CHAPTER- 8 Rural Livelihoods | Important Questions & MCQs | CLASS 6th | Social Science Civics | NCERT| EDUGROWN

NCERT Important Questions & MCQs for Class 6 Social Science History

NCERT Solutions for Class 6 Social Science includes all the questions provided in NCERT Class 6 Social Science Text book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 6 SST all questions are solved with the detailed explanation to score good marks in the exams.

CHAPTER- 8 Rural Livelihoods

MCQs Questions with Answers

Question 1.
In which state of India is the village Kalpattu located?
(a) Tamil Nadu
(b) Mumbai
(c) Delhi
(d) Karnal

Answer

Answer: (a) Tamil Nadu


Question 2.
Which type of food do the people of Tamil Nadu eat?
(a) Idli
(b) Dosa
(c) Upma
(d) All of these

Answer

Answer: (d) All of these


Question 3.
By which land features is the village surrounded?
(a) By low hills
(b) By high mountains
(c) By a group of rivers
(d) By streams

Answer

Answer: (a) By low hills


Question 4.
What is the main crop of village Kalpattu?
(a) Paddy
(b) Wheat
(c) Sweet com
(d) Sugarcane

Answer

Answer: (a) Paddy


Question 5.
What is working time in Paddy fields in Kalpattu?
(a) 8.30 AM – 4.30 PM
(b) 10.00 AM – 5.00 PM
(c) 7.00 AM – 2.00 PM
(d) None of these

Answer

Answer: (a) 8.30 AM – 4.30 PM


Question 6.
How much land does Ramalingam have?
(a) 20 acres
(b) 30 acres
(c) 40 acres
(d) 60 acres

Answer

Answer: (a) 20 acres


Question 7.
Who is the supervisor of the field?
(a) Ramalingam
(b) Ramalingam’s wife
(c) Karuthamma
(d) All of these

Answer

Answer: (b) Ramalingam’s wife


Question 8.
Giving water to the crops is known as
(a) weeding
(b) harvesting
(c) planting
(d) irrigation

Answer

Answer: (d) irrigation


Question 9.
How much did Ramalingam pay to his workers?
(a) 100 rupees per day
(b) 50 rupees per day
(c) 40 rupees per day
(d) 30 rupees per day

Answer

Answer: (c) 40 rupees per day


Question 10.
Which animal’s milk does Ramalingam sell in local milk cooperative?
(a) Of hybrid – Cow
(b) Of hybrid – Goat
(c) Of hybrid – Camel
(d) Of hybrid – Buffalo

Answer

Answer: (a) Of hybrid – Cow


Question 11.
If the farmer fails in repayment of loan he commits
(a) suicide
(b) murder
(c) theft
(d) all of these

Answer

Answer: (a) suicide


Question 12.
What does Ramalingam do with the rice produce in his rice mills?
(a) He distributes it to the poors
(b) He sells it to traders in nearby towns
(c) He sells it to government sector
(d) He sells it to villagers

Answer

Answer: (b) He sells it to traders in nearby towns


Question 13.
What is basic occupation of 80% of Indians?
(a) Agriculture
(b) Business
(c) Trading
(d) Garments

Answer

Answer: (a) Agriculture


Question 14.
Who was Thulasi?
(a) Agricultural labour
(b) Baildar
(c) Contractor
(d) None of these

Answer

Answer: (a) Agricultural labour


Question 15.
What is the main occupation of people living in rural areas?
(a) Working on farms
(b) Working in banks
(c) Working at shops
(d) None of these

Answer

Answer: (a) Working on farms

Very Short Answer Type

Question 1.
Where is Kalpattu village situated?
Answer:
Kalpattu village is situated close to the coast in Tamil Nadu.

Question 2.
What works do the people of this village do?
Answer:
Different works:

  • Farming/agriculture
  • Making Baskets
  • Utensils
  • Pots
  • Bricks
  • Bullock-carts.

Question 3.
What are the main sources of livelihood of some families in the village?
Answer:

  • Some of the people rear cows and sell milk either to the milk societies or take milk to nearby town for selling.
  • In coastal areas people are busy with fishing.

Rural Livelihoods Class 6 Extra Questions Short Answer Type

Question 1.
Which other works/services do the people of the village provide?
Answer:
People engaged in services.

  • Blacksmiths
  • Nurses
  • Teachers
  • Washermen
  • Weavers
  • Barbers
  • Cycle repairs
  • Mechanics
  • Some shopkeepers and traders.

Question 2.
What types of shops are located in the main street which looks alike.
Answer:

  • Tea shops
  • Grocery shops
  • Barber shops
  • Cloth shops
  • Tailor shops
  • Fertiliser and seed shops

Question 3.
How many tea shops are there in the village? What do they sell?
Answer:
There are four tea shops in the village.
They sell:

  • Tiffin in the morning—Idli, Dosa, Upama.
  • Snacks in the evening—Vadai, Bonda and Mysorepak.

Question 4.
Describe other shops of the village Kalpattu.
Answer:
Other shops of the village Kalpattu:

  • Blacksmith,
  • He lives with his family.
  • His house acts as workshop too.
  • Next to the Blacksmith there is cycle hire and repair shop.
  • Washerman’s shops; two families.
  • Some people go to nearby town to work in construction work.
  • Some work as lorry drivers.

Question 5.
Write some sentences on th ? work of agriculture.
Answer:

  • Agriculture is the main work of the village people. ’
  • Paddy is the main crop grown in the irrigated fields.
  • Other crops are cotton, sugarcane and plaintain.
  • Some coconut groves are there.
  • There are several mango orchards.

Question 6.
Why had Thulasi and Raman to sell their cow?
Answer:

  • Thulasi and Raman had school-going daughters. They lived with them with joy-
  • One of the daughters fell ill last year.
  • She was taken to the hospital for treatment.
  • They borrowed money from Ramalingam for her treatment.
  • They had to sell their cow for payment of loan they had borrowed from Ramalingam.

Question 7.
Why do the poor people in rural areas spend time doing non-earning works?
Answer:

  • The poor in the village/rural areas do not earn much money to meet their both ends or to survive with the little money they earn.
  • They spend a lot of time on collecting firewood from forests, fetching water from distant bore well and grazing their cattle.
  • These activities also save their money and fulfil their several needs.

Question 8.
Describe the life of the landless or agricultural labourers in rural areas.
Answer:
Life of agricultural labourers in Rural India.

  • Nearly 66.67% of the population in rural areas is agricultural labourer.
  • Some of them have their own small plots of land which cannot give them enough to earn their livelihood. Most of them are landless.
  • They have to go to distant places to find work. This travel is called migration.

Question 9.
Discuss the life of fishing communities during the period of 4 months of the monsoon.
Answer:

  • Four months of the monsoon are those months when fishermen do not go to sea for fishing as it is a breeding season for fish.
  • During this period the fishermen survive by borrowing money from the traders.
  • During fish catch period they have to sell their fish to the trader and can not auction the fish in open market.
  • This lean period is very difficult period for the fishermen.

Rural Livelihoods Class 6 Extra Questions Long Answer Type

Question 1.
What are the problems of small farmers in rural areas according to Sekar?
Answer:
According to Sekar the problems of small farmers in rural areas are enumerated as under:

  • The farmer’s family does the whole work from sowing to harvesting of crops.
  • They have to take the produce to their house.
  • They have to sell the produce first to the moneylender at lower prices than the market prices.
  • The remaining produce is enough for only 2 months. They have to work as labourer for earning money for 4 months. They may work in rice mill or in other places.
  • They also rear cattle for milk to be sold in the market to earn money.

Question 2.
Why do farming communities commit suicide in some areas?
Answer:
In some areas farming communities commit suicide due to the following reasons:

  • Farmers very often take loan from moneylenders for purchase of seeds, fertilisers and pesticides.
  • Sometimes seeds are not good while on the other occasions pests damage crops resulting in crop failure.
  • Bad monsoon also damages, crops.
  • The farmers have to borrow more money for their daily needs.
  • Loan goes on mounting and there is no way before the farmers to repay loan.
  • They become helpless and sometimes they commit suicide.

