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Punjab State Board PSEB 5th Class Welcome Life Book Solutions Chapter 4 Keep Love in Heart Towards Them Textbook Exercise Questions and Answers.

PSEB Solutions for Class 5 Welcome Life Chapter 4 Keep Love in Heart Towards Them

Welcome Life Guide for Class 5 PSEB Keep Love in Heart Towards Them Textbook Questions and Answers

(a) Information about our state :

Our Punjab is a colorful place. It is like a Rose among other flowers. Here people never lose hope and dream new every day.

We are the natives of Punjab. Punjab is a famous state of India. Punjab has a special recognition across the world. Punjab was named after five rivers – Satluj, Beas, Raavi, Chenab and Jehlum. But two rivers – Chenab and Jhelum became the part of Pakistan at the time of Partition of India in 1947. Now, three rivers – Satluj,Beas and Raavi flow here.

Punjab is a border state. It has been facing many battles because of that. People living here have no fear of enemy. Their culture is full of bravery. Punjabis have a great contribution in the struggle of freedom for the country. These people a re famous for thei r bravery across the world.

Punjabi is the language of Punjab. Punjabi speaking people can be found even far away from Punjab. It is the lQth – llth language of the world on spoken based. Our Gurus, Suffis, Saints, Poets and singers adopted this language to raise its status. Today, Punjabi is known as a rich language.

Bhangra and Gidha is the folk dance of Punjab. Bhangra is the dance of men and Gidha is the dance of women. These dances are performed on the occasion of happiness. Singing and dancing is the food of Punjabi’s soul.

Punjab is very famous for agriculture. Its land is very fertile. There are bumper crops of wheat, rice, maize and sugarcane here. Punjab provides major share in Food store of India in spite of having less area. Animal husbandry is another main occupation here.

Punjabis are very fond of fairs. Many fairs are celebrated in the Punjab. Vaisakhi fair, chappar fair, Jarg fair, Hola mahala, Maghi fair and Prof. Pooran Singh fair are very famous among them.

Punjabis are very open – hearted, happy – go – lucky and helpful people. They have nature of helping other people and arranging Langer for needy ones.

Oral Questions:

Question 1.
How many rivers were there in ancient Punjab?
Answer:
Five.

Question 2.
Which rivers are there in Punjab these days?
Answer:
Sutlej, Bias, Ravi.

Question 3.
Which language is spoken in Punjab?
Answer:
Punjabi.

Question 4.
Which crops are cultivated in Punjab?
Answer:
Sugarcane, Wheat, Rice, Maze.

Question 5.
Which are the major occupations of Punjabis?
Answer:
Agriculture.

Question 6.
Which are main fairs of Punjab?
Answer:
Jarag, Chhappar, Hola Mohala, Vaisakhi, Pro. Mohan Singh Mela.

Question 7.
How is the nature of Punjabis?
Answer:
Broadmindedness, jolly nature and being helpful to others.

Question 8.
What is your viewpoint about Punjab?
Answer:
Very much.

(b) Love with Mother – Tongue:

Teacher : Children, today we’ll discuss about mother – tongue.
Ankur : Sir, What is mother – tongue?

Teacher : Children, Mother – tongue is that which is acquired by a child from his/her parents or his/her family from the very beginning.
Baljit : Sir, if a child learns from parents or family, then why is it called mother – tongue?

Teacher : Yes Baljit, you asked a very good question. In reality, a child lives with his/her mother most of the time from early days. May be that’s why it is named as mother – tongue.
Chandan : Sir, there is a song by Harbhajan Maan – ‘Mainu iyon na mano visaar ve main teri maa boli ha’.

(Don’t forget me from your heart. I’m your mother – tongue.)

Teacher : Well done, you reminded me a very good song.
Baljit : Sir, Satinder Sartaj also has a song – ‘Main Gurmukhi da Beta’.

Teacher : Yes son, it is also a very good song. You listen to very good songs. Son, both these songs highlighted the importance of mother – tongue. They give the message to love mother – tongue.
Savirta : Sir, Is Punjabi our mother – tongue?

Teacher : Yes, Punjabi is our mother – tongue.
Savita : Sir, What is Gurumukhi then?

Teacher : Daughter, Gurumukhi is a script of Punjabi language. The signs that are used for writing Punjabi language is called a script. Like a A e ishwrl, ibhwrl, ibMdl, it pi… The group of signs that are used to write is called a script. Gurumukhi script is used for writing Punjabi.
Savita : Sir, Why do many Hindi movies have Punjabi songs?

Teacher : Children, Punjabi is a very famous language. By the numbers of speakers, this language is on lOth/llth position among the world. Punjabi people have reached in more than 160 countries of the world. Whenever there is a Punjabi song in a Hindi movie, many Punjabis like to watch that movie. Many times, Hindi film makers add a Punjabi song in their movieto make it more popular.
Bharti : Sir, all the members in my house speak in Hindi. Our Real house is in U.P. Our relatives also speak in Hindi.

Teacher : Child, Then your mother – tongue is Hindi. No problem, Hindi and Punjabi our like sisters. Every human being must love his/her own mother – tongue. Mother – tongue has a deep and loveable relationship with our heart and mind. Whatever is listened and read in mother – tongue is easily understood.
Baljit : Yes Sir, That’s right.

Teacher : But children, it doesn’t mean that we needn’t learn other languages. Just keep in mind that other languages are not learnt by forgetting mother – tongue. Harbhajan Maan is also saying that – ‘Mainu iyon na manovisar.
Baljit : Sir, There is a song of Manmohan Waris in my father’s phone – ‘Mawan tin hundiyan ne’. (Mothers are three….)

Teacher : Baljit, your father has a good taste of music. I have also listened to that song – Mothers are three – one is Mother Earth, second is mother – tongue and third is the mother who gave us birth. Really children, these three nurture us. Their debt can’t be repaid.
Savita : Sir, my uncle reads Punjabi books.

