

Question 3.
Bring out the importance of mountains.
Answer:

1. Mountains are the source of rivers.
2. They block the moisture-bearing winds and cause rainfall.
3. They provide shelter to flora and fauna.
4. They promote tourism.
5. During summer people go to mountain regions to enjoy the pleasing cool weather.
6. There are a number of hill stations in the mountains.

Question 4.
Mention some of the early civilizations.
Answer:
The Indus valley civilization, the Mesopotamian civilization, The Egyptian civilization, and the Chinese civilization. Where some of the early civilizations?

Question 5.
Write a few lines about The Indian Ocean.
Answer:

1. The Indian Ocean is the third largest ocean on the earth.
2. It is named after India.
3. It is triangular in shape.
4. The Andaman and Nicobar Islands, Lakshadweep, Maldives, Sri Lanka, and Mauritius are the islands located in the Indian Ocean.
5. Java Trench is the deepest point in this ocean.

IV. Mind Map

 

 

Students can download 6th Social Science Term 1 Geography Chapter 1 The Universe and Solar System Questions and Answers, Notes, Samacheer Kalvi 6th 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 6th Social Science Geography Solutions Term 1 Chapter 1 The Universe and Solar System

Samacheer Kalvi 6th Social Science The Universe and Solar System Text Book Back Questions and Answers

A. Fill in the blanks

1. The Universe was formed after ……………. explosion.
2. …………….. is the unit used to measure the distance between two celestial bodies.
3. …………….. is the centre of the solar system.
4. The word planet means ………………
5. ………………planet has many natural satellites.
6. India’s first ever mission to the moon is ………………
7. Earth is inclined by ……………… degrees.
8. The Equator faces the Sun directly on ………………
9. At the time of Perihelion, the Earth is ………………
10. The line which divides day and night on the Earth’s surface is ……………….

Answer:

1. Big Bang
2. Light year
3. The Sun
4. wanderer
5. Jupiter
6. Chandrayaan
7. 23 1/2
8. 21st March, 23rd Sep to the Sim.
9. Closest
10. Terminator line

B. Choose the best answer

Question 1.
The movement of the Earth on its axis is called _______
(a) Revolution
(b) Seasons
(c) Rotation
(d) Circulation
Answer:
(c) Rotation

Question 2.
The Tropic of Capricorn faces the Sun directly on
(a) March 21
(b) June 21
(c) September 23
(d) December 22
Answer:
(c) September 23

Question 3.
The galaxy in which our solar system is found is _______
(a) Andromeda
(b) Magellanic clouds
(c) Milky way
(d) Starburst
Answer:
(c) Milky way

Question 4.
The only celestial body where man has successfully landed
(a) Mars
(b) Moon
(c) Mercury
(d) Venus
Answer:
(b) Moon

Question 5.
Which of the following planets can float On water?
(a) Jupiter
(b) Saturn
(c) Uranus
(d) Neptune
Answer:
(b) Saturn

C. Circle the odd one out

D. Match the following

Answer:
1. – c
2. – d
3. – a
4. – e
5. – b

E. (i) Consider the following statements

1. Venus rotates from east to west.
2. The Tropic of Cancer faces the Sun on June 21.
3. Mars has rings around it.
Choose the correct answer using the codes given below.
(a) 1 and 2
(b) 2 and 3
(c) 1, 2 and 3
(d) 2 only
Answer:
(a) 1 and 2

(ii) Consider the following statements

Statement I : Earth is called a watery planet.
Statement II. : The rotation of the Earth causes seasons.
Which of the statement(s) is/are true?
(a) I is true; II is wrong
(b) I is wrong; II is true
(c) Both the statements are true
(d) Statements I and II are wrong.
Answer:
(a) I is true; II is wrong

F. Name the following

Question 1.
Cluster of stars.
Answer:
Galaxy

Question 2.
The nearest galaxy to the solar system.
Answer:
Andromeda

Question 3.
The brightest planet.
Answer:
Venus

Question 4.
The living sphere.
Answer:
Biosphere

Question 5.
The year which has 366 days.
Answer:
Leap year

G. Answer in brief

Question 1.
Name the inner planets.
Answer:
The inner planets are Mercury, Venus, Earth, and Mars.

Question 2.
Pluto is no longer a planet, Reason out,

1. In August 2006, the International Astronomical Union (IAU) down-graded the status of Pluto to that of dwarf planet.
2. The three criteria of the IAU for a full sized planet are
   • It is in orbit around the Sun.
   • It has sufficient Mass to assume nearly a round shape.
   • It has cleared the neighbourhood around its orbit.
3. Since Pluto is able to meet only the first two of the criteria, it in no more a planet.

Question 3.
What is perihelion?
Answer:
Perihelion is the Earth’s closest position to the Sun.

Question 4.
How many times in a year would you find the Sun overhead if you lived on 20 N Latitude?
Answer:
Two times. It would be on the 21st March and 23rd September.

Question 5.
Which celestial body shares its orbit with others? Give an example.
Answer:

1. The dwarf planets share their orbits with others.
2. The five dwarf planets of the solar system are Pluto, Ceres, Eris, Makemake, and Haumea.

H. Give reasons

Question 1.
Why is Uranus called the somersaulting planet?
Answer:
It’s axis is tilted so much, that it appears to orbit the Sun on its sides like a rolling ball. So it is called the somersaulting planet.

Question 2.
The surface of the moon has many craters.
Answer:
The craters are formed due to the meteorites which fall on the moon’s surface.

Question 3.
The velocity of Earth’s rotation is zero at poles.
Answer:
It is due to the shape and inclination of the earth.

I. Answer in detail

Question 1.
Distinguish between inner and outer planets.
Answer:
Inner or Terrestrial Planets

1. Mercury, Venus, Earth, Mars.
2. They are comparatively smaller in size.
3. They are composed of rocks. The surface of the inner planets has mountains, volcanoes and craters.
4. None of the inner planets have rings orbiting them

Outer Planets or Jovian Planets, or Gaseous Giants

1. Jupiter, Saturn, Uranus, Neptune.
2. They are huge in size.
3. Most of them are made of gas.
4. All of the outer planets have rings orbiting them.

Question 2.
What are the effects of rotation and revolution?
Answer:
Effects of Rotation:

1. It is the spinning movement of the Earth on its axis
2. The time taken by the Earth to complete one rotation is called a day.
3. The rotation of the Earth causes day and night, As the Earth is spherical in shape, only one half of it is illuminated by the Sun at a time.
4. The other half remains dark.
5. The illuminated portion of the Earth experiences day, whereas the darkened part of the Earth experiences night.

Effects of Revolution:

1. It is the movement of the Earth around the Sun on its elliptical path.
2. The Earth takes 36514 days to complete one revolution.
3. It revolves around the Sun at a speed of 30 km per second.
4. The remaining quarter day is added once in every four years in the month of February.
5. The inclination of the Earth on its axis and its revolution around the Sun cause different seasons.

Question 3.
Explain the characteristics of the various spheres of the Earth.
Answer:
Earth is the most suitable planet to support life. It has three major components that we call the realms of the Earth lithosphere, hydrosphere, and atmosphere.

(i) Lithosphere: The word lithosphere is derived from the Greek word Lithos, which means rocky. The Lithosphere is the land on which we live.

(ii) Hydrosphere: The word Hydro means water in Greek. The hydrosphere consists of water bodies such as oceans, seas, rivers, lakes, ice caps on mountains, and water vapour in the atmosphere.

(iii) Atmosphere: The word Atmo means the air in Greek. The atmosphere is the envelope of air that surrounds the Earth. Different types of gases make up the atmosphere. The major gases are Nitrogen (78%) and Oxygen (21%).

(iv) Biosphere: The narrow belt of interaction among the lithosphere, the hydrosphere, and the atmosphere, where life exists is known as Biosphere. Bio means life in Greek. It consists of distinct zones.

J. Picture Study

Question 1.
Study the picture and answer the given questions.

Question a.
Which is the closest planet to the Sun?
Answer:
Mercury

Question b.
Which is the largest planet?
Answer:
Jupiter

Question c.
Which is the farthest planet from the Sun?
Answer:
Neptune

Question d.
Which is the second smallest planet?
Answer:
Mars

Question 2.
Look at the picture and answer the questions given below.

Question a.
Identify the planet
Answer:
Uranus

Question b.
What is the colour of the planet?
Answer:
Green

Question c.
Why is it of this colour?
Answer:
Due to the presence of Methane

STUDENT ACTIVITY
K. Solve the puzzle

Across:

2. A dwarf planet.
3. Equal days and nights.
7. I am a gas found in the Sun.
8. I appear once in 76 years.

Down:

1. I am the morning star.
2. India’s first moon mission.
4. I have two natural satellites.
5. I am the farthest planet.
6. An imaginary line passing through the centre of the Earth.

Samacheer Kalvi 6th Social Science The Universe and Solar System Additional Important Questions and Answers

I. Fill in the blanks

1. The study of the universe is called ………………
2. A cluster of stars is known as ………………
3. The Roman word ‘Sol’ means ………………
4. The ……………… is at the centre of the solar system.
5. The elliptical path in which the planets move around the Sun is ………………

Answer:

1. Cosmology
2. Galaxy
3. Sun God
4. Sun
5. Orbit

II. Choose the correct answer

Question 1.
The closest planet to the Sun is _______
(a) Mercury
(b) Venus
(c) Uranus
(d) Saturn
Answer:
(a) Mercury

Question 2.
The solar system is believed to have formed about _______billion years ago.
(a) 3
(b) 4.5
(c) 3.5
(d) 5
Answer:
(b) 4.5

Question 3.
The ringed planet is _______
(a) Mars
(b) Venus
(c) Saturn
(d) Mercury
Answer:
(c) Saturn

Question 4.
The Outer Planets are _______
(a) Jupiter and Mercury
(b) Venus and Earth
(c) Saturn and Mars
(d) Uranus and Neptune
Answer:
(d) Uranus and Neptune

Question 5.
The Tropic of Cancer faces the Sun directly on _______
(a) March 21
(b) June 21
(c) September 23
(d) December 22
Answer:
(b) June 21

III. (i) Consider the following statements

1. The earth is the third planet in the solar system
2. The Sun is made up of hot gases like Hydrogen and Nitrogen
3. Mercury has no natural satellites
Choose the correct answer using the codes given below
(a) 1 and 2
(b) 2 and 3
(c) 1 and 3
(d) 2 only
Answer:
(c) 1 and 3

(ii) Consider the following statements

1. The sun revolves around the earth.
2. Mars is named after the Roman God of war.
3. Uranus appears green
Choose the correct answer using the codes given below
(a) 1 and 2
(b) 2 and 3
(c) 1 and 3
(d) 3 only

(iii) Consider the following statements

Question 1.
Statement I: Jupiter is the fastest spinning planet in the solar system.
Statement II: Neptune is the coldest planet Which of the statement (s) is/are true?
(a) I is true, II is wrong
(b) I is wrong, II is true
(c) Both the statements are true
(d) Both statements are wrong.
Answer:
(c) Both the statements are true

(iv) Consider the following statements

Question 1.
Statement I : The earth is inclined at 32 1/2°angle.
Statement II : The specific gravity of Saturn is more than that of water.
Which of the statement (s) is/are true
(a) I is true, II is wrong
(b) I is wrong, II is true
(c) Both the statements are true
(d) Both the statement are wrong
Answer:
(d) Both the Statement are wrong

IV. Answer the following questions

Question 1.
What is meant by light year?
Answer:
A light-year is a distance traversed by light in a year at a velocity of 30,000 km per second.

Question 2.
Mention the hierarchy of the universe.
Answer:

1. Universe
2. Galaxy
3. Solar system
4. Planets
5. Satellites

Question 3.
How many planets are there in the solar family? Name them.
Answer:
There are eight planets in the solar family. They are

1. Mercury
2. Venus
3. Earth
4. Mars
5. Jupiter
6. Saturn
7. Uranus and
8. Neptune.

V. Mind map

 

 

Students can download 6th Social Science Term 1 History Chapter 4 Ancient Cities of Tamilagam Questions and Answers, Notes, Samacheer Kalvi 6th 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 6th Social Science History Solutions Term 1 Chapter 4 Ancient Cities of Tamilagam

Samacheer Kalvi 6th Social Science Ancient Cities of Tamilagam Text Book Back Questions and Answers

I. Choose the correct answer

Question 1.
Which of the following region has a city more than 6500 years old?
(a) Iraq
(b) Indus valley
(c) Tamilagam
(d) Thondaimandalam
Answer:
(a) Iraq

Question 2.
Which one of the following is a Tamil city?
(a) Iraq
(b) Harappa
(c) Mohenjo-Daro
(d) Kancheepuram
Answer:
(d) Kancheepuram

Question 3.
Which city is not related to the Bay of Bengal?
(a) Poompuhar
(b) Thondi
(c) Korkai
(d) Kancheepuram
Answer:
(b) Madurai

Question 4.
The water management system of Tamils are known from
a. Kallanai
b. Tanks in Kancheepuram
c. Prakirama Pandyan Tank
d. River Cauvery
(a) (a) is correct
(b) (b) is correct
(c) (c) is correct
(d) (a) and (b) are correct
Answer:
(d) (a) and (b) are correct

Question 5.
Which is not the oldest city among the following ones?
(a) Madurai
(b) Kancheepuram
(c) Poompuhar
(d) Chennai
Answer:
(a) Madurai

Question 6.
Which city is related to Keezhadi excavation?
(a) Madurai
(b) Kancheepuram
(c) Poompuhar
(d) Harappa
Answer:
(a) Madurai

II. Tick the appropriate answer. Match the statement with the reason

Question 1.
Statement: Goods were imported and exported from the city of Poompuhar.
Reason: the Bay of Bengal was suitable for trading with neighbouring countries.
(a) Statement is correct, but the reason is wrong.
(b) Statement and its reason are correct.
(c) Statement is wrong, but the reason is correct.
(d) Both are wrong.
Answer:
(b) Statement and its reason are correct.

Question 2.
(a) Thirunavukkarasar said “kalviyil karaiillatha”. This statement refers to the city of Kancheepuram.
(b) Hieun Tsang said, “Kancheepuram is one among the seven sacred places of  India”.
(c) Kalidasa said, “Kancheepuram is the best city among the cities”
(a) only a is correct (b) the only b is correct
(c) the only c is correct (d) All are correct
Answer:
(d) All are correct!