Question 3.
Read the following account (terrace farming in Nagaland) and answer the questions that follow it:

Terrace Farming in Nagaland:
This is a village called Chizami which is in Phek district in Nagaland. The people of this village belong to the Chakhesang community. They do ‘terrace’ cultivation.
Rural Livelihoods Class 6 Extra Questions Civics Chapter 8 L - Q3
This means that the land on a hill slope is made into flat plots and carved out in steps. The sides of each plot are raised in order to retain water. This allows water to stand in the field, which is best for rice cultivation.

The people of Chizami have their own individual fields. But, they also work collectively in each other’s fields. They form groups of six or eight and take an entire mountainside to clean the weeds on it.
Each group eats together once their work for the day is over. This goes on for several days until the work is completed.

  1. Which village is referred to in the picture above? Where is it located?
  2. Which community do the villagers of this village belong to?
  3. What type of farming do they practise?
  4. For what is this practice the best?
  5. Why do the people of Chizami work collectively?

Answer:

1. Chizami in Phek district of Nagaland.
2. Chakhesang
3. Terrace cultivation (farming)
4. Rice cultivation
5. To carry out the farming activities.
To clean the mountain side of the weeds.

Question 4.
Describe the life of fishing communities.
Answer:
Life of Fishing Communities.

  • Fishing communities live in their houses close to the sea.
  • They have catamarans and nets lying around.
  • The catamarans leave for sea at around 2 o’clock in the morning for fishing and return at 7 o’clock with fish catch.
  • Women gather to buy and sell fish.
  • The women keep some fish aside for their family.
  • The rest they sell and auction.
  • Money collected from auction is divided in shares equally among the fishermen who bring catch from the sea.
  • One share more is given to the owner of the catamaran, engine and net.
  • Women who buy the catch, keep the catch in baskets and go to the nearby villages for sale of the fish.
  • Traders also buy fish from the acution point to sell fish in the market or for export.
  • In the evening catamaran and nets are repaired by the menfolk.

Question 5.
Give an account of the ways of earning livelihood in rural areas.
Answer:

  • Various ways of earning livelihood in rural areas:
  • Farm and non-farm activities.
  • Farm activities involve the following:
  • Preparing the land.
  • Sowing
  • Weeding
  • Harvesting
  • Farmers depend on nature for growth of crops. Hence life revolves round certain seasons.
  • Different crops are raised in different regions.
  • However there are similarities in their situation and problems they face.
  • Some people work as labourers on the farmland and earn their living.
  • Other ways of livelihood are fishing, crafts etc.
  • Aruna and Paarivelan represent the fishing community.

Rural Livelihoods Class 6 Extra Questions Multiple Choice Questions

Choose the correct option:

Question 1.
In which state of India is the village Kalpattu located?
(a) Tamil Nadu
(b) Mumbai
(c) Delhi
(d) Karnal
Answer:
Tamil Nadu

Question 2.
Which type of food do the people of Tamil Nadu eat?
(a) Idli
(b) Dosa
(c) Upma
(d) All of these
Answer:
All of these

Question 3.
By which land features is the village surrounded?
(a) By low hills
(b) By high mountains
(c) By a group of rivers
(d) By streams
Answer:
By low hills

Question 4.
What is the main crop of village Kalpattu?
(a) Paddy
(b) Wheat
(c) Sweet com
(d) Sugarcane
Answer:
Paddy

Question 5.
What is working time in Paddy fields in Kalpattu?
(a) 8.30 AM – 4.30 PM
(b) 10.00 AM – 5.00 PM
(c) 7.00 AM – 2.00 PM
(d) None of these
Answer:
8.30 AM – 4.30 PM

Question 6.
How much land does Ramalingam have?
(a) 20 acres
(b) 30 acres
(c) 40 acres
(d) 60 acres
Answer:
20 acres

Question 7.
Who is the supervisor of the field?
(a) Ramalingam
(b) Ramalingam’s wife
(c) Karuthamma
(d) All of these
Answer:
Ramalingam’s wif

Question 8.
Giving water to the crops is known as
(a) weeding
(b) harvesting
(c) planting
(d) irrigation
Answer:
irrigation

Question 9.
How much did Ramalingam pay to his workers?
(a) 100 rupees per day
(b) 50 rupees per day
(c) 40 rupees per day
(d) 30 rupees per day
Answer:
40 rupees per day

Question 10.
Which animal’s milk does Ramalingam sell in local milk cooperative?
(a) Of hybrid – Cow
(b) Of hybrid – Goat
(c) Of hybrid – Camel
(d) Of hybrid – Buffalo
Answer:
Of hybrid – Cow

Question 11.
If the farmer fails in repayment of loan he commits
(a) suicide
(b) murder
(c) theft
(d) all of these
Answer:
suicide

Question 12.
What does Ramalingam do with the rice produce in his rice mills?
(a) He distributes it to the poors
(b) He sells it to traders in nearby towns
(c) He sells it to government sector
(d) He sells it to villagers
Answer:
He sells it to traders in nearby towns

Question 13.
What is basic occupation of 80% of Indians?
(a) Agriculture
(b) Business
(c) Trading
(d) Garments
Answer:
Agriculture

Question 14.
Who was Thulasi?
(a) Agricultural labour
(b) Baildar
(c) Contractor
(d) None of these
Answer:
Agricultural labour

Question 15.
What is the main occupation of people living in rural areas?
(a) Working on farms
(b) Working in banks
(c) Working at shops
(d) None of these
Answer:
Working on farms

 

Read More

CHAPTER- 7 Urban Administration | Important Questions & MCQs | CLASS 6th | Social Science Civics | NCERT| EDUGROWN

NCERT Important Questions & MCQs for Class 6 Social Science History

NCERT Solutions for Class 6 Social Science includes all the questions provided in NCERT Class 6 Social Science Text book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 6 SST all questions are solved with the detailed explanation to score good marks in the exams.

CHAPTER- 7 Urban Administration

MCQs Questions with Answers

Choose the correct answer:

Question 1.
In which of the following are lives faster?
(a) In village
(b) In city
(c) In both (a) and (b)
(d) In none of these

Answer

Answer: (b) In city


Question 2.
Where is the relationship between the neighbours healthier?
(a) In villages
(b) In cities
(c) In hospitals
(d) In dispensaries

Answer

Answer: (a) In villages


Question 3.
What type of game were Mala and her friends playing in the street?
(a) Hockey
(b) Cricket
(c) Football
(d) Badminton

Answer

Answer: (b) Cricket


Question 4.
What was broken by the ball hit by Rehana?
(a) Window glass
(b) Street light
(c) Glass of a car
(d) None of these

Answer

Answer: (b) Street light


Question 5.
Which agency replaces the broken street lights, collects the garbage, provides water supply, keeps the market clean?
(a) Municipal Corporation
(b) Hospital
(c) Police
(d) None of these

Answer

Answer: (a) Municipal Corporation


Question 6.
Which are the other tasks of a municipal corporation?
(a) To run the schools
(b) To run hospitals
(c) To maintain parks
(d) All of these

Answer

Answer: (d) All of these


Question 7.
Who takes the complicated decisions that affect the entire city?
(a) A group of councillors
(b) A group of teachers
(c) A group of doctors
(d) None of these

Answer

Answer: (a) A group of councillors


Question 8.
What are Panchayat members called?
(a) Sarpanch
(b) Panch
(c) Secretary
(d) None of these

Answer

Answer: (b) Panch


Question 9.
The big city like Delhi is divided into several
(a) Districts
(b) Janapads
(c) Samitis
(d) All of these

Answer

Answer: (a) Districts


Question 10.
Who prepares budget and spends the money according to this?
(a) Ward Councillors
(b) Ward boys
(c) Nurses
(d) Teachers

Answer

Answer: (a) Ward Councillors


Question 11.
The uncollected garbage attracts dogs, rats, mosquitoes and flies, so we should
(a) cover them
(b) keep them open
(c) throw them on to the roads
(d) throw them here and there

Answer

Answer: (a) cover them


Question 12.
The jobs of contract workers are
(a) temporary
(b) permanent
(c) both (a) and (b)
(d) none of these

Answer

Answer: (a) temporary


Question 13.
If any house keeping staff does not do his duty, whom should we contact?
(a) Sanitation engineer
(b) Local police station
(c) Councillor
(d) Chief Minister

Answer

Answer: (a) Sanitation engineer


Question 14.
What was Gangabai protesting about?
(a) The garbage was not removed for several days
(b) She wanted to open a hospital
(c) She wanted to open a school
(d) None of these

Answer

Answer: (a) The garbage was not removed for several days


Question 15.
Why was Gangabai loved and respected?
(a) For her being active citizen
(b) For her being lazy citizen
(e) For helping the poor
(d) For all of these

Answer

Answer: (a) For her being active citizen

Very Short Answer Type

Question 1.
Who decides where a park should go?
Answer:
Ward Councillors take decisions where a park should go.