Teacher : Yes children, Books of many famous writers like Gurdial Singh, Shiv Kumar, Surjit Patar and Narinder Kapoor are read in Punjabi.
Ankur : Sir, My brother reads Punjabi newspaper on computer.

Teacher : Yes children, many things in Punjabi are there on computer. I also read three Punjabi newspapers early in the morning – Punjabi Tribune, Nawan Jamana (The New World) and Ajit.

Children let’s stop this conversation here. What did you learn today?

Bharti : Sir, today we learnt that we should never forget our mother – tongue ever.

Teacher : Let’s finish this talk with lines of a Pakistani Poet:

ਮੈਨੂੰ ਕਈਆਂ ਨੇ ਆਖਿਆ ਕਈ ਵਾਰੀ
ਤੂੰ ਲੈਣਾ ਪੰਜਾਬੀ ਦਾ ਨਾਂ ਛੱਡ ਦੇ।
ਜਿਦੀ ਗੋਦੀ ‘ਚ ਪਲ ਕੇ ਜਵਾਨ ਹੋਇਓਂ |
ਉਹ ਮਾਂ ਛੱਡ ਦੇ ਤੇ ਗਰਾਂ ਛੱਡ ਦੇ।
ਜੇ ਪੰਜਾਬੀ-ਪੰਜਾਬੀ ਈ ਕੂਕਣਾ ਈ
ਜਿੱਥੇ ਖਲਾ ਖਲੋਤਾ ਉਹ ਥਾਂ ਛੱਡ ਦੇ।
ਮੈਨੂੰ ਇੰਝ ਲੱਗਦਾ ਲੋਕੀਂ ਆਖਦੇ ਨੇ
ਤੂੰ ਪੁੱਤਰਾ ਆਪਣੀ ਮਾਂ ਛੱਡ ਦੇ।

(Many people have asked me to stop using the name of Punjabi just as a child loves his mother and native place after growing up in the lap of his mother.)

Oral Questions:

Question 1.
Which are three mothers of a human being?
Answer:
Earth mother, mother-tongue, birth-giving mother.

Question 2.
Which language is the mother – tongue of Punjab?
Answer:
Punjabi.

Question 3.
Can Punjabi be read or written on computer?
Answer:
Yes.

Question 4.
What did we learn from today’s talk?
Answer:
We should not learn more languages after forgetting Punjabi. But we should learn other languages also so that we can get knowledge about other singers and writers.

(C) On other Languages of the country:

Other people have their mother – tongues just as Punjabi is our mother – tongue. They also love their mother – tongue as we do. Everyone has a right to love his/her own mother – tongue. Everyone must love his/her mother – tongue. Hundreds of languages and dialects are spoken in India. More spoken languages amongthem hold a place in the constitution.

You must have seen any Indian rupee – note. The amount of rupee can be found written on this in seventeen languages including Punjabi, Hindi and English. In Reality, India is a multi language country. India is a bouquet of language flowers. That’s why Indian government gives the deserved right to every language. We must love our mother – tongue but we shouldn’t condemn others’ mother – tongue. Mother – tongue is as loveable to anyone as we love ours.

We must learn as well as speak our mother – tongue very well but other languages also. It is impossible to live without learning Hindi and English. If we have to live in any other state for a longer period, then we should learn their language also. Our many problems will get solved after learning this otherwise also, if we learn as many languages as we can, many doors to knowledge will get open for us. Bangla, Assami, Marathi, Kashmiri, Bodo, Kannad, Malyalam, Gujrati, Dogri, Urdu and Tamil are other languages spoken in India.

Do you know that Munshi Premchand is a well known writer in Hindi? You must have heard the name of Rabindranath Tagore. Tagore was from Bengal. He wrote in Bangali Language. Indian National Anthem ‘JANA GANA MANA’ is written by him. So It is very important to understand the Importance of other languages.

ਦੇਸ ਮੇਰੇ ਦੀਆਂ ਸਭ ਬੋਲੀਆਂ ਨਿਆਰੀਆਂ।
ਦੇਸ ਦੀ ਅਮੀਰੀ ਇਹ ਦਿਖਾਉਣ ਸਾਰੀਆਂ।
ਜਿੰਨੀਆਂ ਭਾਸ਼ਾਵਾਂ ਅਸੀਂ ਸਿੱਖ ਲੈਂਦੇ ਹਾਂ,
ਗਿਆਨ ਦੀਆਂ ਓਨੀਆਂ ਖੁੱਲ੍ਹਣ ਬਾਰੀਆਂ।

(All the languages of my country are different. It increases the richness of the country. As many languages as we learn, more and more windows get open to acquire knowledge.

Oral Questions:

Question 1.
Hundred languages are spoken in India. True Or False?
Answer:
Right.

Question 2.
Write any two languages other than Punjabi, Hindi and English?
Answer:
Marathi, Bodo, Kashmiri.

Question 3.
Where did Rabindranath Tagore belongto?
Answer:
In Bengal.

Question 4.
Learning more languages is beneficial or not?
Answer:
More doors of knowledge are opened for us.

(d) Love with people of the country:

It is a very high human trait of having true love for country. It is not a wholly love for things of the country. Real love for country is a love for its people. People of the country means all the people that belong to that country. Till we don’t love all people of the country, we can’t say that we love our country. As you know that we all are human beings. That’s why the feeling of hatred or partiality shouldn’t exist in our heart.

Any citizen irrespective of his state, religion, caste or language, is a part of the country. Any kind of partiality must not be done with him. We should not have any feelings of superiority or inferiority. Every citizen should be helpful to others. Nobody should think about other’s loss. Nobody should cheat anyone. This is the love for the people of the country.