Question 3.
Find out the correct statement
(a) Naalangadi – Night shop
(b) Allangdi – Day -time shop
(c) Ancient Roman coin factory was found at Poompuhar.
(d) Pearls were exported from Uvari near Korkai.
Answer:
(d) Pearls were exported from Uvari near Korkai

Question 4.
Find out the wrong statement.
(a) Megasthanese has mentioned Madurai in his account.
(b) Hien Tsang came to the Tamil city of Kancheepuram.
(c) Kovalan and Kannagi lived in Kancheepuram.
(d) Iraq is mentioned in Pattinapalai.
Answer:
(c) Kovalan and Kannagi lived in Kancheepuram.

Question 5.
Find out the correct pair
(a) Koodal Nagar – Poompuhar
(b) Thoonga Nagaram – Harappa
(c) City of Education – Madurai
(d) City of Temples – Kancheepuram
Answer:
(d) City of Temples – Kancheepuram

Question 6.
Find out the wrong pair
(a) Vadamalai – Gold
(c) Southern Sea – Pearls
(b) Western Ghats – Sandal
(d) Eastern Sea – Ahil
Answer:
(d) Eastern Sea – Ahil

III. Fill in the blanks

1. Kanchi Kailasanathar temple was built by ……………..
2. …………….. is known as the city of temples.
3. Masathuvan means ……………..

Answer:

1. Raja Simh
2. Kanchi
3. A big trader

IV. State True or False:

1. Cultural relationship with the outside world developed in Poompuhar because of its trade relationship with it.
2. Women also purchased from Allangadi of Madurai without fear.
3. Many rock-cut temples were made during the Pallava period.
4. Bodhi Dharma belonged to Kancheepuram.

Answer:

1. True
2. True
3. False
4. True

V. Answer in one word

Question 1.
What do you know about the term ‘export’?
Answer:
Exports are goods and services produced in one country and purchased by the citizens of another country.

Question 2.
Mention the epic and the Sangam poem you read in this lesson.
Answer:

1. The epic is Silapthikaram (or) Manimegalai.
2. Sangam Literature is Pattinappaalai.

Question 3.
Which is the oldest city in Thondai Nadu?
Answer:
Kanchi is the oldest city in Thondai Nadu.

Question 4.
Point out anyone difference between a village and a city.
Answer:
A village will have a small group of settlements whereas a city will have a large group of settlements.

Question 5.
Which civilization is associated with the city Lothal?
Answer:
The Indus Valley Civilisation is associated with the city Lothal.

Question 6.
Name the oldest civilization of the world
Answer:
Mesopotamian civilization is the earliest civilization in the world.

VI. Answer the following

Question 1.
Write a brief note on ancient cities in India?
Answer:

1. Harappa and Mohenjodaro were prominent cities of ancient India.
2. They developed along the banks of the river Indus.
3. They were the symbol of urban civilization.
4. They had very good town planning, a well-constructed house, well-maintained drainage system.
5. They had very good civic sense.
6. They developed pottery, ornaments as well as a script which is yet to be deciphered.

Question 2.
Mention the ancient cities of Tamil Nadu.
Answer:

1. In Tamizhagam the well-known cities were Madurai, Kanchi, and Poompuhar.
2. Poompuhar is one of the oldest towns in ancient Tamizhagam.
3. Madurai has been one of the oldest cities in India.
4. It is known as “Sangam Valartha Nagaram”
5. Kanchi is the oldest town in Thondai Nadu.
6. Scholars like Dharmabalar, Jothibalar, Sumathi, and Bodhi Dharma were born in Kanchi.

Question 3.
Discuss the sources available to know about Tamil cities?
Answer:

1. Tamil literature, accounts of foreign travellers, and archaeological finds provide information about the ancient towns of Tamizhagam.
2. Sangam Tamil Literature Pattinappaalai and Tamil epics Silappathikaram and Manimegalai have references about Poompuhar.
3. Madurai is proudly associated with three Sangams.
4. The fame of Madurai can be attested from the accounts of the Greek historian Megasthenes.
5. Chanakya mentions Madurai in his famous work Arthashastra.
6. The Chinese Traveller Hieun Tsang writes about the greatness of Kanchi.
7. Poet Kalidasa refers to Kanchi as the best of the towns.

Question 4.
Write about the kings who ruled Madurai.

1. Pandyas, the Cholas and later the Kalabras ruled Madurai in the ancient
2. During medieval times, later Cholas and later Pandyas followed by the Nayaks ruled this historic town.

Question 5.
Mention the other names of Madurai?
Answer:

1. Sangam Valartha Nagaram
2. Thoonga Nagaram (the city that never sleeps).
3. Koodal Nagar are the other names of Madurai

Question 6.
What is the difference between Naalaugadi and Allangadi?
Answer:
Naalangadi

1. It is Day Marget.
2. It works only in the day time.

Allangadi

1. It is the evening Market.
2. It works only in the Evening,

Question 7.
Name the scholars who were born at Kancheepuram
Answer:
Scholars like Dharmabalar, Jothibalar, Sumathi, and Bodhi Dharma were bom in Kanchi.

Question 8.
Which is known as the city of lakes? Why?
Answer:

1. Water management played an important role in the agrarian society of those times.
2. Hundreds of lakes were created for storing water around the town of Kanchi.
3. These lakes were well connected with canals.
4. During the later period, Kanchi came to be known as the district of lakes.

VII. HOTS

Question 1.
Write a short note on Iraq.
Answer:

1. Modem Iraq was called Mesopotamia in the ancient period. It was the birthplace of Sumerian civilization.
2. Iraq is watered by two rivers namely Euphrates and Tigris.
3. It is an important trading centre.
4. Pattinappaalai speaks about the trade relations of Iraq With other countries.

Question 2.
Write a paragraph about the city of Poompuhar with special reference to trade.
Answer:

1. Poompuhar was a port.
2. Big traders and sea traders had settled down there.
3. Numerous merchants from foreign countries such as Greece and Rome landed at Poompuhar.
4. Brisk seaborne trade took place in Puhar.
5. Foreign traders stayed on indefinitely at Puhar.
6. There is evidence of foreign settlements in the town.

Question 3.
Write about the accounts given by scholars about Kanchi.
Answer:

1. Poet Kalidasa says “Kanchi is the best of the towns”.
2. Poet Thirunavukarasar praises Kanchi as “Kalviyil Karaiillatha Kanchi.
3. Hieun Tsang has said,”Kanchi can be counted as one among the seven sacred places like Budh Gaya and Sanchi”.

Question 4.
City of temple Gives short notes.
Answer:

1. Kanchi is also known as the Temple city.
2. The famous Kailasanathar temple is at Kanchi.
3. There are a large number of cave temples in Kanchi. So Kanchi is known as the Temple city.

Question 5.
Kancheepuram was famous for education. Prove this statement
Answer:

1. Several schools were established in great numbers in Kanchi.
2. There were Jainpallis and Viharas.
3. The Chinese traveller Hieun Tsang visited Kanchi Kadigai to continue his studies
4. Tamil poet saint Thirunavukarasar praises Kanchi as’Kalviyil karaiillatha Kanchi’.

VIII. Student Activity

1. Make an album about Keezhadi excavations.
2. Poompuhar was famous for trading activities. Discuss.
3. Collect the pictures of Pallava temple architecture.
4. Prepare a Booklet describing the famous lakes of Tamilnadu.
5. Make a booklet about the famous cities of Tamilnadu.
6. Go to the library and find out the places of importance in your district.

IX. Answer Grid

Question 1.
Poompuhar was located on which riverbank?
Answer:
Cauvery

Question 2.
Name the ancient city which had Tamil Sangam.
Answer:
Madurai

Question 3.
Name a Sangam literary work.
Answer:
Pattinappaalai

Question 4.
Which Greek historian gave accounts about the Pandya kingdom?
Answer:
Megasthanese

Question 5.
To which the Tamil Kingdom did the southern districts of Tamil Nadu belong to during the Sangam Age?
Answer:
Pandyas.

Question 6.
Name the Chinese traveller who stayed and studied in Nalanda University.
Answer:
Hieun Tsang

Question 7.
Thirunavukarasar mentioned Kanchi as _______
Answer:
Kalviyil karaiillatha Kanchi

Question 8.
What is the name of the evening market during the Sangam Age?
Answer:
Allangadi

Question 9.
Name the temple built by Pallava king Rajasimha at Kanchi.
Answer:

1. Kailasanathar
2. Temple.

Question 10.
Which district is known as the district of lakes?
Answer:
Kanchi

Question 11.
What is trade?
Answer:
The act of buying and selling goods and services is called trade.

Question 12.
Name a port located on the shore of the Bay of Bengal
Answer:
Chennai.

X. Life Skill (For Students)

1. Make a handout that shows the importance of the place where you live.

Samacheer Kalvi 6th Social Science Ancient Cities of Tamilagam Additional Important Questions and Answers

I. Choose the correct answer

Question 1.
The earliest civilization in the world is …………….
(a) Egyptian Civilization
(b) Chinese civilization
(c) Indus valley civilization
(d) Mesopotamian civilization
Answer:
(d) Mesopotamian civilization

Question 2.
Name the place related to the export of Sandal.
(a) the Western Ghats
(b) Southern Sea
(c) Eastern Sea
(d) Elam
Answer:
(a) the Western Ghats

Question 3.
Kailasanathar temple was built by …………….
(a) Mahendra varman
(b) Narasimha Varman
(c) Raja Simha
(d) Aparajitha
Answer:
(c) Raja Simha

Question 4.
Ahil was a
(a) Port
(b) Fragrant wood
(c) Educated centre
(d) Ornament
Answer:
(b) Fragrant wood

Question 5.
Puhar served as the port of ……………
(a) Chera kingdom
(b) Chola kingdom
(c) Pandya kingdom
(d) Kalabras
Answer:
(b) Chola kingdom

II. Fill in the blanks

1. Sea traders are known by the name ……………
2. Chanakya was Chandragupta’s ……………
3. The Buddhist monk Manimegalai spent the last part of her life at ……………

Answer:

1. Maanaigan
2. Minister
3. Kanchi

III. State True or False

1. The lead female character of Silappathikaram is Manimegalai
2. The present-day Thanjavur was once part of Chera Nadu
3. Poompuhar served as the port of the early Chola kingdom
4. Silappathikaram speaks about the greatness of Poompuhar
5. Many cave temples were built during the Pallava period

Answer:

1. False
2. False
3. True
4. True
5. True

IV. Answer the following

Question 1.
How was Poompuhar different from other towns?
Answer:
Each social group had a separate settlement
Streets were broad and straight, dotted with well-designed houses.
There was also a dockyard

V. Mind map

 

Students can download 6th Social Science Term 1 History Chapter 3 Indus Civilisation Questions and Answers, Notes, Samacheer Kalvi 6th 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 6th Social Science History Solutions Term 1 Chapter 3 Indus Civilisation

Samacheer Kalvi 6th Social Science Indus Civilisation Text Book Back Questions and Answers

I. Choose the correct answer

Question 1.
What metals were known to the people of Indus Civilisation?
(a) Copper, bronze, silver, gold, but not iron
(b) Copper, silver, iron, but not bronze
(c) Copper, gold, iron, but not silver
(d) Copper, silver, iron, but not gold
Answer:
(a) Copper, bronze, silver, gold, but not iron

Question 2.
Indus Civilisation belonged to.
(a) Old Stone age
(b) Medieval stone age.
(c) New stone age
(d) Metal age
Answer:
(d) Metal age

Question 3.
River Valleys are said to be the cradle of civilisation because ………………..
(a) Soil is very fertile.
(b) They experience good climate.
(c) They are useful for transportation.
(d) Many civilizations flourished on river valleys.
Answer:
(d) Many civilizations flourished on river valleys.

II. Match the statement with the Reason. Tick the appropriate answer:

Question 1.
Statement : Harappan civilisation is said to be an urban civilisation.
Reason : It has well planned cities with advanced drainage system.
(a) Statement and reason are correct.
(b) Statement is wrong.
(c) Statement is true, but the reason is wrong.
(d) Both statement and reason are wrong.
Answer:
(a) Statement and reason are correct

Question 2.
Statement : Harappan civilization belongs to BronzeAge.
Reason : Harappans did not know the use of iron.
(a) Statement and reason are correct.
(b) Statement is wrong.
(c) Statement is correct, but the reason is wrong.
(d) Both statement and reason are wrong.
Answer:
(a) Statement and reason are correct

Question 3.
Statement : The engineering skill of Harappans was remarkable.
Reason : Building of docks after a careful study of tides, waves and currents.
(a) Statement and reason are correct.
(b) Statement is wrong.
(c) Statement is correct, but the reason is wrong.
(d) Both statement and reason are wrong.
Answer:
(a) Statement and reason are correct.

Question 4.
Which of the following statement about mohanjadaro is correct?
(a) Gold ornaments were unknown.
(b) Houses were made of burnt bricks.
(c) Implements were made of iron.
(d) Great Bath was made water tight with the layers f natural bitumen.
Answer:
(b) Houses were made burnt brick.
(d) Greal Bath was made water tight with thc laye of natural bitnmen.

Question 5.
Consider the following statements.
1. Uniformity in layout of town, streets, and brick sizes
2. An elaborate and well laid out drainage system
3. Granaries constituted an important part of Harappan cities Which of the above statements are correct?
(a) 1&2
(b) 1&3
(c) 2&3
(d) all the three
Answer:
(d) all the three

Question 6.
Circle the odd one.
Answer:

1. Oxen
2. Sheep
3. Buffaloes
4. Pigs
5. Horses

Question 7.
Find out the wrong pair.
(a) ASI – John Marshall
(b) Citadel – Granaries
(c) Lothal – dockvard
(d) Harappan Civilisation – River Cauvery
Answer:
(d) Harappan – River Cauvery

III. Fill in the blanks

1. ……………… is the oldest civilisation.
2. Archaeological Survey of India was founded by ………………
3. ……………… were used to store grains.
4. Group of people form ………………

Answer:

1. Mesopotamian civilisation.
2. Alexander Cunningham.
3. Granaries.
4. Community.

IV. State True or False

1. Mehergarh is a Neolithic site.
2. Archaeological survey of India is responsible for preservation of cultural monuments in the country.
3. Granaries were used to store grains.
4. The earliest form of writings was developed by the Chinese.