Question 2.
Did Yasmin Khala have to make interesting decisions like this when she worked in the Municipal Corporation?
Answer:
Yasmin Khala did not have to make interesting decisions like this when she worked in the Municipal Corporation as such decisions are taken by ward councillors and not the employees. Mrs. Yasmin Khala worked in the accounts section of the corporation and was responsible for pay of the employees.

Question 3.
What is a city?
Answer:
A city is much larger and bigger than a village. It is more spread out.

Urban Administration Class 6 Extra Questions Short Answer Type

Question 1.
Who decides different tasks to be done?
Answer:
The committee or group of ward councillors decides what tasks are to be done:

  • Bus stand to be improved.
  • Crowded market places to be cleaned.
  • Drain cutting across the city to be cleaned.
  • Water supply.
  • Electricity.
  • Garbage collection.
  • Electric wires (dangerous) to be replaced. –
  • Street lighting.

Question 2.
When do the local people contact their councillor?
Answer:
The ward people contact their ward councillor when the problem relates to the ward such as:

  • Dangerous electric wires to be replaced.
  • Road repairs (street repairs)
  • Public water pump installation.

Question 3.
What tasks do ward councillors perform?
Answer:
The ward councillors perform the following tasks:

  • All the ward councillors meet and make the budget.
  • They spend money as per the budget provisions.
  • Ward councillors put the demands of their ward before the entire council.
  • They take decisions.
  • They get the works implemented.

Question 4.
What are major features of a city?
Answer:
Features of a city:

  • Crowded markets.
  • Many buses and cars.
  • Water facilities.
  • Electricity facilities.
  • Hospitals.

Question 5.
What are ill effects of garbage lying all over in the streets?
Answer:

  • Garbage attracts dogs, rats, mosquitoes and flies.
  • It gives foul smell which causes people to fall ill.
  • People and children get sick.

Urban Administration Class 6 Extra Questions Long Answer Type

Question 1.
What is recycling of waste things? Give some examples of recycling of waste material.
Answer:
Recycling of waste material is to make the waste material reusable. The following photo gives several examples of recycling.
Urban Administration Class 6 Extra Questions Civics Chapter 7 L - Q1
Recycling is not a new thing. People like the man in the photo above have been recycling paper, metal, glass and plastic for a long time. The kabadi wallah plays a major role in recycling household plastic and paper, including your notebooks.

Urban Administration Class 6 Extra Questions Multiple Choice Questions

Choose the correct answer:

Question 1.
In which of the following are lives faster?
(a) In village
(b) In city
(c) In both (a) and (6)
(d) In none of these
Answer:
In city

Question 2.
Where is the relationship between the neighbours healthier?
(a) In villages
(b) In cities
(c) In hospitals
(d) In dispensaries
Answer:
In villag

Question 3.
What type of game were Mala and her friends playing in the street?
(a) Hockey
(b) Cricket
(c) Football
(d) Badminton
Answer:
Cricket

Question 4.
What was broken by the ball hit by Rehana?
(a) Window glass
(b) Street light
(c) Glass of a car
(d) None of these
Answer:
Street light

Question 5.
Which agency replaces the broken street lights, collects the garbage, provides water supply, keeps the market clean?
(a) Municipal Corporation
(b) Hospital
(c) Police
(d) None of these
Answer:
Municipal Corporation

Question 6.
Which are the other tasks of a municipal corporation?
(a) To run the schools
(b) To run hospitals
(c) To maintain parks
(d) All of these
Answer:
All of these

Question 7.
Who takes the complicated decisions that affect the entire city?
(a) A group of councillors
(b) A group of teachers
(c) A group of doctors
(d) None of these
Answer:
A group of councillors

Question 8.
What are Panchayat members called?
(a) Sarpanch
(b) Panch
(c) Secretary
(d) None of these
Answer:
Panch

Question 9.
The big city like Delhi is divided into several
(a) Districts
(b) Janapads
(c) Samitis
(d) All of these
Answer:
Districts

Question 10.
Who prepares budget and spends the money according to this?
(a) Ward Councillors
(b) Ward boys
(c) Nurses
(d) Teachers
Answer:
Ward Councillors

Question 11.
The uncollected garbage attracts dogs, rats, mosquitoes and flies, so we should
(a) cover them
(b) keep them open
(c) throw them on to the roads
(d) throw them here and there
Answer:
cover them

Question 12.
The jobs of contract workers are
(a) temporary
(b) permanent
(c) both (a) and (b)
(d) none of these
Answer:
temporary

Question 13.
If any house keeping staff does not do his duty, whom should we contact?
(a) Sanitation engineer
(b) Local police station
(c) Councillor
(d) Chief Minister
Answer:
Sanitation engineer

Question 14.
What was Gangabai protesting about?
(a) The garbage was not removed for several days
(b) She wanted to open a hospital
(c) She wanted to open a school
(d) None of these
Answer:
The garbage was not removed for several days

Question 15.
Why was Gangabai loved and respected?
(a) For her being active citizen
(b) For her being lazy citizen
(e) For helping the poor
(d) For all of these
Answer:
For her being active citizen

Read More

CHAPTER- 6 Rural Administration | Important Questions & MCQs | CLASS 6th | Social Science Civics | NCERT| EDUGROWN

NCERT Important Questions & MCQs for Class 6 Social Science History

NCERT Solutions for Class 6 Social Science includes all the questions provided in NCERT Class 6 Social Science Text book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 6 SST all questions are solved with the detailed explanation to score good marks in the exams.

CHAPTER- 6 Rural Administration

MCQs Questions with Answers

Question 1.
How many villages are there in India approximately?
(a) One lakh
(b) Three lakhs
(c) Four lakhs
(d) Six lakhs

Answer

Answer: (d) Six lakhs


Question 2.
Who is Mohan in this chapter?
(a) a farmer
(b) a doctor
(c) an engineer
(d) SHO

Answer

Answer: (a) a farmer


Question 3.
What was the occupation of Mohan’s friend?
(a) Running a post-office
(b) Running a cloth-shop
(c) Running a clinic
(d) Running a chemist shop

Answer

Answer: (a) Running a post-office


Question 4.
Where did Mohan go after being beaten up by Raghu?
(a) Hospital
(b) Clinic
(c) Police Station
(d) None of these

Answer

Answer: (c) Police Station


Question 5.
To whom did Mohan meet at the Police station to complain about what had happened with him?
(a) SHO
(b) SI
(c) ASI
(d) None of these

Answer

Answer: (a) SHO


Question 6.
Who does the work of measuring land and keeping land record?
(a) Doctor
(b) Chemist
(c) Patwari
(d) All of these

Answer

Answer: (c) Patwari


Question 7.
Patwari is also known as
(a) lekhpal
(b) karamchari
(c) village officer
(d) all of these

Answer

Answer: (d) all of these


Question 8.
What is other work of Patwari?
(a) Selling medicine
(b) Collection of land revenue
(c) Growing crops in a field
(d) None of these

Answer

Answer: (b) Collection of land revenue


Question 9.
All the states of India are divided into?
(a) cities
(b) nagars
(c) grams
(d) districts

Answer

Answer: (d) districts


Question 10.
Who is the head of Tehsil?
(a) District collector
(b) Revenue collector
(c) Ticket collector
(d) All of these

Answer

Answer: (a) District collector


Question 11.
District collector is also known as
(a) Tehsildar
(b) Zamindar
(c) Sarpanch
(d) Panchs

Answer

Answer: (a) Tehsildar


Question 12.
Name the person/ persons who inherit the property of a person after his death,
(a) His sons
(b) His daughters
(c) His wife
(d) Sons, daughters and their mother

Answer

Answer: (d) Sons, daughters and their mother

 

Very Short Answer Type

Question 1.
How many villages are there in India?
Answer:
More than 6 lakh villages.

Question 2.
What are the important needs of villages?
Answer:
Important needs:

  • Water
  • Electricity
  • Road connections
  • Sanitation
  • Maintenance of land records
  • Resolution of conflicts.