The most important thing is to think about the rights of poor people in the country. We should try to make poor people’s life prosper. They should be helped in education. A nation can prosper only, if all the people are happy and have essential facilities for life. A Real courtesy is to take weak people along with us. Let’s read a poem :

ਆਓ, ਸਾਰੇ ਲੋਕਾਂ ਨੂੰ ਪਿਆਰ ਕਰੀਏ,
ਦਿਲਾਂ ਚ ਕਦੇ ਨਾਨਫ਼ਰਤ ਭਰੀਏ ।
ਸਾਰੇ ਹੀਨੇ ਆਪਣੇ, ਬੇਗਾਨਾ ਕੋਈਨਾ,
ਪਿਆਰ ਜਿਹਾ ਜੱਗ ਚ ਤਰਾਨਾ ਕੋਈ।
ਸੱਚੇ-ਸੁੱਚੇ ਦਿਲ ’ਚ ਵਿਚਾਰ ਰੱਖੀਏ,
ਦਿਲ ’ਚ ਨਾਕਦੇ ਹੰਕਾਰ ਰੱਖੀਏ।
ਵੰਡੀਆਂਦਿਲਾਂ ਦੇ ਵਿੱਚ ਆਉਣ ਦੇਈਏ ਨਾ,
ਝਗੜਾ ਕਿਸੇ ਨੂੰ ਕਦੇ ਪਾਉਣ ਦੇਈਏ ਨਾ।

(Let us love all the people and never have feeling of hatred in our hearts. All are ours, nobody is strange and nothing is more beautiful song than love in the world. We should keep good and pure thoughts in our hearts in place of pride. We should restrict people to make divisions and stop fighting.)

Oral Questions:

Question 1.
Are we all India ns united?
Answer:
Yes, all Indians are one.

Question 2.
Should we help others or harm others?
Answer:
We should help others.

Question 3.
What are the benefits of living with love?
Answer:
Country and all the people in the country make progress.

Question 4.
The country is also a big family. True or False?
Answer:
Right.

Question 5.
Do all human being’s blood similaror different?
Answer:
Alike.

Question 6.
Is it a good thing to fight on the basis of religion, caste or region?
Answer:
No, it is very bad.

Question 7.
After growing up would you teach people to live with love?
Answer:
Yes, I will start from now.

PSEB 5th Class Welcome Life Guide Keep Love in Heart Towards Them Important Questions and Answers

Multiple Choice Questions :

Question 1.
Which river is not included in Punjab at Present ?
(a) Sutlej
(b) Jhelum
(c) Bias
(d) Ravi.
Answer:
(b) Jhelum.

Question 2.
When did country get freedom ?
(a) 1950
(b) 1947
(c) 1974
(d) 1945.
Answer:
(b) 1947.

Question 3.
Which type of state is Punjab ?
(a) Borderline
(b) Near the sea
(c) Sandy
(d) All are wrong.
Answer:
(a) Borderline.

Question 4.
How many languages are there on the Indian rupee ?
(a) 10
(b) 17
(c) 11
(d) 21
Answer:
(b) 17.

Question 5.
In which language Tagore used to Write ?
(a) Punjabi
(b) Bengali
(c) Urdu
(d) Hindi.
Answer:
(b) Bengali.

Question 6.
Who was Munshi Prem Chand ?
(a) Writer
(b) Poet
(c) Actor
(d) Singer.
Answer:
(a) Writer.

Question 7.
Who has written the national Anthem of India ?
(a) Tagore
(b) Munshi Prem Chand
(c) Amrita Pritam
(d) None of the above.
Answer:
(a) Tagore.

Question 8.
In how many countries have Punjabi people reached ?
(a) More than 160
(b) Less than 95
(c) 340
(d) 460.
Answer:
(a) More than 160.

Question 9.
Who has said in the song that mothers are three in number ?
(a) Sartaj
(b) Batalavi
(c) Manmohan Wans
(d) Harbhajan Mann.
Answer:
(c) Manmohan Waris.

Question 10.
Famous writer is :
(a) Shiv Kumar Batalavi
(b) Narinder Singh Kapoor
(c) Gurdial Singh
(d) All are correct.
Answer:
(d) All are correct.

Question 11.
We should ……….. our mother-tongue.
(a) Love
(b) Partiality
(c) Hate
(d) All of the above.
Answer:
(a) Love

Question 12.
Which newspaper does our teacher read in computer ?
(a) Punjabi Tribune
(b) Nawan Jamana
(c) Ajit
(d) All are correct.
Answer:
(d) All are correct.

Fill in the blanks :

1. We are the citizens of ……………………………… State.
2. People of Punjab are famous all over the world for their …………………………….. .
3. On the basis of number of Punjabi-speaking people in the world, Punjabi is on the ……………………………… number.
4. Punjab has always to face wars due to ……………………………… state.
5. Punjab is very famous for …………………………….. .
6. National Anthem of India ‘Jana Gana Mann’ is written by …………………………….. .
7. To support the ……………………………… person is real goodness.
Answer:
1. Punjab
2. bravery
3. tenth-eleventh
4. borderline
5. agriculture
6. Rabindranath Tagore
7. weak.

Tick Right (✓) or Wrong (✗) :

1. Punjab has got its name by seven rivers.
2. Punjab is at borderline. That is why it always remains peaceful.
3. The language of Punjab is Dogri.
4. Dancing and singing is the diet of souls of Punjabis.
5. Wheat, rice, maze and sugarcane are grown at large scale in Punjab.
6. Amount of note is written in 17 languages on the Indian rupee.
7. Munshi Prem Chand is a great writer of Hindi.
8. There should not be any feeling of casteism.
Answer:
1. ✗
2. ✗
3. ✗
4. ✓
5. ✓
6. ✓
7. ✓
8. ✓

Mind Mapping :

Answer:

Match the following :

1. Punjab (a) Tagore
2. Fair of Punjab (b) Surjeet Pattar
3. Punjabi Poet (c) Borderline State
4. Bengali Writer (d) Jarag.
Answer:
1. (c)
2. (d)
3. (b)
4. (a)

Short Answer Type Questions

Question 1.
Name five rivers on the basis of which Punjab has got its name ?
Answer:
Sutlej, Bias, Ravi, Chenab and Jhelum.