Answer:

1. True
2. True
3. True
4. False

V. Match the following

Answer:
1. – d
2. – c
3. – a
4. – b

VI. Answer in one or two sentences

Question 1.
What are the uses of metal?
Answer:

1. Gold and Silver were used to make ornaments.
2. They used copper and bronze to make weapons and vessels.
3. Bronze was used to make statues. ( Example: Statue of a dancing girl.)

Question 2.
Make a list of baked and raw foods that we eat.
Answer:

1. Baked foods: Rice, wheat, vegetables, greens, roots, mutton, fish etc
2. Raw Foods: Fruits, some vegetables and nuts

Question 3.
Do we have the practice of worshipping animate and trees?
Answer:
Yes, people belonging to some religions worship animals and trees.

Question 4.
River valleys are cradles of civilization. Why?
Answer:

1. In the river valleys, the soil is fertile.
2. Freshwater is available for drinking, watering livestock, and irrigation.
3. Easy movement of people and goods is possible.

So people settled in the river valleys. Many civilizations flourished on river valleys. Florence river valleys are called cradles of civilization.

Question 5.
Just because a toy move doesn’t mean instead batteries?
Answer:
They used wheels.

Question 6.
Dog was the first animal to be tamed. Why?
Answer:

1. Dogs prevented the entry of dangerous animals by its sniffing skill.
2. Dogs helped the people in their hunting activities.

Question 7.
If you were an Archaeologist, what will you do?
Answer:
If I were an archaeologist I would go to Adichanallur which is located in our district and do excavation there.

Question 8.
Name any two Indus sites located on the Indian border
Answer:

1. Kalibangan
2. Lothal

Question 9.
In Indus civilization, which features you like the most? Why?
Answer:

1. I like the drainage system very much.
2. Most of the drains were covered with slabs or bricks. Even after nearly 5000 years many of the modern cities don’t have covered drains.
3. It is said that each house had its own soak pit, which collected all the sediments and allowed only the water to flow into the street drain. I like this system very much.

Question 10.
What instrument is used nowadays to weigh things?
Answer:
Electronic weighing machine.

VII. Answer the following

Question 1.
What method is used to explore buried buildings nowadays?
Answer:

1. To see under the ground, the archaeologists may uSe a magnetic scanner.
2. The presence and absence of archaeological remains can be detected by the Radar and Remote Sensing Method.

Question 2.
Why Indus Civilisation Is called Bronze Age civilization?
Answer:

1. Bronze is an alloy.
2. This period is characterized by the articles made of bronze?
3. So Indus Valley Civilization is also known as bronze age civilization.

Question 3.
Indus civilization is called urban civilization. Give reasons.
Answer:
The reasons are.

1. Well conceived town planning.
2. Astonishing masonry and architecture.
3. Priority for hygiene and public health.
4. Standardized weights and measures.
5. Solid agricultural and artisanal base.

Question 4.
Can you point out the special feature of their drainage system?
Answer:

1. They had well-covered drains. The drains were covered with slabs or bricks,
2. Each drain had a gentle slope, so that water could flow.
3. Manholes were provided at regular intervals to clear the drains.
4. House drains passed below many lanes before finally emptying into the drains.
5. Every house had its own soak pit, which collected all the sediments and allowed only the water to flow into the street drain.

Question 5.
What do you know about the Great Bath?
Answer:

1. The Great Bath is one of the earliest public tanks.
2. It is a waterproof structure.
3. The bath was lined with bricks.
4. It was made watertight using layers of natural bitumen.
5. There were rooms on three sides.
6. The water was drained after use.
7. There were steps on both sides of the pool.

Question 6.
How do you know that Indus people trade with other
Answer:

1. King Naram – the sin of the Akkadian empire has written about buying jewellery from the land of Melukha which is a region of the Indus valley.
2. The same types of seals found in Mesopotamia have been also found in the Indus area.
3. A naval dockyard has been discovered in Lothal in Gujarat. All these things show that the Indus people traded with other countries.

VIII. HOTS

Question 1.
Observe the following features of Indus civilization and compare that with the present day.
Answer:
(a) Lamp post:

1. In the Indus cities, street lights were an important feature. The lamp posts were made of stones.
2. Now we have iron lamp posts and cement lamp posts.

(b) Burnt bricks:

1. The houses were built using burnt brick. The bricks were of uniform size.
2. The bricks were burnt because burnt bricks are strong, hard, durable, resistant to fire, and will not dissolve in water.
3. The present-day buildings are also constructed with burnt bricks.

(c) Underground drainage system:

1. The Indus cities had an underground drainage system. They were covered with slabs or bricks. Holes were provided at regular intervals to clean the drains.
2. Even in some of the modern cities, there is no underground drainage system. This system is being introduced gradually now. In Tamil Nadu, there is an underground drainage system almost in all the corporations.

(d) Weights and measurements:

1. Standardized weights and measures were used by the Indus valley people. They used sticks with marks to measure length.
2. Now we have various types of weighing machines and scales.

(e) Dockyard:

1. Lothal was a port in Gujarat. There was a naval dockyard in Lothal. It shows the maritime activities of the Indus people.
2. Now, dockyards are found almost in all ports. Apart from loading, unloading and repairing of ships new ships are built in these yards.
3. Example: Mazagaon dock at Mumbai.

Question 2.
Agriculture was one of their occupations, How can you prove this? (with the findings)
Answer:

1. Agriculture might have been their main occupation since they settled near the Indus river bank.
2. We find the terracotta plough which might have been used for agriculture.
3. They used granaries to store food grain.
4. A granary with walls made of mud, bricks, which are still in good condition, has been discovered in Rakhigarhi, a village in Haryana belonging to the Mature Harappan phase.

Question 3.
Many potteries and their pieces have been discovered from Indus sites. What do you know from that?
Answer:

1. It shows that they know the art of making pottery.
2. The broken pieces of pottery have animal figures on them.
3. It shows that they reared various animals. It also shows their skill in painting.

Question 4.
A naval dockyard has been discovered In Lothal, What does it convey?
Answer:

1. The Dockyard at Lothal is considered as the first naval dockyard of the world,
2. It has favourable features in terms of height, width, and length compared to the modem dockyards of Mumbai and Visakhapatnam.
3. Boats of 60-75 tonnes capacity and 20-25 metres in length could enter Lothal DOCK.
4. It was designed in such a manner as to ensure berthing 20-30 boats, a fairly large size.
5. Large foreign and Indian ships could enter the harbour without any difficulty

Question 5.
Can you guess what happened to the Harappans?
Answer:
The Harappans might have disappeared due to the following reasons.

1. Repeated floods.
2. Ecological changes.
3. Invasions.
4. Natural calamity.
5. Climatic changes.
6. Deforestation.
7. An epidemic.

IX. Activity (For Students)

1. Prepare a scrapbook. (Containing more information about objects collected from Mohenjo – Daro, and Harappa.)

2. You are a young archaeologist working at a site that was once an Indus city. What will you collect?

3. Make flashcards.
(Take square cards and stick a picture in one card and the information for the same picture in another card. Circulate among the groups and tell them to match the picture with information.)

4. Draw your imaginary town planning in a chart.

5. Make a model of anyone structure of Indus Civilisation using clay, broken pieces of bangles, matchsticks, woollen thread, and ice cream sticks.

6. Can you imagine how toys have changed through the ages?
Collect toys made of Clay → stone → wood → metal → plastic → fur → electric → electronic → ???

7 . Crossword puzzle

Top to Bottom:

1. Director-General of ASI
2. Is older than Mohenjo – Daro
3. This is age civilization
4. Each house had a

Left to Right

5. Place used to store grains
6. A dockyard has been found
7. is unknown to Indus people
8. It is used to make watertight.

Right to Left

9. From this we can get a lot of information
10. This is responsible for research

X. Rapid Fire Quiz (Do it in groups)

Question 1.
Which crop did Indus people use to make clothes?
Answer:
Cotton.

Question 2.
Which was the first Indus city discovered?
Answer:
Harappa.

Question 3.
Where was the Indus civilization?
Answer:
The Indus valley.

Question 4.
Which animal was used to pull carts?
Answer:
Bullocks.

Question 5.
Which metal was unknown to the Indus people?
Answer:
Iron

Question 6.
What was used to make pots?
Answer:
Wheel.

Question 7.
Which is considered the largest civilization among four ancient civilizations of the world?
Answer:
The Indus valley civilization.

XI. Life skill

1. Making an animal or a pot out of clay.
2. Making terracotta toy with movable limbs.
3. Pot painting (with geometric pattern).
4. Make informational charts and posters.

X. Answer Grid

Question 1.
What did Charles Masson see?
Answer:
Some mysterious brick mounds

Question 2.
List three things people used which we use today?
Answer:

1. Toys
2. Carts
3. Jewels

Question 3.
What else has been found?
Answer:
Burnt bricks

Question 4.
Can you say three things unknown to Indus people?
Answer:

1. Gun.
2. Paper.
3. Ink.

Question 5.
Which metal was unknown to the Indus people?
Answer:
Iron.

Question 6.
Which is the oldest civilization in the world?
Answer:

1. Mesopotamian
2. Civilization

Question 7.
Why the dog was the first animal to be tamed?
Answer:
It helped them in hunting.

Question 8.
Who were the first people to grow cotton?
Answer:
Sumerians.

Question 9.
Which institution is responsible for archaeological research?
Answer:
The Archaeological Survey of India

Question 10.
Was there any river valley civilization found in Tamil Nadu?
Answer:
No

Question 11.
Name any two Harappan sites which were found on the Indian border?
Answer:

1. Lothal
2. Kalibangan

Question 12.
Can we say the Indus cities as cities of children?
Answer:
Yes.

Samacheer Kalvi 6th Social Science Indus Civilisation Additional Important Questions and Answers

I. Choose the correct answer

Question 1.
The headquarters of the Archaeological Survey of India is located in ……………
(a) Chennai
(b) Mumbai
(c) Kolkata
(d) Delhi
Answer:
(d) Delhi

Question 2.
The dancing girl statue was made out of
(a) gold
(b) silver
(c) bronze
(d) iron
Answer:
(c) bronze

Question 3.
The word ‘civilization’ comes from the ancient Latin word ‘civis’ which means ……………
(a) City
(b) Village
(c) People
(d) Govern
Answer:
(c) People

Question 4.
The first metal discovered and used by humans was ……………..
(a) Iron
(b) Copper
(c) Bronze
(d) Silver
Answer:
(b) Copper

II. Match the statement with the reason. Tick the appropriate answer

Question 1.
Which of the following statements is true.
(a) Copper was the first metal used by humans.
(b) Horse was used by the Indus people to pull carts.
(c) Mohenjo – Daro was older than Harappa.
(d) Harappan civilization is a rural civilization.
Answer:
(a) Copper was the first metal used by humans.

Question 2.
Consider the following statements.
1. The streets of the Indus area have a grid pattern.
2. There is no evidence of the presence of palaces.
3. There are evidence of the presence of places of worship. Which of the above statements are correct?
(a) 1 and 2
(b) 1 and 3
(c) 2 and 3
(d) All the three
Answer:
(a) 1 and 2

Question 3.
Circle the odd one:
Answer:

1. Harappa
2. Mohenjodaro
3. Lahore
4. Lothal
5. Kalibangan

III. Fill in the blanks

1. In 1924, the Director-General of ASI was ……………..
2. The Archaeological Survey of India was started in ……………..
3. The earliest form of writing was developed by the ……………..
4. The great pyramid of Giza was built by king ……………..
5. Granaries were used to store.

Answer:

1. Sir John Marshall
2. 1861
3. Sumerians
4. Khufu
5. Foodgrains

IV. Answer the following questions

Question 1.
Why did people settle near rivers?
Answer:
People settled near rivers because

1. The soil is fertile.
2. Freshwater is available for drinking, watering livestock, and irrigation.
3. Easy movement of people and goods is possible.

Question 2.
Why do we say that the Indus people were the first to make cotton clothes?
Answer:

1. Cotton fabrics were in common use.
2. Clay spindles unearthed suggest that yam was spun.

Question 3.
Write about the occupations of the Indus people.
Answer:

1. Agriculture, handicrafts, pottery making, jewellery making, weaving, carpentry, and trading were practiced.
2. There were merchants, traders, and artisans.
3. They reared cattle and other animals.

Question 4.
Who built the Pyramid of Giza?
Answer:

1. The Pyramid of Giza was built by King Khufu in 2500 BCE.
2. It was built with limestone (15 tons each)

V. Mind Map

Students can download 6th Social Science History Term 1 Chapter 2 Human Evolution Questions and Answers, Notes, Samacheer Kalvi 6th 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 6th Social Science History Solutions Term 1 Chapter 2 Human Evolution

Samacheer Kalvi 6th Social Science Human Evolution Text Book Back Questions and Answers

I. Choose the correct answer

Question 1.
The process of evolution is …………….
(a) direct
(b) indirect
(c) gradual
(d) fast
Answer:
(c) gradual

Question 2.
Tanzania is situated in the continent of ________.
(a) Asia
(b) Africa
(c) America
(d) Europe
Answer:
(b) Africa

II. Match the statement with the reason. Tick the appropriate answer:

Question 1.
Statement : Migration of man of different parts of the world resulted in changes of physic and colour
Reason : Climatic changes.
(a) Statement is correct.
(b) Reason is wrong.
(c) Statement and Reason are correct.
(d) Statement and Reason are wrong.
Answer:
(c) Statement and Reason are correct

III. Find out the right pair

(a) Australopithecus – Walked on both legs
(b) Homo habilis – Upright man
(c) Homo erectus – Wise man
(d) Homo sapiens – Less protruding face
Answer:
(c) Homo erectus – Wise man

IV. Fill in the blanks

1. ………………. unearthed the footprints of humans in Tanzania.
2. Millions of years ago, our ancestors led a ………………. life.
3. The main occupations of the ancient humans were ………………. and ……………….
4. The invention of ………………. made farming easier.
5. Rock paintings are found at ………………. in Nilgiris.