Question 3.
Comment on the area of a police station.
Answer:
Every police station has an area under its control.

  • All the people of this area can report cases and inform the police station about thefts, accidents, injuries or fights.
  • The police enquires, investigates and takes action on the cases filed with the police station.

Question 4.
Which names are generally given to sub-divisions of a district?
Answer:

  • Tehsil
  • Taluka
  • Pargana.

Rural Administration Class 6 Extra Questions Short Answer Type

Question 1.
Describe the duties of a Patwari.
Answer:
Duties of a Patwari:

  • Responsible for a group of villages.
  • Maintains and updates the records of the village.
  • Measures land with a long chain.
  • Organises collection of land revenue.
  • Provides information to government about crops grown in the area.
  • Updating of records is required because of the following:
  • Change in crops.
  • Digging of wells.

Question 2.
What are the duties of a Tehsildar?
Answer:
Duties of a Tehsildar:

  • He hears disputes.
  • He supervises the work of Patwaris.
  • He ensures that records are properly maintained by Patwaris and revenue is collected.
  • He ensures that farmer gets copy of his records.
  • He issues caste certificates to students.
  • Land disputes are also heard by a Tehsildar.

Rural Administration Class 6 Extra Questions Long Answer Type

Question 1.
Describe the wish of a daughter.
Answer:
A Daughter’s Wish
Father inherited our house from his
father
And everyone says he’ll leave it to
brother
But what about me and my mother?
To expect a share in my father’s home,
Is not very womanly, I am told.
But I really want a place of my own,
Not dowry of silk and gold.
Rural Administration Class 6 Extra Questions Civics Chapter 6 L - Q2
Question 2.
Describe the provisions of Hindu Succession Amendment Act, 2005.
Answer:
Provisions of Hindu Succession Amendment Act, 2005.

  • Till the amendment women did not have the right to share family’s agricultural land.
  • After the death of father his land was distributed among his sons only.

According to New Law:

  • Sons, daughters and their mother get equal share in the land.
  • The law applies to all the states and union territories.
  • Patwari will transfer the land to all sons, daughters and their mother and record their names in the revenue records.

Rural Administration Class 6 Extra Questions Multiple Choice Questions

Choose the correct answer:

Question 1.
How many villages are there in India approximately?
(a) One lakh
(b) Three lakhs
(c) Four lakhs
(d) Six lakhs
Answer:
Six lakhs

Question 2.
Who is Mohan in this chapter?
(a) a farmer
(b)a doctor
(c) an engineer
(d) SHO
Answer:
a farmer

Question 3.
What was the occupation of Mohan’s friend?
(a) Running a post-office
(b) Running a cloth-shop
(c) Running a clinic
(d) Running a chemist shop
Answer:
Running a post-office

Question 4.
Where did Mohan go after being beaten up by Raghu?
(a) Hospital
(b) Clinic
(c) Police Station
(d) None of these
Answer:
Police Station

Question 5.
To whom did Mohan meet at the Police station to complain about what had happened with him?
(a) SHO
(b) SI
(c) ASI
(d) None of these
Answer:
SHO

Question 6.
Who does the work of measuring land and keeping land record?
(a) Doctor
(b) Chemist
(c) Patwari
(d) All of these
Answer:
Patwari

Question 7.
Patwari is also known as
(a) lekhpal
(b) karamchari
(c) village officer
(d) all of these
Answer:
all of these

Question 8.
What is other work of Patwari?
(a) Selling medicine
(b) Collection of land revenue
(c) Growing crops in a field
(d) None of these
Answer:
Collection of land revenue

Question 9.
All the states of India are divided into?
(a) cities
(b) nagars
(c) grams
(d) districts
Answer:
districts

Question 10.
Who is the head of Tehsil?
(a) District collector
(b) Revenue collector
(c) Ticket collector
(d) All of these
Answer:
District collector

Question 11.
District collector is also known as
(a) Tehsildar
(b) Zamindar
(c) Sarpanch
(d) Panchs
Answer:
Tehsildar

Question 12.
Name the person/ persons who inherit the property of a person after his death,
(a) His sons
(b) His daughters
(c) His wife
(d) Sons, daughters and their mother
Answer:
Sons, daughters and their mother

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CHAPTER- 5 Panchayati raj  | Important Questions & MCQs | CLASS 6th | Social Science Civics | NCERT| EDUGROWN

NCERT Important Questions & MCQs for Class 6 Social Science History

NCERT Solutions for Class 6 Social Science includes all the questions provided in NCERT Class 6 Social Science Text book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 6 SST all questions are solved with the detailed explanation to score good marks in the exams.

CHAPTER- 5 Panchayati raj

MCQs Questions with Answers

Question 1.
Where do people directly participate and seek answers from their elected representatives?
(a) Gram Panchayat
(b) Parliament House
(c) Both (a) and (b)
(d) None of these

Answer

Answer: (a) Gram Panchayat


Question 2.
Why was the first day special for the village people?
(a) Gram Panchayat was holding its first meeting after election
(b) There was a wedding ceremony
(c) There was annual function of the school
(d) None of these

Answer

Answer: (a) Gram Panchayat was holding its first meeting after election


Question 3.
Who is called the Sarpanch?
(a) Member of Panchayat
(b) Villagers
(c) Panchayat Head
(d) All of these

Answer

Answer: (c) Panchayat Head


Question 4.
The member of Panchayat is also called
(a) Member of Parliament
(b) Panch
(c) Prime Minister
(d) None of these

Answer

Answer: (b) Panch


Question 5.
Who elects the Panchayat Head?
(a) All members of Gram Sabha
(b) Villagers
(c) Secretary
(d) All of these

Answer

Answer: (a) All members of Gram Sabha


Question 6.
Who appoints Secretary of Gram Panchayat?
(a) Government
(b) Ordinary person
(c) Election Commissioner
(d) Landlord of village

Answer

Answer: (a) Government


Question 7.
From where do the village women have to get water?
(a) Suru river
(b) Ganga river
(c) Yamuna river
(d) Gomati river

Answer

Answer: (a) Suru river


Question 8.
Who is responsible for calling the meeting of Gram Sabha?
(a) President of Gram Sabha
(b) Panchs of Gram Panchayat
(c) Secretary of Gram Sabha
(d) None of these

Answer

Answer: (c) Secretary of Gram Sabha


Question 9.
What is the full form of BPL here?
(a) Bharat Petroleum Ltd
(b) Below Poverty Line
(c) Both (a) and (b)
(d) None of these

Answer

Answer: (b) Below Poverty Line


Question 10.
Who was the earlier Zamindar?
(a) Sukhi Bhai
(b) Amir Chand
(c) Birju
(d) Anwar

Answer

Answer: (b) Amir Chand


Question 11.
Whose names should be included, in BPL families?
(a) Very poor person
(b) Middle family person
(c) High income group
(d) All of these

Answer

Answer: (a) Very poor person


Question 12.
What are the works of Gram Panchayat?
(a) Maintain roads of villages
(b) School buildings in villages
(c) Collecting local taxes
(d) All of these

Answer

Answer: (d) All of these


Question 13.
What is Zila Parishad?
(a) District Panchayat
(b) Block Panchayat
(c) Gram Sabha
(d) None of these

Answer

Answer: (a) District Panchayat


Question 14.
At which level does Zila Parishad actually make development plans?
(a) District level
(b) Panchayat Samiti
(c) Block level
(d) Government level

Answer

Answer: (a) District level

Very Short Answer Type

Question 1.
Describe a Gram Sabha.
Answer:
Gram Sabha:

  • Gram Sabha is the institution consisting of all adults who live in the village or villages.
  • This could be only one village or a few villages.
  • In some states, a village meeting is held for each village.
  • Anyone who is 18 years old or more and who has the right to vote is a member of the Gram Sabha.

Panchayati raj Class 6 Extra Questions Short Answer Type Questions

Question 1.
How is Gram Sabha a key factor in making the Gram Panchayat play its role and be responsible.
Answer:

  • The Gram Sabha is a key factor in making the Gram Panchayat play its role and be responsible.
  • It is the place where all plans for the work of the Gram Panchayat are placed: before the people.
  • The Gram Sabha prevents the Panchayat from doing wrong things like misusing money or favouring certain people.
  • It plays an important role in keeping an eye on the elected representatives and in making them responsible to the persons who elected them.