Question 2.
How many rivers are there in Punjab nowadays ?

Question 3.
How two rivers of Punjab are excluded from it ?
Answer:
At the time of division of 1947, two rivers were included in Pakistan.

Question 4.
What are the folk dances of Punjab ?
Answer:
Bhangra of men and Giddha of women.

Question 5.
Give names of martyrs of Punjab.
Answer:
Shaheed Bhagat Singh, Shaheed Kartar Singh Sarabha, Shaheed Udam Singh.

Question 6.
What is the language of Punjab ?
Answer:
Language of Punjab is Punjabi.

Question 7.
Language of Punjab stands at which number in the world ?
Answer:
On the basis of number of Punjabi-speaking people in the world, Punjabi stands at the tenth-eleventh number.

Question 8.
What is Mother-tongue?
Answer:
Mother-tongue is that language which a child learns from his/her parents or family.

Question 9.
What are the two songs in which mother-tongue is used ?
Answer:
Harbhajan Mann’s ……… Mainu Eyu na Mono Visar, Ve main Teri maa di Boli haan.

Satinder Sartaj’s ……… Main Gurmukhi da Beta.

Question 10.
What is Gurmukhi ?
Answer:
It is the script of Punjabi language.

Question 11.
According to Manmohan Waris’s song, which are the three mothers ?
Answer:
Mother earth, Mother-tongue, Birth giving mother.

Punjab State Board PSEB 5th Class Welcome Life Book Solutions Chapter 3 Responsibility Textbook Exercise Questions and Answers.

PSEB Solutions for Class 5 Welcome Life Chapter 3 Responsibility

Welcome Life Guide for Class 5 PSEB Responsibility Textbook Questions and Answers

(a) How much do you know :

(Teacher will ask brief questions to link them with the topic)

(i) Is it important to live with family?
Answer:
Yes.

(ii) What do we acquire from family?
Answer:
Values, security, food, clothes, fulfillment of more requirements, love, method of living in a society etc. these are the things which we learn from the family.

(iii) Should we obey our parents?
Answer:
Yes

(iv) Howshouldwedothework given by parents?
Answer:
With responsibility.

(Teacher will elaborate last question in detail and will introduce the main topic.)

(b) How to know and understand The Responsibility?

Answer:

Responsibility is doing a work honestly, diligently and timely.

(c) Area of Responsibility :

Children can become responsible by living with family. They can be responsible for more than one aspect.

(d) Let’s Accept Responsibility

(1) True or False and Why?
1. Cleanliness is good. [ ] Why? ___________
2. One Shouldn’t take bath. [ ] Why? ___________
3. Nails should be cut timely. [ ] Why? ___________
4. Washing hair, once in a month. [ ] Why? ___________
5. Yellow teeth look beautiful. [ ] Why? ___________
Answer:
1. It saves us from diseases, (✓)
2. Not taking bath creates smell from the body. (✗)
3. Nails get dirty and we can become ill when this dirt goes to our stomach while eating food. (✓)
4. Washing hair after a long time can create smell and can produce lice. (✗)
5. Yellow teeth are the sign of some disease. So teeth should be cleaned. (✗)

(2) Children, what do you do for physical cleanliness?

1. I work after taking bath in the morning. [ ]
2. I brush my teeth daily. [ ]
3. I wash hair twice a week. [ ]
4. I keep hair combed. [ ]
5. I cut nails on time. [ ]
6. I wash hands before taking a meal. [ ]
7. I wash hands after taking a meal. [ ]
8. I wear clean clothes. [ ]
9. I change clothes daily. [ ]
10. I keep a handkerchief. [ ]
Answer:
1. 1
2. 1
3. 1
4. 1
5. 0
6. 1
7. 1
8. 1
9. 0
10. 0

(At the end, Students can be motivaled for physical cleanliness on the basis of grading.)

PSEB 5th Class Welcome Life Guide Responsibility Important Questions and Answers

Multiple Choice Questions :

1. Any work done with is responsibility.
(a) Hardwork
(b) Dedication
(c) Loyalty
(d) All of the above.
Answer:
(d) All of the above.

2. Responsibility towards house hold works :
(a) Cleanliness of the body
(b) Getting up early
(c) Looking after the house
(d) All of the above.
Answer:
(d) All of the above.

3. Not being responsible towards household works :
(a) Cleanliness of the body
(b) Getting up early
(c) Looking after the house
(d) To become agree.
Answer:
(d) To become agree.

4. Responsibility towards parents and elderly people :
(a) Cleanliness of the body
(b) Getting up early
(c) Looking after the house
(d) Not opposing any order.
Answer:
(d) Not opposing any order.

5 is a good habit.
(a) Taking bath after a week
(b) Not cutting nails
(c) Washing hair once in a month
(d) Cleaning teeth daily.
Answer:
(d) Cleaning teeth daily.

6. Which good habit do we learn while living in a family?
(a) To get angry
(b) To fight
(c) To respect elders
(d) Getting late.
Answer:
(c) To respect elders.

Fill in the blanks :
1. Doing work with hard work, dedication, loyalty and in proper; time is ……………………………… .
2. ……………………………… of the body is being responsible towards household] works.
3. To become agree is the responsibility towards ……………………………… .
Answer:
1. responsibility
2. body
3. parents.