Answer:

1. Anthropologist.
2. Nomadic.
3. hunting, gathering.
4. Plough.
5. Porivarai cave.

V. State True or False

1. Anthropology is the study of coins.
2. Homo erectus (Java man) had the knowledge of fire.
3. The first scientific invention of humans was wheel.
4. Goat was the first animal to be domesticated by humans.

Answer:

1. False
2. True
3. True
4. False

VI. Answer in one word

Question 1.
What method is used to find out the age of the excavated materials?
Answer:
Radio Carbon dating method.

Question 2.
What did early humans wear?
Answer:
Hides of animals and barks of trees and leaves.

Question 3.
Where did early humans live?
Answer:
In caves.

Question 4.
Which animal was used for ploughing?
Answer:
Oxen

Question 5.
When did humans settle in one place?
Answer:
When people began to practice agriculture, life became an organised one. It made the people settle in one place.

VII. Answer the following

Question 1.
What is evolution?
Answer:
Evolution is the process through which humankind changes and develops towards an advanced stage of life.

Question 2.
Write any two characteristics of Homo sapiens,
Answer:

1. Homo sapiens were wise men.
2. They migrated out of Eastern Africa settled in different parts of the world.
3. Their lifestyle also evolved and they made it suitable to the environs in which they lived.

Question 3.
Why did humans move from place to place?
Answer:
Humans kept on moving in search of food.

Question 4.
Describe the ancient methods of hunting,
Answer:

1. Collective hunting: Went as a group and hunted the prey
2. They dung a pit and trapped the animals and hunted.

Question 5.
Why were axes made?
Answer:
The axes were made to cut trees, remove barks, dig pits, hunt animals and remove the skin of animals.

Question 6.
How would you define archaeology?
Answer:

1. Archaeology is the study of pre-historic humans.
2. Excavated material remains are the main source for archaeological studies.

Question 7.
What do you know about anthropology?
Answer:
Anthropology is the study of humans and evolutionary history.

VIII. HOTS

Question 1.
Importance of invention of the wheel from the ancient period to the modern period
Answer:

1. Early homosapiens realised that round objects could be easily moved by rolling them.
2. Their descendants advanced this rolling technique into the transportation of large objects on cylindrical logs.
3. The invention of the wheel and axle allowed a rolling log to be placed through a hole in the wheel to create a cart.
4. Chariot racing was influential in the evolution of the spoked wheel as it allowed chariots to move much faster.
5. The invention of air-filled rubber tyres allowed wheels to be much faster, sturdier, and stronger.

IX. Activity ( For Student)

Prepare an album collecting the pictures of ancient humans of different ages.

X. Answer Grid

Question 1.
The invention of …………….. made pot making it easier.
Answer:
Wheel

Question 2.
Barter system means ……………..
Answer:
Exchanging one thing for another.

Question 3.
Name any two weapons used by early humans for hunting.
Answer:
Stones, bones, and horns of animals.

Question 4.
Which is the best stone for making weapons?
Answer:
chikki – mukki – kal

Question 5.
Towns and cities emerged because ……………. of …………….. and.
Answer:
trade, commerce

Question 6.
Which was the first scientific invention of humans?
Answer:
Wheel.

Question 7.
Identify the pictures in rock paintings.
Answer:
Hunting and dancing pictures

Question 8.
Which was the main occupation of early humans? What do cave paintings tell us?
Answer:
Information about the past.

Question 9.
Where did the early humans live?
Answer:
In caves.

Question 10.
…………….. is related to the field of archaeology.
Answer:
Anthropology

Question 11.
Name any two animals domesticated by an early humans.
Answer:
Dogs and Oxen

XI. Life Skill (For Students)

1. Make pots and tools by using clay.
2. Collect different types of moving dolls and tell them to change the wheels with different shapes like square, triangle, etc., and find out how it moves.

Samacheer Kalvi 6th Social Science Human Evolution Additional Important Questions and Answers

I. Choose the correct answer

Question 1.
The word ‘anthropology’ is derived from two …………….. words.
(a) Greek
(b) Latin
(c) Sanskrit
(d) Prakrit
Answer:
(a) Greek

Question 2.
Harpoons and spear throwers were used by _______
(a) Homo erectus
(b) Homo sapiens
(c) Cromagnons
(d) Homo habilis

II. Match the statement with the reason

Question 1.
Statement: Early humans decided to use guns for hunting.
Reason: It was difficult for them to kill big animals with a stick or stone.
a. Both statement and reason are correct
b. Both statement and reason are the wrong
c. The statement is wrong and the reason is correct.
d. Statement is correct and the reason is wrong.
Answer:
(c) Statement is wrong and the reason is correct.

III. Find out the wrong pair

(a) Homo sapiens – Africa
(b) Homo habits – South Africa
(c) Homo erectus – Asia
(d) Cro – magnons – China
Answer:
(d) Cro – magnons – China

IV. State True or False

1. The Neanderthal people buried the dead.
2. During the prehistoric period, horses were used to draw carts. Homo sapiens were wise.
3. Flintstones were easily available.
4. Coins made of iron were used by prehistoric people.

Answer:

1. True
2. False
3. True
4. False
5. False

V. Answer in brief

Question 1.
Write a short note on the mode of transport in 1850.
Answer:

1. There were no buses or cycles.
2. A cart pulled by mules and bullocks were seen on the roads.
3. A horse-drawn cart was a rare occurrence.

Question 2.
What is meant by the barter system?
Answer:
The early men exchanged the surplus grains with other groups for the other things they were in need of. This is called the barter system.

V. Answer in brief

Question 1.
Write a short note on the mode of transport in 1850.
Answer:

1. There were no buses or cycles.
2. A cart pulled by mules and bullocks were seen on the roads.
3. A horse-drawn cart was a rare occurrence.

Question 2.
What is meant by the barter system?
Answer:
The early men exchanged the surplus grains with other groups for the other things they were in need of. This is called the barter system.

VI. Mind map

 

Tamilnadu State Board New Syllabus Samacheer Kalvi 6th Social Science Guide Pdf History Term 1 Chapter 1 What is History?Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 6th Social Science Solutions History Term 1 Chapter 1 What is History?

6th Social Science Guide What is History? Text Book Back Questions and Answers

I. Choose the correct answer

Question 1.
What was the step taken by the early man to collect his food?
(a) trade
(b) hunting
(c) painting
(d) rearing of animals
Answer:
(b) hunting

II. Match the statement with the reason. Tick the appropriate answer

Question 1.
Statement: Pre historic man went along with the dog for hunting.
Reason: Dogs with its sniffing power would find out other animals.
(a) Statement is true, but reason is wrong.
(b) Statement and reason are correct.
(c) Statement is wrong, but reason is correct.
(d) Both statement and reason are wrong.
Answer:
(b) Statement and reason are correct

Question 2.
Statement: The objects used by the early man are excavated. They are preserved to know the lifestyle of the people.
Find out which of the following is related to the statement.
(a) Museum
(b) Burial materials
(e) Stone tools
(d) Bones
Answer:
(a) Museum

Question 3.
Find out the wrong pair:
(a) Old stone age – Stone tools
(b) Rock paintings – Walls of the caves
(c) Copper plates – A source of history
(d) Cats – First domesticated
Answer:
(d) Cats – First domesticated

Question 4.
Find the odd one:
(a) Paintings were drawn on rocks and caves.
(b) There were paintings depicting hunting scenes.
(c) It was drawn to show his family members about hunting.
(d) The paintings were painted by using many colours.
Answer:
(c) It was drawn to show his family members about hunting.

III. Fill in the blanks

1. The Old Stone age man lived mostly in ………………
2. ……………… is the Father of history.
3. ………………was the first animal tamed by Old Stone Age man.
4. Inscriptions are ……………… sources
5. Ashoka Chakra has ……………… spokes.

Answer:

1. Caves
2. Herodotus
3. Dog
4. archaeological
5. 24

IV. State True or False

1. Stone tools belonging to the Old Stone age have been excavated at Athtirampakkam near Chennai.
2. The materials used by the ancient people are preserved in the museums by the Archaeological Department.
3. During the period of Ashoka, Buddhism spread across the country.

Answer:

1. True
2. True
3. True

V. Match the following

1. – d
2. – a
3. – b
4. – c

VI. Answer in one word

Question 1.
Can you say any two advantages of writing a diary?
Answer:

1. Diary writing helps to record the events.
2. It reveals the lifestyle of people of that period.

Question 2.
How do we know the people’s lifestyle of the Old Stone Age?
Answer:
We understand the lifestyle of people of the Old Stone Age from used stone tools, their paintings on the rocks and walls of the caves.

Question 3.
Is inscription a written record?
Answer:
Yes. The inscription is a written record.

Question 4.
What is proto history?
Answer:
Protohistory is the period between prehistory and history.

Question 5.
Name an epic.
Answer:
Silapadhikaram.

VII. Answer the following

Question 1.
What is history?
Answer:

1. History is a record of past events in chronological order.
2. The term History has been derived from the Greek word Istoria which means learning by enquiry.

Question 2.
What do you know about the prehistoric period?
Answer:

1. The period between the use of the first stone tools and the invention of writing systems is pre-history.
2. Stone tools excavated materials, and rock paintings are the major sources of pre-history

Question 3.
What are the sources available to know about the prehistoric period?
Answer:
Paintings on the rocks and the walls of the caves, stone tools, excavated materials are the sources available to know about the pre-historic period.

Question 4.
Mention the places from where we got pre-historic tools.
Answer:
We find the pre-historic tools at Kondapur, Nevasa, Mehrgash, Rock shelters of Bhimbetka, and Edakkal caves in India. In Tamilnadu Attirampakkam, Ariyalur, Perambulur, Adichanalur are the places where we came across the pre-historic tools.

Question 5.
What are the benefits of a museum?
Answer:

1. Museums are community centres designed to inform and teach the public.
2. The educational benefit of a museum is academic learning.
3. Museums are the caretakers of history as much as they offer connections to history.
4. Museums are full of stories, and it is interesting for students to hear these stories.
5. Museums offer opportunities for children to compare and contrast leading to critical thinking skills.
6. Children’s curiosity comes out in the form of questions.
7. Students are exposed to new ideas and concepts.
8. Museums inspire students to wonder, imagine, and dream Of possibilities that are beyond what they know.
9. Students are exposed to opportunities that spark creative moments.

Question 6.
Name some tools used by early man to hunt animals.
Answer:

1. Blade cores were used. These were chunks of Sharp rocks.
2. An end scraper is a tear-drop shaped piece of stone used to scrap fur and fatty tissue from the hides of animals.
3. Burins were stone tools with a rounded grasping end and at the sharp, razor-like working end.
4. Awls were small circular stone flakes.

Question 7.
Why were paintings drawn on rocks?
Answer:

1. Paintings could have been drawn or rocks to convey their lifestyles to future generations.
2. They might have wished to record their activities through their paintings.

Question 8.
Name any two artifacts.
Answer:
Potteries, Toys, Tools, and Ornaments.

1. An artefact is something made or given shape by men, such as a tool or a work of art, especially an object of archaeological interest.
2. Some of the artefacts are potteries, toys, tools, and ornaments.

VIII. HOTS

Question 1.
How dogs were useful to prehistoric man?
Answer:

1. Dogs with their sniffing power helped them find out other wild animals.
2. Dog helped them prevent the entry of dangerous animals.
3. Thus dogs helped them in hunting and protection.

Question 2.
Compare the lifestyle of Old. Stone Age man with present-day lifestyle.
Answer:
Old Stone age man

1. He was a nomad.
2. Took shelter on branches of trees, in holes and caves.
3. Wore dresses made out of leaves, the skin of animals, and barks of trees.
4. Ate vegetables, fruits, and roots which he gathered from jungles.
5. Not civilized.

Present-day man:

1. Settled in villages and towns.
2. Lives in well-built houses.
3. Wears dresses made out of cotton and other materials.
4. Eats all kinds of food grains.
5. Well civilized.

IX. Activity (For Students)

1. Write down the important events of your family with years. Draw a timeline with the help of your teacher of with your classmates.
2. Early man used stones as a weapon. Make an album showing the various uses of stone.
3. Identify the category of the following sources of history.
   • Urns excavated from Adhichanallur.
   • Copper plates of Velvikudi.
   • Mahabharatha.
   • Sanchi Stupa
   • Pattinappaalai.
   • The earthernwares form keezhadi
   • Toys of Indus Civilisation.
   • Big Temple of Thanjavur.

X. Life Skill (For Students)

1. Make some weapon models used by the old stone Age man using clay.
2. Discuss with your grandpa, grandma, neighbours, and teachers and collect information about your street, villages, town or school. With the collected data, try to write its history titling your writing as “I am a Historian”.

XI. Answer Grid

Question 1.
Early men scribbled and painted on me Today they used me to build houses and lay roads. Who am I?
Answer:
Rock.

Question 2.
Name any two archaeological sources?
Answer:

1. Coins
2. Inscriptions

Question 3.
Name the types of literary sources?
Answer:

1. Secular literature
2. Religious literature

Question 4.
Expand BC (BCE).
Answer:
Before the common era

Question 5.
What is the meaning of the Greek word “Istoria”?
Answer:
Learning by enquiry

Question 6.
Expand AD (CE).
Answer:
Common era

Question 7.
…………….. is the study of inscriptions..
Answer:
Epigraphy

Question 8.
…………….. is the study of coins.
Answer:
Numismatics

Question 9.
I can help you to talk, see, hear, write, and read. There is no world without me. Who am I?
Answer:
Mobile Phone

6th Social Science Guide What is History? Additional Important Questions and Answers

I. Choose the correct answer

Question 1.
Dhamma is a word.
(a) Prakrit
(b) Sanskrit
(c) Latin
(d) Greek
Answer:
(a) Prakrit

II. Match the statement with the reason

Question 1.
Statement: Ashoka was the first ruler to give up war after victory.
Reason: He was upset and grief-stricken at the sight of the war.
(a) Statement is true but the reason is wrong.
(b) Both statement and reason are correct.
(c) Both statement and reason are wrong.
(d) Statement is wrong but the reason is correct.
Answer:
(b) Both statement and reason are correct

Question 2.
(a) Statement: Archaeological sources help to know about the early man.
Find out which of the following is related to the statement.
(a) Monuments
(b) Pictures
(c) Metals
(d) Books
Answer:
(a) Monuments

Question 3.
Find out the wrong pair.
(a) Numismatics – The study of coins
(b) Epigraphy – The study of Inscription
(c) Epic – Pattinapaalai
(d) Copper plates – Velvikudi
Answer:
(c) Epic – Pattinapaalai

Question 4.
Find the odd one.
(a) The dharma chakra has 24 spokes.
(b) It is seen in our National Flag.
(c) It was taken from Sanchi Stupa.
(d) It belongs to the Mauryan period
Answer:
(c) It was taken from Sanchi Stupa

III. Fill in the blanks

1. The Big Temple is in ……………
2. The most famous ruler of ancient India was ……………
3. Istoria means ……………

Answer:

1. Thanjavur.
2. Ashoka.
3. Learning by enquiry.

IV. State True or False

1. The term History has been derived from the Latin word ‘Istoria’.
2. We understand the lifestyle of old stone age people from used stone tools.
3. Thirumalai Nayakkar Mahal is in Thanjavur.