Question 2.
In some states Gram Sabhas form committees. Why?
Answer:
In some states Gram Sabhas form committees to carry out specific works.

  • Construction committee is formed to carry out the construction work.
  • Development committee is engaged in development work.
  • These committees are composed of some members of Gram Sabha and some members of the Gram Panchayats.
  • They work together to carry out specific tasks.

Question 3.
Enumerate the works of Gram Panchayats? What are the sources of funds of Gram Panchayats?
Answer:
The works of a Gram Panchayat:

  • The construction and maintenance of water sources, roads, drainage, school buildings and other common property resources.
  • Levying and collecting local taxes.
  • Executing government schemes related to generating employment in the village. Sources of funds for the

Gram Panchayat:

  • Collection of taxes on houses, market places etc.
  • Government scheme funds received through various departments of the government— through the Janpad and Zila Panchayats.
  • Donations for community works etc.

Question 4.
Describe the three levels of Panchayats.
Answer:
Panchayati Raj System is a process through which people participate in their own government.
There are three levels of Panchayats:

  • Gram Panchayat.
  • Block level Panchayat (Janpad Panchayat or Panchayat Samiti)

District Panchayat or Zila Parishad:

  • Gram Panchayat: at village level, Panchayat President and ward members.
  • Block Level Panchayat (Panchayat Samiti): Numerous village Panchayats as its members.
  • Zila Parishad:
  • Prepares the developmental plans for the whole district.
  • Controls the money distributed to Block and Village Panchayats.

Panchayati raj Class 6 Extra Questions Long Answer Type Questions

Question 1.
Describe the composition of the Gram Panchayat.
Answer:
Composition of the Gram Panchayat:

  • Every village Panchayat is divided into wards, i.e., smaller areas.
  • Each ward elects a representative who is known as the Ward Member (Panch).
  • All the members of the Gram Sabha also elect a Sarpanch who is the Panchayat
    President. ,
  • The Ward Panchs and the Sarpanch form the Gram Panchayat.

The Gram Panchayat has a Secretary who is also the Secretary of the Gram Sabha.

  • This person is not an elected person but is appointed by the government.
  • He is responsible for calling the meeting of the Gram Sabha and Gram Panchayat.
  • He also keeps record of the proceedings.

Question 2.

The Gram Sabha meeting begins with the Panchayat President (who is also called the Sarpanch) and the members of the Panchayat (the Panchs) presenting a plan on repairing the road that connects the village to the main highway. After this, the discussion moves to the subject of water and water shortages.

A villager called Tijia begins the meeting by saying, “The water problem in Hardas has become very acute. The handpump water has gone well below the point up to which the ground has been drilled. We hardly get any water in the taps. Women have to go to the Suru river which is 3 k.m. away to get water.” One of the members suggests piping water from the Suru and making an overhead tank in the village to increase the supply. But the others think that this will be expensive. It’s better, they feel, to deepen the handpumps and clean the wells for this season. Tijia says, “This is not enough. We need to do something more permanent as groundwater levels seem to be going down every year. We’re using more water than is seeping into the ground.”

Another member, Anwar then tells everyone that he has seen ways of conserving water and recharging (refilling) it in a village in Maharashtra where he’d once gone to visit his brother. It was called watershed development and he had heard that the government gave money for this work.

In his brother’s village people had planted trees, constructed check-dams and tanks. Everyone thought this was an interesting idea and the Gram Panchayat was asked to find out about it in detail.

  1. What is a Gram Sabha?
  2. In the meeting of the Gram Sabha so far what are the problems that are being discussed? What sort of solutions are being suggested?

Answer:
1. A Gram Sabha is an institution of the adult village people.

  • The people ask the questions.
  • The elected representatives answer to these questions.

2. Problems being discussed in the Gram Sabha are:

  • Water and water shortage.
  • Watershed development – conserving water and recharging the underground water.

Question 3.
The next item on the agenda for the Gram Sabha is the finalisation of list of people below the poverty line (BPL) which had to be approved by the Gram Sabha. As soon as the list is read out people begin to whisper. “Natwar has just bought a colour T.V. and his son has sent him a new motorcycle. How can he be below the poverty line?” Soorajmal mutters to the person sitting next to him. Saroj says to Sukhi Bai “How did Birju’s name get on to the list? He has so much land. This list should have only poor people. And Om Prakctsh is a landless labourer who can barely make ends meet, yet his name is not on the list.” “You know that both Natwar and Birju are friends of Amirchand. Who can counter Amirchand’s power?’ Sukhi Bai says, “Amirchand was the earlier Zamindar (landowner) of the village and still has control over a lot of land. But we should get Om Prakash’s name put in.”

The Sarpanch (Panchayat President) notices people whispering and asks if anyone has anything to say. Saroj tries to provoke Soorajmal to ask about Natwar arid Birju. But he keeps quiet. Amirchand is sitting in the Gram Sabha keeping an eye on everyone. Then Saroj gets up and says that Om Prakash’s name should be in the BPL list. Others agree that he and his family are very poor.
Panchayati raj Class 6 Extra Questions Civics Chapter 5 L - Q3
The Sarpanch asks how his name had been missed out. The teacher who did the survey of BPL families says, “Om Prakash’s house was locked when I went there. He may have gone somewhere to look for work.” The Sarpanch gives instructions that Om Prakash’s family income be looked at and if it is less than what has been decided by the government, his name should be included in the list.

  1. What is being discussed in this meeting of the Gram Sabha?
  2. Who are Natwar and Birju?
  3. Who is Om Prakash?
  4. Who is Amirchand? What did he do in the past?
  5. Why was Om Prakash’s name missed from the BPL list according to the teacher who surveyed the BPL families

Answer:

  1. List of BPL families was being discussed in the meeting of the Gram Sabha.
  2. Natwar and Birju are affluent people of the village but their names appeared in the list of BPL families because of the interference or manipulation of Sh. Amirchand, a big landlord of the village.
  3. Om Prakash is a poor villager. His name was missed from the list of the BPL families.
  4. Amirchand was the landlord of the village. He got the names of Natwar and Birju enlisted in the BPL families.
  5. According to the teacher who surveyed the BPL families the name of Om Prakash was missed from the list of BPL families as his house was locked at the time of the survey and he could not be listed in the BPL families.

Panchayati raj Class 6 Extra Questions Multiple Choice Questions

Choose the correct answer:

Question 1.
Where do people directly participate and seek answers from their elected representatives?
(a) Gram Panchayat
(b) Parliament House
(c) Both (a) and (b)
(d) None of these
Answer:
Gram Panchayat

Question 2.
Why was the first day special for the village people?
(a) Gram Panchayat was holding its first meeting after election
(b) There was a wedding ceremony
(c) There was annual function of the school
(d) None of these
Answer:
Gram Panchayat was holding its first meeting after election

Question 3.
Who is called the Sarpanch?
(a) Member of Panchayat
(b) Villagers
(c) Panchayat Head
(d) All of these
Answer:
Panchayat Head

Question 4.
The member of Panchayat is also called
(a) Member of Parliament
(b) Panch
(c) Prime Minister
(d) None of these
Answer:
Panch

Question 5.
Who elects the Panchayat Head?
(a) All members of Gram Sabha
(b) Villagers
(c) Secretary
(d) All of these
Answer:
All members of Gram Sabha

Question 6.
Who appoints Secretary of Gram Panchayat?
(a) Government
(b) Ordinary person
(c) Election Commissioner
(d) Landlord of village
Answer:
Government

Question 7.
From where do the village women have to get water?
(a) Suru river
(b) Ganga river
(c) Yamuna river
(d) Gomati river
Answer:
Suru river

Question 8.
Who is responsible for calling the meeting of Gram Sabha?
(a) President of Gram Sabha
(b) Panchs of Gram Panchayat
(c) Secretary of Gram Sabha
(d) None of these
Answer:
Secretary of Gram Sabha

Question 9.
What is the full form of BPL here?
(a) Bharat Petroleum Ltd
(b) Below Poverty Line
(c) Both (a) and (b)
(d) None of these
Answer:
Below Poverty Line

Question 10.
Who was the earlier Zamindar?
(a) Sukhi Bhai
(b) Amir Chand
(c) Birju
(d) Anwar
Answer:
Amir Chand

Question 11.
Whose names should be included, in BPL families?
(a) Very poor person
(b) Middle family person
(c) High income group
(d) All of these
Answer:
Very poor person

Question 12.
What are the works of Gram Panchayat?
(a ) Maintain roads of villages
(b) School buildings in villages
(c) Collecting local taxes
(d) All of these
Answer:
School buildings in villages

Question 13.
What is Zila Parishad?
(a) District Panchayat
(b) Block Panchayat
(c) Gram Sabha
(d) None of these
Answer:
District Panchayat

Question 14.
At which level does Zila Parishad actually make development plans?
(a) District level
(b) Panchayat Samiti
(c) Block level
(d) Government level
Answer:
District level

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CHAPTER-  4 Key Elements of a Democratic Government | Important Questions & MCQs | CLASS 6th | Social Science Civics | NCERT| EDUGROWN

NCERT Important Questions & MCQs for Class 6 Social Science History

NCERT Solutions for Class 6 Social Science includes all the questions provided in NCERT Class 6 Social Science Text book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 6 SST all questions are solved with the detailed explanation to score good marks in the exams.