Tick Right (✓) or Wrong (✗) :

1. Looking after the house is the responsibility towards parents.
2. Not getting angry is the responsibility towards parents.
3. Cleanliness of the body and getting up early are the responsibilities towards household works.
4. There is no benefit to live with love.
Answer:
1. ✗
2. ✓
3. ✓
4. ✗

Mind Mapping :

Answer:

Match the following :

1. Responsibility towards house hold work (a) Responsibility towards parents
2. Responsibility (b) Responsibility towards parents
3. To do hardwork (c) To get up early
4. To agree with parents (d) To being agree.
Answer:
1. (c)
2. (d)
3. (b)
4. (a).

Short Answer Type Questions

Question 1.
What is meant by responsibility?
Answer:
To do the work with hardwork, loyalty, dedication and on time is called responsibility.

Question 2.
Tell responsibility towards your elders.
Answer:
Obey the order, not get angry towards the elders listen carefully and keep it in mind.

Question 3.
Tell responsibility towards your household work.
Answer:
Getting up early, looking after the house, cleanliness of body.

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 10 ਠੋਸ ਅਕਾਰਾਂ ਦਾ ਚਿਤਰਨ InText Questions and Answers.

PSEB 8th Class Maths Solutions Chapter 10 ਠੋਸ ਅਕਾਰਾਂ ਦਾ ਚਿਤਰਨ InText Questions

ਇਹਨਾਂ ਨੂੰ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਹੇਠ ਲਿਖਿਆਂ ਨੂੰ ਮਿਲਾਉ ਤੁਹਾਡੇ ਲਈ, ਪਹਿਲਾਂ ਮੇਲ ਕੀਤਾ ਹੋਇਆ ਹੈ ) :


ਹੱਲ:

ਇਹਨਾਂ ਨੂੰ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਹੇਠਾਂ ਦਿੱਤੇ ਚਿੱਤਰਾਂ ਵਸਤੂਆਂ) ਦਾ ਉਹਨਾਂ ਦੇ ਅਕਾਰਾਂ ਵਿਚ ਮਿਲਾਣ ਕਰੋ :


ਹੱਲ:

ਇਹਨਾਂ ਨੂੰ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਇਕ ਨਗਰ ਦੇ ਨਾਲ ਦਿੱਤੇ ਨਕਸ਼ੇ ਨੂੰ ਦੇਖੋ ।

(a) ਇਸ ਨਕਸ਼ੇ ਵਿਚ ਇਸ ਤਰ੍ਹਾਂ ਰੰਗ ਭਰੋ : ਨੀਲਾ ਪਾਣੀ, ਲਾਲ-ਫਾਇਰ ਸਟੇਸ਼ਨ, ਸੰਤਰੀ-ਲਾਇਬਰੇਰੀ, ਪੀਲਾ-ਸਕੂਲ, ਹਰਾ-ਪਾਰਕ, ਗੁਲਾਬੀ-ਪੰਚਾਇਤ ਘਰ, ਬੈਗਨੀ-ਹਸਪਤਾਲ, ਭੂਰਾ-ਕਬਰਸਤਾਨ
(b) ਦੂਸਰੀ ਸੜਕ ਅਤੇ ਦਾਨਿਮ ਸੜਕ ਦੇ ਕੱਟਣ ਵਾਲੀ ਥਾਂ (intersection) ਤੇ ਇਕ ਹਰਾ ‘X’ ਅੰਕਿਤ ਕਰੋ । ਜਿੱਥੇ ਨਦੀ, ਤੀਜੀ ਸੜਕ ਨੂੰ ਮਿਲਦੀ ਹੈ, ਉੱਥੇ ਇਕ ਕਾਲਾ ‘Y’ ਅੰਕਿਤ ਕਰੋ ਅਤੇ ਮੁੱਖ ਸੜਕ ਅਤੇ ਪਹਿਲੀ ਸੜਕ ਦੇ ਕੱਟਣ ਵਾਲੀ ਥਾਂ ਤੇ ਇਕ ਲਾਲ ‘Z) ਅੰਕਿਤ ਕਰੋ ।
(c) ਕਾਲਜ ਤੋਂ ਝੀਲ ਤੱਕ ਦੇ ਲਈ ਇਕ ਛੋਟਾ ਸੜਕ ਦਾ ਮਾਰਗ ਗੂੜੇ ਗੁਲਾਬੀ ਰੰਗ ਵਿਚ ਖਿੱਚੋ ।
ਹੱਲ:
ਆਪ ਕੋਸ਼ਿਸ਼ ਕਰੋ ।

ਪ੍ਰਸ਼ਨ 2.
ਆਪਣੇ ਘਰ ਤੋਂ ਆਪਣੇ ਸਕੂਲ ਤੱਕ ਦੇ ਮਾਰਗ ਦਾ ਉਸ ਤੇ ਆਉਣ ਵਾਲੇ ਮਹੱਤਵਪੂਰਨ ਸੀਮਾ ਚਿੰਨ੍ਹਾਂ ਨੂੰ ਦਰਸਾਉਂਦੇ ਹੋਏ ਇਕ ਨਕਸ਼ਾ ਖਿੱਚੋ ।
ਹੱਲ:
ਆਪ ਕੋਸ਼ਿਸ਼ ਕਰੋ ।

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 10 ਠੋਸ ਅਕਾਰਾਂ ਦਾ ਚਿਤਰਨ Ex 10.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 10 ਠੋਸ ਅਕਾਰਾਂ ਦਾ ਚਿਤਰਨ Exercise 10.3