Answer:

1. False
2. True
3. False

V. Match the following

Answer:
1. – b
2. – a
3. – d
4. – c

VI. Mind Map

Students can Download Tamil Nadu 12th Maths Model Question Paper 5 English Medium Pdf, Tamil Nadu 12th Maths 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.

TN State Board 12th Maths Model Question Paper 5 English Medium

Instructions:

1.  The question paper comprises of four parts.
2.  You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. questions of Part I, II. III and IV are to be attempted separately
4. Question numbers 1 to 20 in Part I are objective type questions of one -mark each. These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 21 to 30 in Part II are two-marks questions. These are to be answered in about one or two sentences.
6. Question numbers 31 to 40 in Parr III are three-marks questions, These are to be answered in about three to five short sentences.
7. Question numbers 41 to 47 in Part IV are five-marks questions. These are to be answered) in detail. Draw diagrams wherever necessary.

Time: 3 Hours
Maximum Marks: 90

Part – I

I. Choose the correct answer. Answer all the questions. [20 × 1 = 20]

Question 1.
If | adj(adj A) | = |A|⁹, then the order of the square matrix A is _______.
(a) 3
(b) 4
(c) 2
(d) 5
Answer:
(b) 4

Question 2.
If |z₁| = 1, |z₂| = 2, |z₃| = 3 and |9z₁z₂ + 4z₁z₂ + z₂z₃| = 12, then the value of |z₁ + z₂+ z₃| is ________.
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(b) 2

Question 3.
The value of \(\left(\frac{1+\sqrt{3} i}{1-\sqrt{3} i}\right)^{10}\) is ________.

Answer:
(a) cis \(\frac{2 \pi}{3}\)

Question 4.
If \(\cot ^{-1}(\sqrt{\sin \alpha})+\tan ^{-1}(\sqrt{\sin \alpha})=u\), then cos 2u is equal to _____.
(a) tan² α
(b) 0
(c) -1
(d) tan 2α
Answer:
(c) -1

Question 5.
If \(\cot ^{-1} x=\frac{2 \pi}{5}\) for some x∈R, the value of tan^-1 x is _______.

Answer:
(c) \(\frac{\pi}{10}\)

Question 6.
The radius of the circle passing through the point (6, 2) two of whose diameter are x + y = 6 and x + 2y = 4 is ____.
(a) 10
(b) \(2 \sqrt{5}\)
(c) 6
(d) 4
Answer:
(b) \(2 \sqrt{5}\)

Question 7.
The length of the L.R. of x² = -4y is _______.
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(d) 4

Question 8.
Distance from the origin to the plane 3x – 6y + 2z + 7 = 0 is ______.
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(b) 1

Question 9.
The distance from the origin to the plane \(\vec{r} \cdot(2 \vec{i}-\vec{j}+5 \vec{k})=7\) is _____.

Answer:
(a) \(\frac{7}{\sqrt{30}}\)

Question 10.
The number given by the Mean value theorem for the function \(\frac{1}{x}\), x ∈ [1, 9] is ______.
(a) 2
(b) 2.5
(c) 3
(d) 3.5
Answer:
(c) 3

Question 11.
f is a differentiable function defined on an interval I with positive derivative. Then f is ______.
(a) increasing on I
(b) decreasing on I
(c) strictly increasing on I
(d) strictly decreasing on I
Answer:
(c) strictly increasing on I

Question 12.
If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is ________.
(a) 0.4 cu.cm
(b) 0.45 cu.cm
(c) 2 cu.cm
(d) 4.8 cu.cm
Answer:
(d) 4.8 cu.cm

Question 13.
If u(x, y) = \(e^{x^{2}+y^{2}}\), then \(\frac{\partial u}{\partial x}\) is equal to _______.
(a) \(e^{x^{2}+y^{2}}\)
(b) 2xu
(c) x²u
(d) y²u
Answer:
(b) 2xu

Question 14.
The value of \(\int_{0}^{\infty} e^{-3 x} x^{2} d x\) is _______.
(a) \(\frac{7}{27}\)
(b) \(\frac{5}{27}\)
(c) \(\frac{4}{27}\)
(d) \(\frac{2}{27}\)
Answer:
(d) \(\frac{2}{27}\)

Question 15.
\(\int_{0}^{a} f(x) d x\) is _____.

Answer:
(b) \(\int_{0}^{a} f(a-x) d x\)

Question 16.
The integrating factor of the differential equation \(\frac{d y}{d x}\) + P(x) y = Q (x) is x, then P(x) ______.
(a) x
(b) \(\frac{x^{2}}{2}\)
(c) \(\frac{1}{x}\)
(d) \(\frac{1}{x^{2}}\frac{1}{x^{2}}\)
Answer:
(c) \(\frac{1}{x}\)

Question 17.
The order and degree of the differential equation p\(\frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{1 / 3}+x^{1 / 4}=0\) are respectively _______.
(a) 2, 3
(b) 3, 3
(c) 2, 6
(d) 2, 4
Answer:
(a) 2, 3

Question 18 .
Which of the following is a discrete random variable?
I. The number of cars crossing a particular signal in a day.
II. The number of customers in a queue to buy train tickets at a moment.
III. The time taken to complete a telephone call.
(a) I and II
(b) II only
(c) III only
(d) II and III
Answer:
(a) I and II

Question 19.
If p is true and q is false then which of the following is not true?
(a) p → q is false
(b)p ∨ q is true
(c)p ∧ q is false
(d) p ↔ q is true
Answer:
(d) p ↔ q is true

Question 20.
The operation * defined by a*b = \(\frac{a b}{7}\) is not a binary operation on ______.
(a) Q⁺
(b) Z
(c) R
(c) C
Answer:
(b) Z

Part – II

II. Answer any seven questions. Question No. 30 is compulsory. [7 × 2 = 14]

Question 21.
Using elementary transformations find the inverse of the following matrix \(\left[\begin{array}{ll}
4 & 7 \\
3 & 0
\end{array}\right]\)
Answer:

Question 22.
If Z₁ = 1 – 3i, z₂ = -4i, and z₃ = 5, show that (z₁ + z₂) + z₃ = Z₁ + (z₂ + z₃)
Answer:
z₁ = 1 – 3i, z₂ = 4i, z₃ = 5
(z₁ + z₂) + z₃ = (1 – 3i – 4i) + 5(1 – 7i) + 5
= 6 – 7i …..(1)
z₁ + (z₂ + z₃) = (1 – 3i) + (-4i + 5)
= 6 – 7i …..(2)
from(1)& (2)we get
∴ (z₁ + z₂) + z₃ = z₁ + (z₂ + z₃)

Question 23.
Find a polynomial equation of minimum degree with rational coefficients, having 2+ \(\sqrt{3}\) i as
a root.
Answer:
Given roots is (2 + \(\sqrt{3}\) i)
∴ The other root is (2 – \(\sqrt{3}\) i), since the imaginary roots with real co-efficient occur as conjugate
pairs.
x² – x(S.O.R) + P.O.R = 0 ⇒ x² – x(4) + (4 + 3) = 0
x² – 4x + 7 = 0.

Question 24.
Evaluate: \(\lim _{x \rightarrow \infty}\left(\frac{x^{2}+17 x+29}{x^{4}}\right)\)
Answer:
This is an indeterminate of the form (\(\frac{\infty}{\infty}\)). To evaluate this limit, we apply l’Hôpital Rule.

Question 25.
Let g(x, y) = 2y + x², x = 2r – s, y = r² + 2s, r, s ∈R. Find \(\frac{\partial g}{\partial r}, \frac{\partial g}{\partial s}\).
Answer:

Question 26.
Evaluate: \(\int_{0}^{\frac{\pi}{2}}\left(\sin ^{2} x+\cos ^{4} x\right) d x\)
Answer:

Question 27.
Find the differential equation corresponding to the family of curves represented by the equation y = Ae^8x + Be^-8x, where A and B are arbitrary constants.
Answer:
y = Ae^8x + Be^-8x Where A and B are arbitrary constants.
Differentiate with respect to ‘x’

Question 28.
If F(x) = \(\frac{1}{\pi}\left(\frac{\pi}{2}+\tan ^{-1} x\right)\) – ∞ < x < ∞ is a distribution function of a continuous variable X, find P (0 ≤ x ≤ 1).
Answer:

Question 29.
Show that p → q and q → p are not equivalent.
Answer:
Truth table for p → q

Truth table for q → p

The entries in the column corresponding to p → q and q → p are not identical, hence they are not equivalent.

Question 30.
Show that the lines \(\frac{x-1}{4}=\frac{2-y}{6}=\frac{z-4}{12}\) and \(\frac{x-3}{-2}=\frac{y-3}{3}=\frac{5-z}{6}\) are parallel.
Answer:
We observe that the straight line \(\frac{x-1}{4}=\frac{2-y}{6}=\frac{z-4}{12}\) is parallel to the vector \(4 \hat{i}-6 \hat{j}+12 \hat{k}\) and the straight line \(\frac{x-3}{-2}=\frac{y-3}{3}=\frac{5-z}{6}\) is parallel to the vector \(-2 \hat{i}+3 \hat{j}-6 \hat{k}\).
Since \(4 \hat{i}-6 \hat{j}+12 \hat{k}=-2(-2 \hat{i}+3 \hat{j}-6 \hat{k})\) the two vectors are parallel, and hence the two straight lines are parallel.

Part – III

II. Answer any seven questions. Question No. 40 is compulsory. [7 × 3 = 21]

Question 31.
Using elementary transformations find the inverse of the matrix \(\left[\begin{array}{ccc}
1 & -1 & 1 \\
2 & 1 & -3 \\
1 & 1 & 1
\end{array}\right]\)

Question 32.
Find the square roots of – 15 – 8i

Question 33.
Find the sum of the squares of the roots of ax⁴ + bx³ + cx² + dx + e = 0, a ≠ 0

Question 34.
For what value of x, the inequality \(\frac{\pi}{2}\) < cos^-1 (3x – 1) < π holds?

Question 35.
Find the foot of the perpendicular drawn from the point (5, 4, 2) to the line \(\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}\). Also, find the equation of the perpendicular.

Question 36.
Evaluate \(\int_{0}^{\infty} \frac{x^{n}}{n^{x}} d x\), where n is a positive integer ≥ 2.

Question 37.
The engine of a motor boat moving at 10 m/s is shut off. Given that the retardation at any subsequent time (after shutting off the engine) equal to die velocity at that time. Find the velocity after 2 seconds of switching off the engine.

Question 38.
The probability that Mr.Q hits a target at any trial is \(\frac{1}{4}\). Suppose he tries at the target 10 times. Find the probability that he hits the target (i) exactly 4 times (ii) at least one time.

Question 39.
Consider the binary operation * defined on the set A = {a, b, c, d} by the following table:

Is it commutative and associative?

Question 40.
Evaluate the following limit, if necessary use l’Hopital Rule. \(\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^{x}\)

Part – IV

IV. Answer all the questions. [7 × 5 = 35]

Question 41.
(a) Find the inverse of A = \(\left[\begin{array}{lll}
2 & 1 & 1 \\
3 & 2 & 1 \\
2 & 1 & 2
\end{array}\right]\) by Gauss-Jordan method
[OR]
(b) Find the point of intersection of the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=z\).

Question 42.
(a) Suppose z₁, z₂ and z₃ are the vertices of an equilateral triangle inscribed in the circle.
|z| = 2. If z₁ = 1 + i\(\sqrt{3}\), then find z₂ and z₃.
[OR]
(b) If A = \(\left[\begin{array}{cc}
5 & 3 \\
-1 & -2
\end{array}\right]\) show that A² – 3A – 7I₂ = O₂. Hence Find A^-1.

Question 43.
(a) Solve the equation 3x³ – 16x² + 23x – 6 = 0 if the product of two roots is 1.
[OR]
(b) The mean and variance of a binomial variate X are respectively 2 and 1.5.
Find (i) P(X = 0) (ii) P(X = 1) (iii) P(X ≥ 1)

Question 44.
(a) Find the value of \(\cos \left(\sin ^{-1}\left(\frac{4}{5}\right)-\tan ^{-1}\left(\frac{3}{4}\right)\right)\)
[OR]
(b) Find, by integration, the volume of the solid generated by revolving about y-axis the region bounded between the curve y = \(\frac{3}{4} \sqrt{x^{2}-16}\), x ≥ 4, the y-axis, and the lines y = 1 and y = 6.

Question 45.
(a) A semielliptical archway over a one-way road has a height of 3m and a width of 12m. The truck has a width of 3m and a height of 2.7m. Will the truck clear the opening of the archway?
[OR]
(b) For the function f(x, y) = \(\frac{3 x}{y+\sin x}\) find the f_x, f_y, and show that f_xy = f_yx.

Question 46.
(a) Derive the equation of the plane in the intercept form.
[OR]
(b) Let A be Q\{1}. Define * on A by x * y = x +y – xy. Is * binary on A ? If so, examine the existence of identity, existence of inverse properties for the operation * on A .