CHAPTER- 4 Key Elements of a Democratic Government

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CHAPTER-  3 What is Government | Important Questions & MCQs | CLASS 6th | Social Science Civics | NCERT| EDUGROWN

NCERT Important Questions & MCQs for Class 6 Social Science History

NCERT Solutions for Class 6 Social Science includes all the questions provided in NCERT Class 6 Social Science Text book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 6 SST all questions are solved with the detailed explanation to score good marks in the exams.

CHAPTER- 3 What is Government

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CHAPTER- 2 Diversity and Discrimination | Important Questions & MCQs | CLASS 6th | Social Science Civics | NCERT| EDUGROWN

NCERT Important Questions & MCQs for Class 6 Social Science History

NCERT Solutions for Class 6 Social Science includes all the questions provided in NCERT Class 6 Social Science Text book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 6 SST all questions are solved with the detailed explanation to score good marks in the exams.

CHAPTER- 2 Diversity and Discrimination

 

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CHAPTER- 1 Understanding Diversity | Important Questions & MCQs | CLASS 6th | Social Science Civics | NCERT| EDUGROWN

NCERT Important Questions & MCQs for Class 6 Social Science History

NCERT Solutions for Class 6 Social Science includes all the questions provided in NCERT Class 6 Social Science Text book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 6 SST all questions are solved with the detailed explanation to score good marks in the exams.

CHAPTER- 1 Understanding Diversity

 

Read More

RS Agarwal Solution | Class 10th | Chapter-2 | Polynomials | Edugrown

Exercise Ex. 2A

Question 1

Find the zeros of the quadratic polynomial (x2 + 3x – 10) and verify the relation between its zeros and coefficients.Solution 1

Question 2

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

x2 – 2x – 8Solution 2

Question 3

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

x2 + 7x + 12Solution 3

Question 5

Find the zeros of the quadratic polynomial (4x2 – 4x – 3) and verify the relation between its zeros and coefficients.Solution 5

We have

Question 6

Find the zeros of the quadratic polynomial (5x2 – 4 – 8x) and verify the relationship between its zeros and coefficients of the given polynomial.Solution 6

Question 7

Find the zeros of the quadratic polynomial (2x2 – 11x + 15) and verify the relation between its zeros and coefficients.Solution 7

Question 8

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

Solution 8

Question 9

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

4x2 – 4x + 1Solution 9

Question 10

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

3x2 – x – 4Solution 10

Question 11

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

5y2 + 10ySolution 11

Question 12

Find the zeros of the quadratic polynomial (8x2 – 4) and verify the relation between its zeros and coefficients.Solution 12

Let

Question 14

Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence, find the zeros of the polynomial.Solution 14

Question 15

Find the quadratic polynomial, sum of whose zeros is 0 and their product is -1. Hence, find the zeros of the polynomial.Solution 15

Question 16

Find the quadratic polynomial, sum of whose zeros is  and their product is 1. Hence, find the zeros of the polynomial.Solution 16

Question 18

Find the quadratic polynomial whose zeros are . Verify the relation between the coefficients and the zeros of the polynomial.Solution 18

Question 20

If x = and x = -3 are the roots of the quadratic equation ax2 + 7x + b = 0 then find the values of a and b.Solution 20

Question 21

One zero of the polynomial 3x3 + 16x+ 15x – 18 is  Find the other zeros of the polynomial.Solution 21

Exercise Ex. 2B

Question 1

Verify that 3, -2, 1 are the zeros of the cubic polynomial p(x) = x3 – 2x2 – 5x + 6 and verify the relation between its zeros and coefficients.Solution 1

Question 2

Verify that  are the zeros of the cubic polynomial p(x) = 3x3 – 10x2 – 27x + 10 and verify the relation between its zeros and coefficients.Solution 2

Question 3

Find a cubic polynomial whose zeros are 2, -3 and 4.Solution 3

Question 4

Find a cubic polynomial whose zeros are  1 and -3.Solution 4

Question 5

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, -2 and -24 respectively.Solution 5

Question 6

Find the quotient and the remainder when:

f(x) = x3 – 3x2 + 5x – 3 is divided by g(x)= x2 – 2.Solution 6

Question 7

Find the quotient and the remainder when:

f(x)= x4 -3x2 + 4x + 5 is divided by g(x)= x2 + 1 – x.Solution 7

Question 8

Find the quotient and the remainder when:

f(x)= x4 – 5x + 6 is divided by g(x) = 2 – x2.Solution 8

Question 9

By actual division, show that x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12.Solution 9

Question 11

On dividing 3x3 + x2 + 2x + 5 by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).

Solution 11

Question 12

Verify division algorithm for the polynomials f(x) = 8 + 20x + x2 – 6x3 and g(x) = 2 + 5x – 3x2.Solution 12

Question 13

It is given that -1 is one of the zeros of the polynomial x3 + 2x2 – 11x – 12. Find all the zeros of the given polynomial.Solution 13

1
Question 14

If 1 and -2 are two zeros of the polynomial, find its third zero.Solution 14

Question 15

If 3 and -3 are two zeros of the polynomial, find all the zeroes of the given polynomial.
Solution 15

Question 16

If 2 and -2 are two zeros of the polynomial, find all the zeros of the given Polynomial.
Solution 16

Question 17

Find all the zeros of, if it is given that two of its zeros are Solution 17

Question 18

Obtain all other zeros of , if two of its zeros are .Solution 18

Question 23

Find all the zeros of the polynomial , it being given that two of its zeros are .Solution 23

Exercise Ex. 2C

Question 1

If one zero of the polynomial x2 – 4x + 1 is (2 + ), write the other zero.Solution 1

Question 2

Find the zeros of the polynomial x2 + x – p(p + 1).Solution 2

Question 3

Find the zeros of the polynomial x2 – 3x – m(m + 3).Solution 3

Question 4

Solution 4

Question 5

If one zero of the quadratic polynomial kx2 + 3x + k is 2 then find the value of k.Solution 5

Question 6

If 3 is a zero of the polynomial 2x2 + x + k, find the value of k.Solution 6

Question 7

If -4 is a zero of the polynomial x– x – (2k + 2) then find the value of k.Solution 7

Question 8

If 1 is a zero of the polynomial ax2 – 3(a – 1)x – 1 then find the value of a.Solution 8

Question 9

If -2 is a zero of the polynomial 3x2 + 4x + 2k then find the value of k.Solution 9

Question 10

Write the zeros of the polynomial x2 – x – 6.Solution 10

Question 11

If the sum of the zeros of the quadratic polynomial kx2 – 3x + 5 is 1, write the value of k.Solution 11

Question 12

If the product of the zeros of the quadratic polynomial x2 – 4x + k is 3 then write the value of k.Solution 12

Question 13

If (x + a) is a factor of (2x2 + 2ax + 5x + 10), find the value of a.Solution 13

Question 14

If (a – b), a and (a + b) are zeros of the polynomial 2x3 – 6x2 + 5x – 7, write the value of a.Solution 14

Question 15

If x3 + x2 – ax + b is divisible by (x2 – x), write the values of a and b.Solution 15

Question 16

Solution 16

Question 17

State division algorithm for polynomials.Solution 17

If f(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can always find polynomials q(x) and r(x) such that f(x) = q(x)g(x) + r(x),

where r(x) = 0 or degree r(x) < degree g(x).Question 18

The sum of the zeros and the product of zeros of a quadratic polynomial are  and -3 respectively. Write the polynomial.Solution 18

Question 19

Write the zeros of the quadratic polynomial f(x) = 6x2 – 3.Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

If the zeros of the polynomial f(x) = x3 – 3x2 + x + 1 are (a – b), a and (a + b), find a and b.Solution 25

Exercise MCQ

Question 1

Which of the following is a polynomial?