ਪ੍ਰਸ਼ਨ 1.
ਕੀ ਕਿਸੇ ਬਹੁਫਲਕ ਦੇ ਫਲਕ ਹੇਠਾਂ ਦਿੱਤੇ ਗਏ ਅਨੁਸਾਰ ਹੋ ਸਕਦੇ ਹਨ ?
(i) 3 ਤ੍ਰਿਭੁਜ
(ii) 4 ਤ੍ਰਿਭੁਜ
(iii) ਇਕ ਵਰਗ ਅਤੇ ਚਾਰ ਤ੍ਰਿਭੁਜ ।
ਹੱਲ:
(i) ਨਹੀਂ
(ii) ਹਾਂ, ਪਿਰਾਮਿਡ
(iii) ਹਾਂ, ਵਰਗਾਕਾਰ ਪਿਰਾਮਿਡ ॥

ਪ੍ਰਸ਼ਨ 2.
ਕੀ ਇਸ ਤਰ੍ਹਾਂ ਦਾ ਬਹੁਫਲਕ ਸੰਭਵ ਹੈ ਜਿਸਦੇ ਫੁਲਕਾਂ ਦੀ ਗਿਣਤੀ ਕੋਈ ਵੀ ਸੰਖਿਆ ਹੋਵੇ ?
ਹੱਲ:
ਹਾਂ, ਪਿਰਾਮਿਡ । ਇਹ ਤਦ ਹੀ ਸੰਭਵ ਹੈ ਜਦੋਂ ਫੁਲਕਾਂ ਦੀ ਸੰਖਿਆ 4 ਜਾਂ ਉਸ ਤੋਂ ਜ਼ਿਆਦਾ ਹੋਵੇ ।

ਪ੍ਰਸ਼ਨ 3.
ਹੇਠ ਲਿਖਿਆਂ ਵਿਚੋਂ ਕਿਹੜੇ-ਕਿਹੜੇ ਪ੍ਰਿਜ਼ਮ ਹਨ ?

ਹੱਲ:
(ii) ਬਿਨਾਂ ਛਿੱਲੀ ਹੋਈ ਪੈਨਸਿਲ
(iii) ਕਾਗ਼ਜ਼ਾਂ ਉੱਤੇ ਰੱਖਣ ਵਾਲਾ ਭਾਰ ।

ਪ੍ਰਸ਼ਨ 4.
(i) ਪਿਜ਼ਮ ਅਤੇ ਵੇਲਣ ਕਿਸ ਤਰ੍ਹਾਂ ਇੱਕੋ ਜਿਹੇ ਹਨ ?
(ii) ਪਿਰਾਮਿਡ ਅਤੇ ਸ਼ੰਕੁ ਕਿਸ ਤਰ੍ਹਾਂ ਇੱਕੋ ਜਿਹੇ ਹਨ ?
ਹੱਲ:
(i) ਪ੍ਰਿਜ਼ਮ ਅਤੇ ਵੇਲਨ ਦੋਨਾਂ ਦਾ ਸਰਵ ਧਰਵਾਧਕ ਅਕਸ਼ ਹੋ ਸਕਦਾ ਹੈ ।
(ii) ਪਿਰਾਮਿਡ ਅਤੇ ਸ਼ੰਕੁ ਦੋਨਾਂ ਦੇ ਸਮਤਲ ਆਧਾਰ ਤੇ ਕੇਵਲ ਇਕ ਸ਼ਿਖਰ ਹੁੰਦਾ ਹੈ ।

ਪ੍ਰਸ਼ਨ 5.
ਕੀ ਇਕ ਵਰਗ, ਪ੍ਰਿਜ਼ਮ ਅਤੇ ਇਕ ਘਣ ਇਕ ਹੀ ਹੁੰਦੇ ਹਨ ? ਸਪੱਸ਼ਟ ਕਰੋ ।
ਹੱਲ:
ਹਾਂ, ਇਕ ਵਰਗ, ਪ੍ਰਿਜ਼ਮ ਅਤੇ ਇਕ ਘਣ ਇਕ ਹੀ ਹੁੰਦੇ ਹਨ, ਜਿਵੇਂ ਕਿ ਆਇਤਾਕਾਰ ਪ੍ਰਿਜ਼ਮ ਇਕ ਘਣਾਵ ਜਿਹਾ ਹੁੰਦਾ ਹੈ ।

ਪ੍ਰਸ਼ਨ 6.
ਇਹਨਾਂ ਠੋਸਾਂ ਦੇ ਲਈ ਇਊਲਰ ਸੂਤਰ ਦੀ ਪੜਤਾਲ ਕਰੋ :

ਹੱਲ:
(i) ਫੁਲਕਾਂ ਦੀ ਸੰਖਿਆ F = 5
ਸ਼ਿਖਰਾਂ ਦੀ ਸੰਖਿਆ V = 9
ਕਿਨਾਰਿਆਂ ਦੀ ਸੰਖਿਆ E = 12
∴ ਇਊਲਰ ਸੂਤਰ ਅਨੁਸਾਰ :
F + V – E = 2
5 + 9 – 12 = 2 .
2 = 2

(ii) ਫੁਲਕਾਂ ਦੀ ਸੰਖਿਆ F = 10
ਸ਼ਿਖਰਾਂ ਦੀ ਸੰਖਿਆ V = 9
ਕਿਨਾਰਿਆਂ ਦੀ ਸੰਖਿਆ E = 17
∴ ਇਊਲਰ ਸੂਤਰ ਅਨੁਸਾਰ :
F + V – E
10 + 9 – 17 = 2
2 = 2

ਪ੍ਰਸ਼ਨ 7.
ਇਊਲਰ ਸੂਤਰ ਦਾ ਪ੍ਰਯੋਗ ਕਰਦੇ ਹੋਏ, ਅਗਿਆਤ ਸੰਖਿਆ ਨੂੰ ਪਤਾ ਕਰੋ :

ਹੱਲ:
ਇਊਲਰ ਦੇ ਸੂਤਰ ਅਨੁਸਾਰ
F + V = E + 2
ਇਸ ਲਈ, ਸਾਨੂੰ ਪ੍ਰਾਪਤ ਹੈ :

ਪ੍ਰਸ਼ਨ 8.
ਕੀ ਕਿਸੇ ਬਹੁਲਕ ਦੇ 10 ਫਲਕ, 20 ਕਿਨਾਰੇ ਅਤੇ 15 ਸ਼ਿਖਰ ਹੋ ਸਕਦੇ ਹਨ ?
ਹੱਲ:
ਨਹੀਂ, ਕਿਉਂਕਿ ਇਹ ਇਊਲਰ ਦੇ ਸੂਤਰ ਨੂੰ ਸੰਤੁਸ਼ਟ ਨਹੀਂ ਕਰਦਾ ਹੈ ।
ਅਰਥਾਤ F + V – E = 2
⇒ 10 + 15 – 20
⇒ 25 – 20 = 5 ≠ 2.