Question 47.
(a) Find the angle between the rectangular hyperbola xy = 2 and the parabola x² + 4y = 0.
[OR]
(b) A pot of boiling water at 100° C is removed from a stove at time t = 0 and left to cool in the kitchen. After 5 minutes, the water temperature has decreased to 80° C, and another 5 minutes later it has dropped to 65° C. Determine the temperature of the kitchen.

Students can Download Tamil Nadu 12th Maths Model Question Paper 4 English Medium Pdf, Tamil Nadu 12th Maths 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.

TN State Board 12th Maths Model Question Paper 4 English Medium

Instructions:

1.  The question paper comprises of four parts.
2.  You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. questions of Part I, II. III and IV are to be attempted separately
4. Question numbers 1 to 20 in Part I are objective type questions of one -mark each. These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 21 to 30 in Part II are two-marks questions. These are to be answered in about one or two sentences.
6. Question numbers 31 to 40 in Parr III are three-marks questions, These are to be answered in about three to five short sentences.
7. Question numbers 41 to 47 in Part IV are five-marks questions. These are to be answered) in detail. Draw diagrams wherever necessary.

Time: 3 Hours
Maximum Marks: 90

Part – I

I. Choose the correct answer. Answer all the questions. [20 × 1 = 20]

Question 1.
If A^T A^-1 is symmetric, then A² = _______
(a) A^-1
(b) (A^T)²
(c) A^T
(d) (A^-1)²
Answer:
(b) (AT)2

Question 2.
If p + iq = \(\frac{a+i b}{a-i b}\), then p² + q² = ________.
(a) 0
(b) 2
(c) 1
(d) -1
Answer:
(c) 1

Question 3.
If ω ≠ 1 is a cubic root of unity and \(\left|\begin{array}{ccc}
1 & 1 & 1 \\
1 & -\omega^{2}-1 & \omega^{2} \\
1 & \omega^{2} & \omega^{7}
\end{array}\right|\) = 3k, then k is equal to _______.
(a) 1
(b) -l
(c) \(\sqrt{3} i\)
(d) \(-\sqrt{3} i\)
Answer:
(d) \(-\sqrt{3} i\)

Question 4.
The value of sin^-1 (cos x), 0 ≤ x ≤ π is _______.
(a) π – x
(b) x – \(\frac{\pi}{2}\)
(c) \(\frac{\pi}{2} – x\)
(d) π – x
Answer:
(c) \(\frac{\pi}{2} – x\)

Question 5.
The radius of the circle 3x² + by² + 4bx – 6by + b² = 0 is ________.
(a) 1
(b) 3
(c) \(\sqrt{10}\)
(d) \(\sqrt{11}\)
Answer:
(c) \(\sqrt{10}\)

Question 6.
The equation of the directrix of the parabola y² = -8x is ______.
(a) y + 2 = 0
(b) x – 2 = 0
(c) y – 2 = 0
(d) x + 2 = 0
Answer:
(b) x – 2 = 0

Question 7.
If \(\vec{a}\) and \(\vec{b}\) are parallel vector, then \([\vec{a}, \vec{c}, \vec{b}]\) is equal to _____
(a) 2
(b) -1
(c) 1
(d) 0
Answer:
(d) 0

Question 8.
The length of the perpendicular from the origin to the plane \(\vec{r} \cdot(3 \vec{i}+4 \vec{j}+12 \vec{k})=26\) is _______.
(a) 26
(b) \(\frac{26}{169}\)
(c) 2
(d) \(\frac{1}{2}\)
Answer:
(c) 2

Question 9.
The curve y = ax⁴ + bx² with ab > 0
(a) has no horizontal tangent
(b) is concave up
(c) is concave down
(d) has no points of inflection
Answer:
(d) has no points of inflection

Question 10.
The asymptote to the curve y² (1 + x) = x² (1 – x) is _______.
(a) x = 1
(b) y = 1
(c) y = -1
(d) x = -1
Answer:
(d) x = -1

Question 11.
If f(x, y, z) = xy + yz + zx, then f_x – f_z is equal to ________.
(a) z – x
(b) y – z
(c) x – z
(d) y – x
Answer:
(a) z – x

Question 12.
If f(x, y) = e^xy , then \(\frac{\partial^{2} f}{\partial x \partial y}\) is equal to ________.
(a) xye^xy
(b) (1 + xy) e^xy
(c) (1 + y) e^xy
(d) (1 + x) e^xy
Answer:
(b) (1 + xy) e^xy

Question 13.
The value of \(\int_{0}^{\frac{\pi}{6}} \cos ^{3} 3 x d x\) is _______.
(a) \(\frac{2}{3}\)
(b) \(\frac{2}{9}\)
( c) \(\frac{1}{9}\)
(d) \(\frac{1}{3}\)
Answer:
(b) \(\frac{2}{9}\)

Question 14.
If f(x) is even then \(\int_{-a}^{a} f(x) d x \) _______.

Answer:
(b) \(2 \int_{0}^{a} f(x) d x\)

Question 15.
The order and degree of the differential equation \(\sqrt{\sin x}\)(dx + dy) = \(\sqrt{\sin x}\) (dx- dy) is ________.
(a) 1, 2
(b) 2, 2
(c) 1, 1
(d) 2, 1
Answer:
(c) 1, 1

Question 16.
The solution of the differential equation \(\frac{d y}{d x}\) = 2xy is _______.
(a) y = c e^x2
(b) y = 2x² + c
(c) = ce^-x2 + c
(d) y = x² + c
Answer:
(a) y = c e^x2

Question 17.
If P{X = 0} = 1 – P{X = 1}. If E[X] = 3Var(X), then P{X = 0} ________.
(a) \(\frac{2}{3}\)
(b) \(\frac{2}{5}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{1}{3}\)
Answer:
(d) \(\frac{1}{3}\)

Question 18.
Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are _________.
(a) i + 2n, i = 0, 1, 2 … n
(b) 2i – n, i = 0, 1, 2 … n
(c) n – i, i = 0, 1, 2 … n
(d) 2i + 2n, i = 0, 1, 2 … n
Answer:
(b) 2i – n, i = 0, 1, 2 … n

Question 19.
In the set Q define a Θ b= a + b + ab. For what value of y, 3 Θ (y Θ 5) = 7 ?

Answer:
(b) y = \(\frac{-2}{3}\)

Question 20.
If X is a continuous random variable then P(X > a) =
(a) P (X < a)
(b) 1 – P (X > a)
(c) P (X > a)
(d) 1 – P (x ≥ a)
Answer:
(c) P (X > a)

Part – II

II. Answer any seven questions. Question No. 30 is compulsory. [7 × 2 = 14]

Question 21.
Reduce the matrix \(\left[\begin{array}{ccc}
3 & -1 & 2 \\
-6 & 2 & 4 \\
-3 & 1 & 2
\end{array}\right]\) to a row-echelon form.
Answer:

Question 22.
Find the least positive integer n such that \(\left(\frac{1+i}{1-i}\right)^{n}=1\)
Answer:

Question 23.
Find the value of \(\sin ^{-1}\left(\sin \left(\frac{5 \pi}{4}\right)\right)\)
Answer:

Question 24.
Identify the type of conic section for the equation 3x² + 3y² – 4x + 3y + 10 = 0
Answer:
Comparing this equation with the general equation of the conic
Ax² + Bxy + cy² + Dx + Ey +F = 0
We get A = C also B = 0
So the given conic is a circle.

Question 25.
If U(x, y, z) = log(x³ + y³ + z³), find \(\frac{\partial \mathrm{U}}{\partial x}+\frac{\partial \mathrm{U}}{\partial y}\) and \(\frac{\partial U}{\partial z}\)
Answer:

Question 26.
Find, by integration, the volume of the solid generated by revolving about the x-axis, the region enclosed by y = 2x², y = 0 and x = 1.
Answer:

Question 27.
Solve the differential equation: \(\frac{d y}{d x}-x \sqrt{25-x^{2}}=0\)
Answer:

Question 28.
Three fair coins are tossed simultaneously. Find the probability mass function for number of heads occurred.
Answer:
When three coins are tossed, the sample space is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
‘X’ is the random variable denotes the number of heads.
∴ ‘X’ can take the values of 0, 1, 2 and 3
Hence, the probabilities
P(X = 0) = P (No heads) = \(\frac{1}{8}\);
P(X = 1) = P (1 head) = \(\frac{3}{8}\);
P(X = 2) = P (2 heads) = \(\frac{3}{8}\);
P(X = 3) = P (3 heads)= \(\frac{1}{8}\);
∴ The probability mass function is
\(f(x)=\left\{\begin{array}{lll}
1 / 8 & \text { for } & x=0,3 \\
3 / 8 & \text { for } & x=1,2
\end{array}\right.\)

Question 29.
Construct the truth table for the following statements. \(\neg p \wedge \neg q\)
Answer:
Truth table for \(\neg p \wedge \neg q\)

Question 30.
Write the Maclaurin series expansion of the function: ex
Answer:
f (x) = e^x; f (0) = e⁰ = 1
f’ (x) = e^x; f’ (0) = 1
f”(x) = e^x; f”(0) = 1

Part – III

III. Answer any seven questions. Question No. 40 is compulsory. [7 × 3 = 21]

Question 31.
If A = \(\left[\begin{array}{lll}
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0
\end{array}\right]\)show that A^-1 = \(\frac{1}{2}\) (A² – 3I).

Question 32.
Find the values of the real numbers x and y, if the complex numbers.
(3 – i)x – (2 – i) y + 2i + 5 and 2x + (-1 + 2i) y + 3 + 2i are equal.

Question 33.
It is known that the roots of the equation x³ – 6x² – 4x + 24 = 0 are in arithmetic progression. Find its roots.

Question 34.
Prove that: \(\cos \left[\tan ^{-1}\left\{\sin \left(\cot ^{-1} x\right)\right\}\right]=\sqrt{\frac{x^{2}+1}{x^{2}+2}}\)

Question 35.
Find the equation of a circle of radius 5 whose centre lies on x-axis and which passes through the point (2, 3).

Question 36.
Using the l’ Hopital Rule prove that, \(\lim _{x \rightarrow 0^{+}}(1+x)^{\frac{1}{x}}=e\)

Question 37.
If v(x, y) = x² – xy + \(\frac{1}{4}\) y² + 7, x, y ∈ R, find the differential dv.

Question 38.
Find the area of the region bounded by 2x – y + 1 =0, y = – 1, y = 3 and y-axis..

Question 39.
Solve: \(\frac{d y}{d x}\) + 2y cot x = 3x² cosec²x

Question 40.
If the straight lines \(\frac{x-5}{5 m+2}=\frac{2-y}{5}=\frac{1-z}{-1}\) and x = \(\frac{2 y+1}{4 m}=\frac{1-z}{-3}\) are perpendicular to each other, find the value of m.

Part – IV

IV. Answer all the questions. [7 × 5 = 35]

Question 41.
(a) Investigate the values of X and p the system of linear equations.
2x + 3y + 5z = 9, 7x + 3y – 5z = 8, 2x + 3y + λz = µ, have
(i) no solution (ii) a unique solution (iii) an infinite number of solutions.
[OR]
(b) If z(x, y) = x tan^-1 (xy), x = t², y = s e^t, s, t ∈ R, Find \(\frac{\partial z}{\partial t}\) and \(\frac{\partial z}{\partial t}\) at s = t = 1.

Question 42.
(a) Form the equation whose roots are the squares of the roots of the cubic equation
x³ + ax² + bx + c = 0.
[OR]
(b) Find the intervals of concavity and the points of inflection of the function.
f(θ) = sin 2θ in (0, π)

Question 43.
(a) If a = cos 2α + i sin 2α, b = cos 2β + i sin 2β and c = cos 2γ + i sin 2γ, prove that.

(b) A closed (cuboid) box with a square base is to have a volume of 2000 c.c. The material for the top and bottom of the box is to cost Rs. 3 per square cm and the material for the sides is to cost Rs. 1.50 per square cm. If the cost of the materials is to be the least, find the dimensions of the box.

Question 44.
(a) Prove that a straight line and parabola cannot intersect at more than two points.
[OR]
(b) Solve \(\left(y-e^{\sin ^{-1} x}\right) \frac{d x}{d y}+\sqrt{1-x^{2}}=0\)

Question 45.
(a) Solve \(\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}\)
[OR]
(b) Show that the lines \(\frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}\) and \(\frac{x-4}{2}=\frac{y}{0}=\frac{z+1}{3}\) the point of intersection.

Question 46.
(a) A tank initially contains 50 liters of pure water. Starting at time t = 0 a brine containing with 2 grams of dissolved salt per litre flows into the tank at the rate of 3 liters per minute. The mixture is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the tank at the same rate. Find the amount of salt present in the tank at any time t > 0.
[OR]
(b) If X ~ B(n, p) such that 4P (X = 4) = P (x = 2) and n = 6 . Find the distribution, mean and standard deviation.

Question 47.
(a) Find the centre, foci, and eccentricity of the hyperbola 11x² – 25y² – 44x + 50y – 256 = 0
[OR]
(b) Verify (i) closure property (ii) commutative property (iii) associative property (iv) existence of identity and (v) existence of inverse for the operation +5 on Z5 using table corresponding to addition modulo 5.

Students can Download Tamil Nadu 12th Maths Model Question Paper 3 English Medium Pdf, Tamil Nadu 12th Maths 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.

TN State Board 12th Maths Model Question Paper 3 English Medium

Instructions:

1.  The question paper comprises of four parts.
2.  You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. questions of Part I, II. III and IV are to be attempted separately
4. Question numbers 1 to 20 in Part I are objective type questions of one -mark each. These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 21 to 30 in Part II are two-marks questions. These are to be answered in about one or two sentences.
6. Question numbers 31 to 40 in Parr III are three-marks questions, These are to be answered in about three to five short sentences.
7. Question numbers 41 to 47 in Part IV are five-marks questions. These are to be answered) in detail. Draw diagrams wherever necessary.