Solution 1

Correct answer: (d)

An expression of the form p(x) = a0 + a1x + a2x2 + ….. + anxn, where an ≠ 0, is called a polynomial in x of degree n.

Here, a0, a1, a2, ……, an are real numbers and each power of x is a non-negative integer.

Question 2

Which of the following is not a polynomial?

Solution 2

Correct answer: (d)

An expression of the form p(x) = a0 + a1x + a2x2 + ….. + anxn, where an ≠ 0, is called a polynomial in x of degree n.

Here, a0, a1, a2, ……, an are real numbers and each power of x is a non-negative integer.

Question 3

The zeros of the polynomial x– 2x – 3 are

(a)-3, 1

(b)-3, -1

(c) 3, -1

(d) 3, 1Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

The sum and the product of the zeros of a quadratic polynomial are 3 and -10 respectively. The quadratic polynomial is

(a) x2 – 3x + 10

(b) x2 + 3x – 10

(c) x2 – 3x – 10

(d) x2 + 3x + 10Solution 8

Question 9

A quadratic polynomial whose zeros are 5 and -3, is

(a) x2 + 2x – 15

(b) x2 – 2x + 15

(c) x2 – 2x – 15

(d)none of theseSolution 9

Question 10

(a) 10x2 +x + 3

(b) 10x2 + x – 3

(c) 10x2 – x + 3

(d) 10x2 – x – 3Solution 10

Question 11

The zeros of the quadratic polynomial x+ 88x + 125 are

(a) both positive

(b) both negative

(c) one positive and one negative

(d) both equalSolution 11

Question 12

If 𝛼 and 𝛽 are the zeroes of x+ 5x + 8 then the value of (𝛼 + 𝛽) is

(a) 5

(b) -5

(c) 8

(d) -8Solution 12

Question 13

If 𝛼 and 𝛽 are the zeros of 2x+ 5x – 9 then the value of 𝛼𝛽 is

Solution 13

Question 14

If one zero of the quadratic polynomial kx+ 3x + k is 2 then the value of k is

Solution 14

Question 15

If one zero of the quadratic polynomial (k – 1)x+ kx + 1 is -4, then the value of k is

Solution 15

Question 16

If -2 and 3 are the zeros of the quadratic polynomial x+ (a + 1)x + b then

(a) a = -2, b = 6

(b) a = 2, b = -6

(c) a = -2, b = -6

(d) a = 2, b = 6Solution 16

Question 17

If one zero of 3x2 + 8x + k be the reciprocal of the other then k = ?

(a) 3

(b) -3

(c) 

(d) Solution 17

Question 18

If the sum of the zeros of the quadratic polynomial kx+ 2x + 3k is equal to the product of its zeros then k = ?

Solution 18

Question 19

(a) 3

(b) -3

(c) 12

(d)-12Solution 19

Question 20

If 𝛼, 𝛽, 𝛾 are the zeros of the polynomial x– 6x– x + 30, then (𝛼𝛽 + 𝛽𝛾 + 𝛾𝛼) = ?

(a) -1

(b) 1

(c) -5

(d)30Solution 20

Question 21

If 𝛼, 𝛽, 𝛾 be the zeros of the polynomial 2x+ x– 13x + 6, then 𝛼𝛽𝛾 

(a) -3

(b) 3

(c) 

(d)   Solution 21

Question 22

If 𝛼, 𝛽, 𝛾 be the zeros of the polynomial p(x) such that (𝛼 + 𝛽 + 𝛾) = 3, (𝛼𝛽 + 𝛽𝛾 + 𝛾𝛼) = -10 and 𝛼𝛽𝛾 = -24, then p(x) =?

(a) x+ 3x– 10x + 24

(b) x+ 3x+ 10x – 24

(c) x– 3x– 10x + 24

(d) None of theseSolution 22

Question 23

If two of the zeros of the cubic polynomial ax+ bx+ cx + d are 0, then the third zero is

Solution 23

Question 24

If one of the zeros of the cubic polynomial ax+ bx+ cx + d is 0, then the product of other two zeros are

Solution 24

Question 25

If one of the zeros of the cubic polynomial x+ ax+ bx + c is -1, then the product of the other two zeros is

(a) a – b – 1

(b) b – a – 1

(c) 1 – a + b

(d) 1 + a – bSolution 25

Question 26

(a) 3

(b) -3

(c) -2

(d) 2Solution 26

Question 27

On dividing a polynomial p(x) by a non-zero polynomial q(x), let g(x) be the quotient and r(x) be the remainder, then p(x) = q(x).g(x) + r(x), where

(a)r(x) = 0 always

(b)deg r(x) < deg g(x) always

(c) either r(x) = 0 or deg r(x) < deg g(x)

(d) r(x) = g(x)Solution 27

Question 28

Which of the following is a true statement?

(a)x+ 5x – 3 is a linear polynomial

(b)x+ 4x – 1 is a binomial

(c) x + 1 is a monomial

(d) 5x3 is a monomialSolution 28

Exercise FA

Question 1

Zeros of p(x) = x– 2x – 3 are

(a) 1, -3

(b) 3, -1

(c) -3, -1

(d)1, 3Solution 1

Question 2

If 𝛼, 𝛽, 𝛾 are the zeros of the polynomial x– 6x– x + 30, then (𝛼𝛽 + 𝛽𝛾 + 𝛾𝛼) = ?

(a) -1

(b) 1

(c) -5

(d)30Solution 2

Question 3

If 𝛼, 𝛽 are the zeros of kx– 2x + 3k such that 𝛼 + 𝛽 = 𝛼𝛽, then k = ?

Solution 3

Question 4

It is given that the difference between the zeros of 4x2 – 8kx + 9 is 4 and k > 0. Then, k = ?

Solution 4

Question 5

Find the zeros of the polynomial x+ 2x – 195.Solution 5

Question 6

If one zeros of the polynomial (a+ 9)x+ 13x + 6a is the reciprocal of the other, find the value of a.Solution 6

Question 7

Find a quadratic polynomial whose zeros are 2 and -5.Solution 7

Question 8

If the zeros of the polynomial x– 3x+ x + 1 are (a – b), a and (a + b), find the values of a and b.Solution 8

Question 9

Verify that 2 is a zero of the polynomial x+ 4x– 3x – 18.Solution 9

Question 10

Find the quadratic polynomial, the sum of whose zeros is -5 and their product is 6.Solution 10

Question 11

Find a cubic polynomial whose zeros are 3, 5 and -2.Solution 11

Question 12

Using remainder theorem, find the remainder when p(x) = x+ 3x– 5x + 4 is divided by (x – 2).Solution 12

Question 13

Show that (x + 2) is a factor of f(x) = x+ 4x+ x – 6.Solution 13

Question 14

Solution 14

Question 15

If 𝛼, 𝛽 are the zeros of the polynomial f(x) = x– 5x + k such that 𝛼 – 𝛽 = 1, find the value of k.Solution 15

Question 16

Show that the polynomial f(x) = x+ 4x+ 6 has no zero.Solution 16

Question 17

If one zero of the polynomial p(x) = x– 6x+ 11x – 6 is 3, find the other two zeros.Solution 17

Question 18

Solution 18

Question 19

Find the quotient when p(x) = 3x+ 5x– 7x+ 2x + 2 is divided by (x+ 3x + 1).Solution 19

Question 20

Use remainder theorem to find the value of k, it being given that when x+ 2x+ kx + 3 is divided by (x – 3), then the remainder is 21.Solution 20

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RD SHARMA SOLUTION CHAPTER-7 Adjoint and Inverse of a Matrix I CLASS 12TH MATHEMATICS-EDUGROWN

Chapter 7 Adjoint and Inverse of a Matrix Ex 7.1

1. Find the adjoint of each of the following matrices:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 1
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 2
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 3
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 4

Verify that (adj A) A = |A| I = A (adj A) for the above matrices.