Punjab State Board PSEB 5th Class Welcome Life Book Solutions Chapter 2 Communal Harmony (Sharing Brotherhood) Textbook Exercise Questions and Answers.

PSEB Solutions for Class 5 Welcome Life Chapter 2 Communal Harmony (Sharing Brotherhood)

Welcome Life Guide for Class 5 PSEB Communal Harmony (Sharing Brotherhood) Textbook Questions and Answers

Let us do a group activity :
Instructions are given by teacher: students prepare a chart together in which you write slogans, giving good directions to society. We will paste it on our school wall. I will give some other work to rest of the students.

(For this work, Students advise each other how to do this work)

Gurleen : I have a beautiful pink chart, I will give itto you.
Shivam : I have colours. We will use colours on this chart. I will help you with colouring.

Karanvier Singh : I can paint and write beautifully.
Balkar Singh : Take this pencil, ruler, sharpener and eraser.

Gagandeep : But we don’t have the slogans that we have to write on this chart.
Sharanjit Kaur : I and Jaspreet have a lot of slogans. Our headmaster sir speaks them in the

morning assembly, we have written those in our notebooks.
Jaspreet Singh : Yes! Yes! I also have them. My elder brother made me writethem.

Harsimran and Navjot : Let’s make it! We will give you cello tape and gum.

(All students sit on the floor to prepare the chart. They start with the work by placing the chart in the middle. Karanbir draws line on the chart and prepares to write. Other kids are very excited. Sharanjit Kaur is standing with the notebook of hergreat ideas)

Sharanjit Kaur :
Write
Education is a priceless jewel
One who reads will wear it.
(Karanbir starts writing)

Sharanjit Kaur : (stops for a while) This Idea is very good, our sir Speaks it.
Save girl child, water and trees.
To make a natural equilibrium

Gagandeep Singh : Sister Sharan, please write it neatly on the rough notebook and give. Karan can’t write it quickly.

Karanbir Singh : Yes! Write and give it to me (Sharanjeet Kaur writes it on her notebook)
Our Gurus have taught us
Earn by working with your hands.

We don’t fight over caste creed colour or religion We are like brothers No one is our enemy
Jaspreet Singh : Sister, write this idea.
There is no such problem that does not have a sol ution

(Sharanjit Kaur writes and all the children make the chart together)

For teacher:- The above activity will be explained. And meaning of communal harmony will be told. We can do greater things with collective harmony.

List of things to be done in the class :

(1) Decorate the room.
(2) Cover the notebook.
(3) Celebrate the child’s birthday.
(4) Celebrate some special day.

Give your ideas:

Question 1.
What is said about education in the first slogan?
Answer:
Education is a valuable ornament. Those students who will work hard in studies, will be able to achieve the ornament of education.

Question 2.
Which things are said to be saved in the second slogan and why ?
Answer:
In motto two, it is told to save the daughters, water and trees. Because daughters are being killed before taking birth, water is being polluted and trees and forests are being destroyed. Therefore, it is necessary to save all these.

Question 3.
Why should we work hard with our own hands?
Answer:
Earning money honestly means that we should do hard work to earn money. We should not grab money or other things from others.

Question 4.
How should we live together?
Answer:
We should live with each other with love and brotherhood.

Question 5.
What does the fifth slogan mean?
Answer:
We become depressed while dealing with some problem. Here it is adviced that every problem has a solution. We should not become depressed.

(b) On school level

To prepare a handwritten magazine

Note : Headmaster sir has told us to prepare a handwritten magazine which has poems, stories and paintings written by us.

(Students, sitting in the free period are thinking how to prepare a handwritten magazine)

Gurvinder, Gurleen and deepjot : Our handwriting is very beautiful we have learnt it from Jasmeet Singh sir. We will write the compositions beautifully.

Farida and Simran : We will read poems and stories and make pictures of them, which will make our magazine very beautiful.
Gursewak : I will makethetitle page very beautiful.

Tanya and Arun : We have composed a few poems ourselves on mother , military uncle, ice cream, butterfly. We will give those.
Sahil : I have written stories about home and school. Vishnu and Harpreet also have written stories. We will also put those in the magazine.

Khushi : My grandmother asks me puzzles. I have written those on my notebook. I will write them down.
Anil : I have written thoughts of the day on my notebook. Our teacher used to make us write. You can have them.

Preeti : I have a big register and colours. Take them. I have pencil, ruler, gum, everything. Let us start the work.

(Students prepare the handwritten magazine together. Everyone works very hard. A few days later, they go to their teacher.)

Students : Mam, we have prepared the magazine.
Teacher : (looking at the magazine) very good children ! You all have done a great job. You have done so much work in such a short time. Wow!

(Stops for a while) Now we will paste the pictures of our national flag, Martyrs, holy Gurus, prophets, sportsmen, writers in it. We will also paste all your and pictures of our promising students in it.

students : Yes madam. We will definitely do that.
Teacher : Finish it completely. Next week, we will get this magazine released from our headmaster sir.

students : Yes madam.
Teacher : But students I What have you kept the name of this magazine?