Time: 3 Hours
Maximum Marks: 90

Part – I

I. Choose the correct answer. Answer all the questions. [20 × 1 = 20]

Question 1.
If A is a 3 × 3 non-singular matrix such that AA^T = A^T A and B = A^-1 A^T, then BB^T = ________.
(a) A
(b) B
(c) I₃
(d) B^T
Answer:
(c) I₃

Question 2.
The rank of the matrix \(\left[\begin{array}{cc}
7 & -1 \\
2 & 1
\end{array}\right]\) is ________.
(a) 9
(b) 2
(c) 1
(d) 5
Answer:
(b) 2

Question 3.
The value of \(\sum_{i=1}^{13}\left(i^{n}+i^{n-1}\right)\) is ________.
(a) 1 + i
(b) i
(c) 1
(d) 0
Answer:
(a) 1 + i

Question 4.
Which of the following is incorrect?
(d) Re(z) ≤ |z|
(b) Im (z) ≤ |z|
(c) \(z \bar{z}=|z|^{2}\)
(d) Re(z) ≥ |z|
Answer:
(d) Re(z) ≥ |z|

Question 5.
According to the rational root theorem, which number is not possible rational zero of 4x⁷ + 2x⁴ – 10x³ – 5?
(a) -1
(b) \(\frac{5}{4}\)
(c) \(\frac{4}{5}\)
(d)5
Answer:
(c) \(\frac{4}{5}\)

Question 6.
If \(\cot ^{-1}(\sqrt{\sin \alpha})+\tan ^{-1}(\sqrt{\sin \alpha})=u\), then cos 2u is equal to ______.
(a) tan² α
(b) o
(c) -1
(d) tan 2α
Answer:
(c) -1

Question 7.
The domain of the function defined by f(x) = sin^-1 \(\sqrt{x-1}\) is _______.
(a) [1, 2]
(b) [-1, 1]
(c) [0, 1]
(d) [-1, 0]
Answer:
(a) [1, 2]

Question 8.
The area of quadrilateral formed with foci of the hyperbolas \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) and \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=-1\) is ________.
(a) 4(a² + b²)
(b) 2(a² + b²)
(c) a² + b²
(d) \(\frac{1}{2}\) (a² + b²)
Answer:
(b) 2(a² + b²)

Question 9.
The directrix of the parabola x² = -4y is ________.
(a) x = 1
(b) x = 0
(c) y = 1
(d) y = 0
Answer:
(c) y = 1

Question 10.
If the line \(\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}\) lies in the plane x + 3y – αz + b = β, then (α, β) is ______
(a) (-5, 5)
(b) (-6, 7)
(c) (5, -5)
(d) (6, -7)
Answer:
(b) (-6, 7)

Question 11.
If \(\vec{a} \times(\vec{b} \times \vec{c})=(\vec{a} \times \vec{b}) \times \vec{c}\) for non-coplanar vectors \(\vec{a}, \vec{b}, \vec{c}\) then ________.
(a) \(\vec{a}\) parallel to \(\vec{b}\)
(b) \(\vec{b}\) parallel to \(\vec{c}\)
(c) \(\vec{c}\) parallel to \(\vec{a}\)
(d) \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\)
Answer:
(c) \(\vec{c}\) parallel to \(\vec{a}\)

Question 12.
The maximum product of two positive numbers, when their sum of the squares is 200, is ________.
(a) 100
(b) \(25 \sqrt{7}\)
(c) 28
(d) \(24 \sqrt{14}\)
Answer:
(a) 100

Question 13.
If w(x,y, z) = x² (y – z) + y² (z – x) + z² (x – y), then \(\frac{\partial w}{\partial x}+\frac{\partial w}{\partial y}+\frac{\partial w}{\partial z}\) is ________.
(a) xy + yz + zx
(b) x (y + z)
(c) y (z + x)
(d) 0
Answer:
(d) 0

Question 14.
If u (x, y) = x² + 3xy + y – 2019, then \(\left.\frac{\partial u}{\partial x}\right|_{(4,-5)}\) is equal to ______.
(a) -4
(b) -3
(c) -7
(d) 13
Answer:
(c) -7

Question 15.
The volume of solid of revolution of the region bounded by y² = x (a – x) about x-axis is ________.

Answer:
(d) \(\frac{\pi a^{3}}{6}\)

Question 16.
\(\int_{0}^{a} f(x) d x+\int_{0}^{a} f(2 a-x) d x\) = _________.

Answer:
(c) \(\int_{0}^{2 a} f(x) d x\)

Question 17.
The differential equation of the family of curves y = Ae^x + Be^-x, where A and B are arbitrary constants is _______.

Answer:
(b) \(\frac{d^{2} y}{d x^{2}}-y=0\)

Question 18.
The differential equation corresponding to xy = c² where c is an arbitrary constant, is ______.
(a) xy”+ x = 0
(b) y” = 0
(c) xy’ + y = 0
(d) xy”- x = 0
Answer:
(c) xy’ + y = 0

Question 19.
If \(f(x)=\left\{\begin{array}{ll}
2 x, & 0 \leq x \leq a \\
0 & , \text { otherwise }
\end{array}\right.\)
is a probability density function of a random variable, then the value of a is _________.
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(a) 1

Question 20.
The proposition \(p \wedge(\neg p \vee q)\) is
(a) a tautology
(b) a contradiction
(c) logically equivalent to p ∧ q
(d) logically equivalent to p ∨ q
Answer:
(c) logically equivalent to p ∧ q

Part – II

II. Answer any seven questions. Question No. 30 is compulsory. [7 × 2 = 14]

Question 21.
A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.
Answer:
Let the two parts be x and (12 – x)
Given that x = \(\sqrt[3]{12-x}\)
Cubing on both side, x³ = 12 – x
x³ + x – 12 = 0

Question 22.
Find the value of \(\sin ^{-1}\left(\sin \frac{5 \pi}{9} \cos \frac{\pi}{9}+\cos \frac{5 \pi}{9} \sin \frac{\pi}{9}\right)\)
Answer:

Question 23.
Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.
Answer:

Given radius = 5 cm and the circle is touching x axis
So centre will be (0, ± 5) and radius = 5
The equation of the circle with centre (0, ± 5) and radius 5 units is
(x – 0)² + (y ± 5)² = 5²
(i.e) x² + y² ± 10y + 25 – 25 = 0
(i.e) x² + y² ± 10y = 0

Question 24.
Find the length of the perpendicular from the origin to the plane.
\(\bar{r} \cdot(3 \vec{i}+4 \bar{j}+12 \vec{k})=26\).
Answer:
Taking the equation of the plane in cartesian form we get,
\((x \vec{i}+y \vec{j}+z \vec{k}) \cdot(3 \vec{i}+4 \vec{j}+12 \vec{k})=26\)
i.e. 3x + 4y + 12z – 26 = 0
The length of the perpendicular from (0, 0, 0) to the above plane is

Question 25.
Evaluate \(\lim _{x \rightarrow \pi / 2} \frac{\log (\sin x)}{(\pi-2 x)^{2}}\)
Answer:

Note that here l’ Hospitals rule, applied twice yields the result.

Question 26.
Evaluate \(\int_{-1}^{1} e^{-\lambda x}\left(1-x^{2}\right) d x\)
Answer:
Taking u = 1 – x² and v= e^-λx, and applying the Bernoulli’s formula, we get

Question 27.
Solve: \(\frac{d y}{d x}+2 y=e^{-x}\)
Answer:
Given that \(\frac{d y}{d x}+2 y=e^{-x}\)
This is a linear differential equation.
Here P = 2; Q = e
∫P dx = ∫2 dx = 2x
Thus, I.F = e^∫Pdx = e^2x
Hence the solution of (1) is \(y e^{\int \mathrm{P} d x}=\int \mathrm{Q} e^{\int \mathrm{P} d x} d x+c\)
That is, ye^2x = ∫e^-x e^2x dx + c (or) ye^2x = e^x + c (or) y = e^-x + ce^-2x is the required solution.

Question 28.
Three fair coins are tossed simultaneously. Find the probability mass function for number of heads occurred.
Answer:
When three coins are tossed, the sample space is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
‘X’ is the random variable denotes the number of heads.
∴ ‘X’ can take the values of 0, 1, 2 and 3
Hence, the probabilities
P(X = 0) = P (No heads) = \(\frac{1}{8}\);
P(X = 1) = P (1 head) = \(\frac{3}{8}\);
P(X = 2) = P (2 heads) = \(\frac{3}{8}\);
P(X = 3) = P (3 heads)= \(\frac{1}{8}\);
∴ The probability mass function is
\(f(x)=\left\{\begin{array}{lll}
1 / 8 & \text { for } & x=0,3 \\
3 / 8 & \text { for } & x=1,2
\end{array}\right.\)

Question 29.
Construct the truth table for \((p \vee q) \vee \neg q\)
Answer:
truth table for \((p \vee q) \vee \neg q\)

Question 30.
Show that f(x, y) = \(\frac{x^{2}-y^{2}}{y^{2}+1}\) is continuous at every (x, y) ∈ R².
Answer:

Here, f satisfies all the three conditions of continuity at (a, b). Hence, f is continuous at every point of R² as (a, b) ∈ R².

Part – III

III. Answer any seven questions. Question No. 40 is compulsory. [7 × 3 = 21]

Question 31.
Form a polynomial equation with integer coefficients with \(\sqrt{\frac{\sqrt{2}}{\sqrt{3}}}\) as a root.

Question 32.
Find the equation of the tangents from the point (2, -3) to the parabola y² = 4x

Question 33.
Find the vector and cartesian equations of the straight line passing through the points (-5, 2, 3) and (4,-3, 6).

Question 34.
Find the points on the curve y = x³ – 6x² + x + 3 where the normal is parallel to the line x + y =1729.

Question 35.
Assuming log₁₀ e = 0.4343, find an approximate value of log₁₀ 1003.

Question 36.
Evaluate: \(\int_{0}^{\frac{\pi}{2}} \sin ^{2} x \cos ^{4} x d x\)

Question 37.
Solve the differential equation: \(\frac{d y}{d x}\) = e^x+y + x³ e^y

Question 38.
Using binomial distribution find the mean and variance of X for the following experiments
(i) A fair coin is tossed 100 times, and X denote the number of heads.
(ii) A fair die is tossed 240 times, and X denote the number of times that four appeared.

Question 39.
Let

be any three Boolean matrices of the same type. Find (A ∨ B) ∧C

Question 40.
Sketch the graph of y = sin\(\left(\frac{1}{3} x\right)\) for 0 ≤ x < 6π.

Part – IV

IV. Answer all the questions. [7 × 5 = 35]

Question 41.
(a) A fish tank can be filled in 10 minutes using both pumps A and B simultaneously. However, pump B can pump water in or out at the same rate. If pump B is inadvertently run in reverse, then the tank will be filled in 30 minutes. How long would it take each pump to fill the tank by itself ? (Use Cramer’s rule to solve the problem).
[OR]
(b) Using elementary transformations find the inverse of the matrix \(\left[\begin{array}{ccc}
1 & 3 & -2 \\
-3 & 0 & -5 \\
2 & 5 & 0
\end{array}\right]\)

Question 42.
42. (a) Let z₁, z₂, and z₃ be complex numbers such that |z₁| = |z₂| = |z₃| = r > 0 and z₁ +z₂ + z₃ ≠ 0.
Prove that \(\left|\frac{z_{1} z_{2}+z_{2} z_{3}+z_{3} z_{1}}{z_{1}+z_{2}+z_{3}}\right|=r\)
[OR]
(b) Find all cube roots of \(\sqrt{3}\) + i.

Question 43.
(a) Find all zeros of the polynomial x⁶ – 3x⁵ – 5x⁴ + 22x³ – 39x² – 39x + 135, if it is known that 1 + 2i and \(\sqrt{3}\) are two of its zeros.
[OR]
(b) Let W(x, y, z) = x² – xy + 3 sin z, x, y, z∈R. Find the linear approximation at (2, -1, 0)

Question 44.
(a) Prove p → (q → r) ≡ (p ∧ q) → r without using truth table.
[OR]
(b) Evaluate \(\int_{0}^{\frac{\pi}{4}} \frac{1}{\sin x+\cos x} d x\)

Question 45.
(a) Prove that \(\text { (i) } \tan ^{-1} \frac{2}{11}+\tan ^{-1} \frac{7}{24}=\tan ^{-1} \frac{1}{2} \text { (ii) } \sin ^{-1} \frac{3}{5}-\cos ^{-1} \frac{12}{13}=\sin ^{-1} \frac{16}{65}\)
[OR]
(b) Find two positive numbers whose product is 100 and whose sum is minimum.

Question 46.
(a) If X is the random variable with distribution function F (x) given by,
\(\mathrm{F}(x)=\left\{\begin{array}{ll}
0, & x<0 \\
\frac{1}{2}\left(x^{2}+x\right) & 0 \leq x<1 \\
1, & x \geq 1
\end{array}\right.\)
then find (i) the probability density function f(x) (ii) P(0.3 ≤ X ≤ 0.6)
[OR]
(b) Find the vertex, focus, equation of directrix and length of the latus rectum of the following: y² – 4y – 8x + 12 = 0

Question 47.
(a) The rate at which the population of a city increases at any time is proportional to the population at that time. If there were 1,30,000 people in the city in 1960 and 1,60,000 in 1990, what population may be anticipated in 2020? [log_e \(\left(\frac{16}{3}\right)\) = 0.2070; e^-0.42 = 1.52]
[OR]
(b) Find the parametric vector, non-parametric vector and Cartesian form of the equation of the plane passing through the point (3, 6, -2), (-1, -2, 6) and (6, 4, -2).

Students can Download Tamil Nadu 12th Maths Model Question Paper 2 English Medium Pdf, Tamil Nadu 12th Maths 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.

TN State Board 12th Maths Model Question Paper 2 English Medium

Instructions:

1.  The question paper comprises of four parts.
2.  You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. questions of Part I, II. III and IV are to be attempted separately
4. Question numbers 1 to 20 in Part I are objective type questions of one -mark each. These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 21 to 30 in Part II are two-marks questions. These are to be answered in about one or two sentences.
6. Question numbers 31 to 40 in Parr III are three-marks questions, These are to be answered in about three to five short sentences.
7. Question numbers 41 to 47 in Part IV are five-marks questions. These are to be answered) in detail. Draw diagrams wherever necessary.