Solution:

(i) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 5

Cofactors of A are

C11 = 4

C12 = – 2

C21 = – 5

C22 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 6
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 7

(ii) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 8

Therefore cofactors of A are

C11 = d

C12 = – c

C21 = – b

C22 = a

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 9
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 10

(iii) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 11

Therefore cofactors of A are

C11 = cos α

C12 = – sin α

C21 = – sin α

C22 = cos α

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 12
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 13

(iv) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 14

Therefore cofactors of A are

C11 = 1

C12 = tan α/2

C21 = – tan α/2

C22 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 15
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 16

2. Compute the adjoint of each of the following matrices.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 17
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 18
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 19
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 20

Solution:

(i) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 21

Therefore cofactors of A are

C11 = – 3

C21 = 2

C31 = 2

C12 = 2

C22 = – 3

C23 = 2

C13 = 2

C23 = 2

C33 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 22
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 23

(ii) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 24

Cofactors of A

C11 = 2

C21 = 3

C31 = – 13

C12 = – 3

C22 = 6

C32 = 9

C13 = 5

C23 = – 3

C33 = – 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 25
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 26

(iii) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 28

Therefore cofactors of A

C11 = – 22

C21 = 11

C31 = – 11

C12 = 4

C22 = – 2

C32 = 2

C13 = 16

C23 = – 8

C33 = 8

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 32

(iv) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 33

Therefore cofactors of A

C11 = 3

C21 = – 1

C31 = 1

C12 = – 15

C22 = 7

C32 = – 5

C13 = 4

C23 = – 2

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 34
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 35
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 36

Solution:

Given

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 37

Therefore cofactors of A

C11 = 30

C21 = 12

C31 = – 3

C12 = – 20

C22 = – 8

C32 = 2

C13 = – 50

C23 = – 20

C33 = 5

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 38

Solution:

Given

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 41

Cofactors of A

C11 = – 4

C21 = – 3

C31 = – 3

C12 = 1

C22 = 0

C32 = 1

C13 = 4

C23 = 4

C33 = 3

Solution:

Given

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 44

Cofactors of A are

C11 = – 3

C21 = 6

C31 = 6

C12 = – 6

C22 = 3

C32 = – 6

C13 = – 6

C23 = – 6

C33 = 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 45
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 46

Solution:

Given

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 47

Cofactors of A are

C11 = 9

C21 = 19

C31 = – 4

C12 = 4

C22 = 14

C32 = 1

C13 = 8

C23 = 3

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 48
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 49

7. Find the inverse of each of the following matrices:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 50
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 51
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 52
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 53

Solution:

(i) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = cos θ (cos θ) + sin θ (sin θ)

= 1

Hence, A – 1 exists.

Cofactors of A are

C11 = cos θ

C12 = sin θ

C21 = – sin θ

C22 = cos θ

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 54
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 55

(ii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = – 1 ≠ 0

Hence, A – 1 exists.

Cofactors of A are

C11 = 0

C12 = – 1

C21 = – 1

C22 = 0

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 56

(iii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 57

(iv) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = 2 + 15 = 17 ≠ 0

Hence, A – 1 exists.

Cofactors of A are

C11 = 1

C12 = 3

C21 = – 5

C22 = 2

8. Find the inverse of each of the following matrices.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 60
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 61
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 62

Solution:

(i) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 67

= 1(6 – 1) – 2(4 – 3) + 3(2 – 9)

= 5 – 2 – 21

= – 18≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 5

C21 = – 1

C31 = – 7

C12 = – 1

C22 = – 7

C32 = 5

C13 = – 7

C23 = 5

C33 = – 1

(ii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 70

= 1 (1 + 3) – 2 (– 1 + 2) + 5 (3 + 2)

= 4 – 2 + 25

= 27≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 4

C21 = 17

C31 = 3

C12 = – 1

C22 = – 11

C32 = 6

C13 = 5

C23 = 1

C33 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 71
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 72

(iii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 73

= 2(4 – 1) + 1(– 2 + 1) + 1(1 – 2)

= 6 – 2

= – 4≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 3

C21 = 1

C31 = – 1

C12 = + 1

C22 = 3

C32 = 1

C13 = – 1

C23 = 1

C33 = 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 74

(iv) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 75

= 2(3 – 0) – 0 – 1(5)

= 6 – 5

= 1≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 3

C21 = – 1

C31 = 1

C12 = – 15

C22 = 6

C32 = – 5

C13 = 5

C23 = – 2

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 76

(v) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 77

= 0 – 1 (16 – 12) – 1 (– 12 + 9)

= – 4 + 3

= – 1≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 0

C21 = – 1

C31 = 1

C12 = – 4

C22 = 3

C32 = – 4

C13 = – 3

C23 = 3

C33 = – 4

(vi) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 79

= 0 – 0 – 1(– 12 + 8)

= 4≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = – 8

C21 = 4

C31 = 4

C12 = 11

C22 = – 2

C32 = – 3

C13 = – 4

C23 = 0

C33 = 0

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 80

(vii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 81 – 0 + 0

= – (cos2 α – sin2 α)

= – 1≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = – 1

C21 = 0

C31 = 0

C12 = 0

C22 = – cos α

C32 = – sin α

C13 = 0

C23 = – sin α

C33 = cos α

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 82

9. Find the inverse of each of the following matrices and verify that A-1A = I3.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 83
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 84

Solution:

(i) We have

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 85

= 1(16 – 9) – 3(4 – 3) + 3(3 – 4)

= 7 – 3 – 3

= 1≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 7

C21 = – 3

C31 = – 3

C12 = – 1

C22 = 1

C32 = 0

C13 = – 1

C23 = 0

C33 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 86
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 87
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 88

(ii) We have

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 89

= 2(8 – 7) – 3(6 – 3) + 1(21 – 12)

= 2 – 9 + 9

= 2≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 1

C21 = 1

C31 = – 1

C12 = – 3

C22 = 1

C32 = 1

C13 = 9

C23 = – 5

C33 = – 1

10. For the following pair of matrices verify that (AB)-1 = B-1A-1.

Solution:

(i) Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 94
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 95

Hence, (AB)-1 = B-1A-1

(ii) Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 96
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 97

Hence, (AB)-1 = B-1A-1

Solution:

Given

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 102
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 103
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 104

Solution:

Given

Solution:

Solution:

Given

A = 
https://gradeup-question-images.grdp.co/liveData/PROJ23872/1543574054891449.png and B – 1 = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 113

Here, (AB) – 1 = B – 1 A – 1

|A| = – 5 + 4 = – 1

Cofactors of A are

C11 = – 1

C21 = 8

C31 = – 12

C12 = 0

C22 = 1

C32 = – 2

C13 = 1

C23 = – 10

C33 = 15

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 114
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 115

(i) F(α)-1 = F (-α)

(ii) G(β)-1 = G (-β)

(iii) F(α)G(β)-1 = G (-β) F (-α)

Solution:

(i) Given

F (α) = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 116

|F (α)| = cos2 α + sin2 α = 1≠ 0

Cofactors of A are

C11 = cos α

C21 = sin α

C31 = 0

C12 = – sin α

C22 = cos α

C32 = 0

C13 = 0

C23 = 0

C33 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 117
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 118

(ii) We have

|G (β)| = cos2 β + sin2 β = 1

Cofactors of A are

C11 = cos β

C21 = 0

C31 = -sin β

C12 = 0

C22 = 1

C32 = 0

C13 = sin β

C23 = 0

C33 = cos β

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 119
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 120

(iii) Now we have to show thatF(α)G(β) – 1 = G (– β) F (– α)

We have already know thatG(β) – 1 = G (– β)F(α) – 1 = F (– α)

And LHS = F(α)G(β) – 1

= G(β) – 1 F(α) – 1

= G (– β) F (– α)

Hence = RHS

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 121

Solution:

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 122
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 123
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 124

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 125
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 126
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 127
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 128

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 129
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 130

Chapter 7 Adjoint and Inverse of a Matrix Ex 7.2


Find the inverse of the following matrices by using elementary row transformations:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 131

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 132
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 133
134

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 135
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 136
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 137

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 138
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 139
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 140

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 141
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 142
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 143

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 144
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 145
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 146

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 147
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 148
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 149
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 150

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 151
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 152
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 153
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 154

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 155
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 156
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