Time: 3 Hours
Maximum Marks: 90

Part – I

I. Choose the correct answer. Answer all the questions. [20 × 1 = 20]

Question 1.
If A = \(\left[\begin{array}{cc}
2 & 3 \\
5 & -2
\end{array}\right]\) be such that λA^-1 = A, then λ is _______.
(a) 17
(b) 14
(c) 19
(d) 21
Answer:
(c) 19

Question 2.
If ω ≠ 1 is a cubic root of unity and (1+ ω)⁷ = A+ B ω, then (A, B) equals to _______.
(a) (1,0)
(b) (-1, 1)
(c) (0, 1)
(d) (1, 1)
Answer:
(d) (1, 1)

Question 3.
The value of z – \(\bar{Z}\) is ______.
(a) 2 Im (z)
(b) 2 i Im (z)
(c) Im (z)
(d) i Im (z)
Answer:
(b) 2 i Im (z)

Question 4.
If x³ + 12x² + 10ax + 1999 definitely has a positive zero, if and only if ________.
(a) a ≥ 0
(b) a > 0
(c) a < 0
(d) a < 0
Answer:
(c) a < 0

Question 5.
sin(tan^-1 x), |x| < 1 is equal to _______.

Answer:
(d) \(\frac{x}{\sqrt{1+x^{2}}}\)

Question 6.
The centre of the circle inscribed in a square formed by the lines x² – 8x – 12 = 0 and y² – 14y + 45 = 0 is _____.
(a) (4, 7)
(b) (7, 4)
(c) (9, 4)
(d) (4, 9)
Answer:
(a) (4, 7)

Question 7.
The axis of the parabola x² = – 4y is ______.
(a) y= 1
(b) x = 0
(c) y = 0
(d) x = 1
Answer:
(b) x = 0

Question 8.
The coordinates of the point where the line \(\vec{r}=(6 \hat{i}-\hat{j}-3 \hat{k})+t(-\hat{i}+4 \hat{k})\) meets the plane \(\vec{r} \cdot(\hat{i}+\hat{j}-\hat{k})=3\) are _______.
(a) (2, 1, 0)
(b) (7, -1, -7)
(c) (1, 2, -6)
(d) (5, -1, 1)
Answer:
(d) (5, -1, 1)

Question 9.
If the vectors \(\vec{a}=3 \vec{i}+2 \vec{j}+9 \vec{k}\) and \(\vec{b}=\vec{i}+m \vec{j}+3 \vec{k}\) are parallel then m is _________.

Answer:
(b) \(\frac{2}{3}\)

Question 10.
The minimum value of the function |3 – x | + 9 is ________.
(a) 0
(b) 3
(c) 6
(d) 9
Answer:
(d) 9

Question 11.
The curve y² = x² (1 – x²) has ______.
(a) an asymptote x = -1
(b) an asymptote x = 1
(c) two asymptotes x = 1 and x = -1
(d) no asymptote
Answer:
(d) no asymptote

Question 12.
If /(x, y, z) = xy + yz + zx, then f_x – f_z is equal to _______.
(a) z – x
(b) y – z
(c) x – z
(d) y – x
Answer:
(a) z – x

Question 13.
A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is _______.
(a) 0.2%
(b) 0.4%
(c) 0.04%
(d) 0.08%
Answer:
(b) 0.4%

Question 14.
The value of \(\int_{0}^{\pi} \sin ^{4} x d x\) is _______.

Answer:
(b) \(\frac{3 \pi}{8}\)

Question 15.
\(\int_{a}^{b} f(x) d x\) is _______.

Answer:
(d) \(\int_{a}^{b} f(a+b-x) d x\)

Question 16.
The degree of the differential equation \(y(x)=1+\frac{d y}{d x}+\frac{1}{1.2}\left(\frac{d y}{d x}\right)^{2}+\frac{1}{1.2 .3}\left(\frac{d y}{d x}\right)^{3}+\ldots\) is ________.
(a) 2
(b) 3
(c) 1
(d) 4
Answer:
(c) 1

Question 17.
In finding the differential equation corresponding toy = e^mx where m is the arbitrary constant, then m is ____.
(a) \(\frac{y}{y^{\prime}}\)
(b) \(\frac{y^{\prime}}{y}\)
(c) y’
(d) y
Answer:
(b) \(\frac{y^{\prime}}{y}\)

Question 18.
Let X be random variable with probability density function f(x) = \(\left\{\begin{array}{ll}
2 / x^{3} & x \geq 1 \\
0 & x<1
\end{array}\right.\)
Which of the following statement is correct
(a) both mean and variance exist
(b) mean exists but variance does not exist
(c) both mean and variance do not exist
(d) variance exists but mean does not exist
Answer:
(b) mean exists but variance does not exist

Question 19.
The random variable X has the probability density function f(x) = \(\left\{\begin{array}{cc}
a x+b, & 0<x<1 \\
0, & \text { otherwise }
\end{array}\right.\)
and E(X) = \(\frac{7}{12}\), then a and b are respectively _______.
(a) 1 and \(\frac{1}{2}\)
(b) \(\frac{1}{2}\) and 1
(c) 2 and 1
(d) 1 and 2
Answer:
(a) 1 and \(\frac{1}{2}\)

Question 20.
A binary operation on a set S is a function from ________.
(a) S → S
(b)(S x S) → S
(c) S → (S x S)
(d) (S x S) → (S x S)
Answer:
(b)( S x S) → S

Part – II

II. Answer any seven questions. Question No. 30 is compulsory. [7 × 2 = 14]

Question 21.
Solve the following system of homogeneous equations.
3x + 2y + 7z = 0, 4x – 3y – 2z = 0, 5x + 9y + 23z = 0
Answer:
The matrix form of the above equation is

The augmented matrix [A, B] is

The above matrix is in echelon form. Here ρ(A, B) = ρ( A) < number of unknowns.
⇒ The system is consistent with infinite number of solutions. To find the solutions.
Writing the equivalent equations.
We get 3x + 2y + 7z = 0 ……..(1)
-17y – 34z = 0 …….(2)
Taking z = t in (2) we get -17y – 34t = 0
⇒ -17y = 34t
⇒ y= \(\frac{34 t}{-17}\) = -2t
Taking z = t; y = -2t in (1) we get
3x + 2 (-2t) + 7t = 0
3x – 4t + 7t = 0
⇒ 3x = -3t ⇒ x = -t
So the solution is x = -t; y = -2t; and z = t, t∈R

Question 22.
Show that |3z – 5 + i| = 4 represents a circle, and, find its centre and radius.
Answer:
The given equation |3z – 5 + i| = 4 can be written as

It is of the form |z – z| = r and so it represents a circle, whose center and radius are \(\left(\frac{5}{3},-\frac{1}{3}\right)\) and 4/3 respectively.

Question 23.
Find the equation of the circle whose centre is (2, -3) and passing through the intersection of the line 3x – 2y = 1 and 4x + y = 27.
Answer:
Solving 3x – 2y = 1 and 4x + y = 27
Simultaneously, we get x = 5 and y = 7
∴ The point of intersection of the lines is (5, 7)
Now we have to find the equation of a circle whose centre is
(2, -3) and which passes through (5, 7)

∴ Required equation of the circle is
(x – 2)² + (y + 3)² = \((\sqrt{109})^{2}\)
⇒ x² + y² – 4x + 6y – 96 = 0

Question 24.
Find the intercepts cut off by the plane \(\vec{r} \cdot(6 \hat{i}+4 \hat{j}-3 \hat{k})=12\) on the coordinate axes.
Answer:
\(\vec{r} \cdot(6 \vec{i}+4 \vec{j}-3 \vec{k})=12\)
Compare the above equations into \(\vec{r} \cdot \vec{n}=q\) so q = 12
Let a, b, c are intercepts of x-axis, y-axis and z-axis respectively.
Clearly

x – intercept = 2; y – intercept = 3; z – intercept = -4

Question 25.
Find the values in the interval (1, 2) of the mean value theorem satisfied by the function f(x) = x – x² for 1 ≤ x ≤ 2.
Answer:
f(1) = 0 and f(2) = -2. Clearly f(x) is defined and differentiable in 1 < x < 2. Therefore, by the Mean Value Theorem, there exists a c ∈(1, 2) such that
f'(c) = \(\frac{f(2)-f(1)}{2-1}\) = 1 – 2c
That is, 1 – 2c = -2 ⇒ c = \(\frac{3}{2}\)

Question 26.
Show that the percentage error in the n^th root of a number is approximately \(\frac{1}{n}\) times the percentage error in the number.
Answer:

Question 27.
Solve the differential equation: tany \(\frac{d y}{d x}\) = cos (x + y) + cos (x -y)
Answer:
tan y \(\frac{d y}{d x}\) = cos (x + y) + cos(x – y)
tan y \(\frac{d y}{d x}\) = cos x cos y – sin x sin y + cos x cos y + sin x sin y
tan y \(\frac{d y}{d x}\) = 2 cos x cos y
seperating the variables
\(\int \frac{\tan y}{\cos y}\) dy = 2∫cos x dx ⇒ ∫sec y tan y dy = 2∫cos x dx
sec y = 2 sin x + c

Question 28.
The probability density function of X is given by \(f(x)=\left\{\begin{array}{cc}
k e^{-\frac{x}{3}} & \text { for } x>0 \\
0 & \text { for } x \leq 0
\end{array}\right.\)
Find the value of k.
Answer:

Question 29.
Construct the truth table for the following statement. \(\neg(p \wedge \neg q)\).
Answer:

Question 30.
Find an approximate value of \(\int_{1}^{1.5} x^{2} d x\) by applying the right-hand rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}.
Answer:
Here a = 1; b = 1.5; n = 5; f(x) = x²
So, the width of each subinterval is

x₀ = 1; x₁ = 1.1; x₂ = 1.2; x₃ = 1.3; x₄ = 1.4; x₅ = 1.5
The Right hand rule for Riemann sum,
S = [f(x₁) + f(x₂) + f(x₃) + f(x₄) + f(x₅)] Δx
= [f(1.1) + f(1.2) + f(1.3) + f(1.4) + f(1.5)] (0.1)
= [1.21 + 1.44 + 1.69 + 1.96 + 2.25] (0.1)
= [8.55] (0.1)
= 0.855.

Part – III

III. Answer any seven questions. Question No. 40 is compulsory. [7 × 3 = 21]

Question 31.
Find a matrix A if adj (A) = \(\left[\begin{array}{ccc}
7 & 7 & -7 \\
-1 & 11 & 7 \\
11 & 5 & 7
\end{array}\right]\)

Question 32.
Obtain the Cartesian form of the locus of z = x + iy in the following case Im[(1 – i)z +1] = 0

Question 33.
If \(\vec{a}=\hat{i}-\hat{k}, \vec{b}=x \hat{i}+\hat{j}+(1-x) \hat{k}, \vec{c}=y \hat{i}+x \hat{j}+(1+x-y) \hat{k}\), show that \([\vec{a} \vec{b} \vec{c}]\) depends on neither x nor y.

Question 34.
The Taylor’s series expansion of f(x) = sin x about x = \(\frac{\pi}{2}\) is obtained by the following way.

Question 35.
The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum possible error in computing (i) the volume of the cube and (ii) the surface area of cube.

Question 36.
Evaluate \(\int_{0}^{1} \frac{\sin \left(3 \tan ^{-1} x\right) \tan ^{-1} x}{1+x^{2}} d x\)

Question 37.
Find the particular solution of (1 + x³) dy – x² ydx = 0 satisfying the condition y(1) = 2.

Question 38.
If X is the random variable with distribution function F(x) given by,
\(\mathrm{F}(x)=\left\{\begin{array}{ll}
0, & x<0 \\
x, & 0 \leq x<1 \\
1, & 1 \leq x
\end{array}\right.\)
then find (z) the Probability density function f(x)

Question 39.
Show that \(((\neg q) \wedge p) \wedge q\) is a contradiction.

Question 40.
Show that the absolute value of difference of the focal distances of any point P on the hyperbola is the length of its transverse axis.

Part – IV

IV. Answer all the questions. [7 × 5 = 35]

Question 41.
(a) By using Gaussian elimination method, balance the chemical reaction equation:
C₂H₆ + O₂ → H₂O + CO₂.
[OR]
(b) \(\frac{d y}{d x}+\frac{3 y}{x}=\frac{1}{x^{2}}\), given that y = 2 when x = 1

Question 42.
(a) Find the real values of x and y for the equation \(\frac{(1+i) x-2 i}{3+i}+\frac{(2-3 i) y+i}{3-i}=i\)
[OR]
(b) Find the area between the line y = x + 1 and the curve y = x² – 1.

Question 43.
(a) Determine k and solve the equation 2x³ – 6x² + 3x + k = 0 if one of its roots is twice the sum of the other two roots.
[OR]
(b) Evaluate: \(\int_{0}^{\frac{\pi}{2}} \frac{d x}{5+4 \sin ^{2} x}\)

Question 44.
(a) A tunnel through a mountain for a four lane highway is to have a elliptical opening. The total width of the highway (not the opening) is to be 16 m, and the height at the edge of the road must be sufficient for a truck 4 m high to clear if the highest point of the opening is to be 5 m approximately. How wide must the opening be?
[OR]
(b) Using truth table check whether the statements \(\neg(p \vee q) \vee(\neg p \wedge q)\) and \(\neg p\) are logically equivalent.

Question 45.
(a) Find the value of cot^-1 x – cot^-1 (x + 2) = \(\frac{\pi}{12}\), x > 0
[OR]
(b) Verify Euler’s theorem for f(x, y) = \(\frac{1}{\sqrt{x^{2}+y^{2}}}\)

Question 46.
(a) Find the points where the straight line passes through (6, 7, 4) and (8, 4, 9) cuts the xz and yz planes.
[OR]
(b) If X is the random variable with probability density function f(x) given by,
\(f(x)=\left\{\begin{array}{rc}
x+1, & -1 \leq x<0 \\
-x+1, & 0 \leq x<1 \\
0, & \text { otherwise }
\end{array}\right.\)
then find (z) the distribution function f(x) (ii) P (-0.5 ≤ X ≤ 0.5)

Question 47.
(a) Sketch the graph of the function: y = \(x \sqrt{4-x}\)
(b) The velocity v, of a parachute falling vertically satisfies the equation, \(v \frac{d v}{d x}=g\left(1-\frac{v^{2}}{k^{2}}\right)\)
where g and k are constants. If v and x are both initially zero, find v in terms of x.