Tanya : We have kept it “spread unity”
Teacher : This name is not suitable. We should name it Little stars You all are stars, we love you.

Questions/Answers:

Question 1.
What is the name of your school’s handwritten magazine?
Answer:
Nikke-Nikke Tare.

Question 2.
Has any of your writings published in school magazine? If yes, then name it and recite it?
Answer:
Yes, it is published. It is a poem, whose name is ‘mosquito’.
Mosquito It is small, does noise in our ear, keeps us in trouble.
Papa is asked this question how this can be found.
He told that it finds us by the heat of our body.
It is very dangerous one sting of it can make us ill.
We can catch Malaria, Dengu and Chickengunia.
To save from it-Not collecting water at any place-Sonu, finish it.

Question 3.
If any student knows a puzzle, then ask it? The rest of the students will solve it.
Answer:
Peacock.

Question 4.
Name the teacher, who taught good handwriting to students?
Answer:
Jasmeet Singh Sir.

Question 5.
Name some children’s magazines.

Answer:
Primary Education, Pankharian, Aale-Bhole.

(c) On village level

(i) To carry out a rally:

(The teacher will tell that students of 10th to 12th class are carrying out a rally with their teachers and wise villagers for the development of the village. They wil I carry cardboards, attached to wooden sticks with slogans written on them. Every student will have a cardboard and they will go shouting slogans The slogans about human values education, water conservation, pure air, saving trees , quitting drugs, sports, cleanliness, etc. Will be mentioned on cardboards.)

Specifically : cardboards will be made of chart prepared by students in activity -1, in which they had written the slogans.

New slogans :

1. Save girl-Educate girl
2. Government school gives admission free Teach every child without fee.
3. Every child has taken a swear. They will keep their village clear
4. Let’s have a medical camp for our good health
5. Quit drugs today. Live tomorrow.

(ii) prize distribution ceremony of village

(There is a function in the village. Many people have come. Sarpanch of the village S.Prem Singh, headmaster, teachers and other well-known people of the village are standing on the stage in a position to distribute prizes.)

Teacher : Today we will honour those students and young men, Who have contributed a lot in order to illuminate the name of their village. Balraj and his ten friends planted more than hundred trees and took care of them, watered them. Now those trees have grown. They also contributed to the cleanliness of the village.

11 students carried out rally in the village and inspired the entire village with good values and noble works. One team set up a medical camp where suffering patients of the village were checked and treated.

15 students, who gave free education to illiterate people, elderly and weak students of the village will also be honoured.

Teacher : Now, I would request the sarpanch of the village to come up on the stage and share his ideas with us.

Sarpanch : Respected elders of the village, brothers and sisters, respected teachers and dear students. I am very glad that these young men and students of our village have made it very beautiful, neat and clean, healthy and happy. It is because of these young men that our village has Stood on the first position. Give them a big round of applause I Thanks a lot to all of you.

(Loud applause echoes)

Teacher : Thank you sir. On this happy occasion, now I present before you, a fifth class student sharanjeet Kaur, who is going to sing a beautiful song, dedicated to communal unity in her melodious voice.

Sharanjit sings her song :

What lies in fighting with each other
We will work for our unity
We will leave all bad rituals
And keep on moving ahead

We have to save our earth
air and water
We need to save the girl child
We don’t listen to dirty songs
we will sing our song of unity
We will together, drive away
the damn caste and creed.

Let us pray together
May our Punjab be happy
Happiness be in everything
May it smells like a rose
And be far away from drugs.
And we only eat our rightful bread.

(Applause)

Questionnaire (i)

Scenes of Communal Unit

Questionnaire (ii)

The teacher will discuss that communal unity is shown in which pictures.

PSEB 5th Class Welcome Life Guide Communal Harmony (Sharing Brotherhood) Important Questions and Answers

Multiple Choice Questions :

Question 1.
Brotherhood is :
(a) Believe in each other
(b) Love
(c) Surrender
(d) All of the above.
Answer:
(d) All of the above.

Question 2.
Which motto has been told by Saranjeet?
(a) Education is a valuable ornament one who will get education will be able to wear it.
(b) Save daughters, Water and Trees balance the nature.
(c) Gurus have given advice earn money by hard work and honesty.
(d) There is not any problem which has no solution.
Answer:
(b) Save daughters, Water and Trees balance the nature.

Question 3.
Who could do painting?
(a) Gurleen
(b) Shivam
(c) Karanbeer Singh
(d) Gagandeep.
Answer:
(c) Karanbeer Singh.

Question 4.
Gurvinder and Gurleen learnt the art of good hand-writing from whom?
(a) From Jasmeet Singh Sir
(b) From Lamber Singh Sir
(c) From Saranjeet Sir
(d) From Karamjeet Sir.
Answer:
(b) From Lamber Singh Sir.

Question 5.
What was the name of the school magazine?
(a) Pankharian
(b) Nikke-Nikke Tare
(c) Aale Bhole
(d) None of the above.
Answer:
(b) Nikke-Nikke Tare.

Fill in the blanks :

1. Many children from a …………………. .
2. The name of the school magazine was …………………..
3. ………………….. was told to make the front page of magazine.
Answer:
1. Class
2. Nikke-Nikke Tare
3. Gurusevak.

Tick Bight (✓) or Wrong (✗) :

1. Gurwinder has a good hand writing.
2. Sharanjeet Kaur sung a song.
3. Khushi has written the riddles of her grandmother in her notebook.
4. Vishnu and Harpreet had composed poems.
Answer:
1. ✓
2. ✓
3. ✓
4. ✗

Mind Mapping :

Answer:

Match the following :

1. Karanbeer Singh (a) Sung Song
2. Gurleen (b) Can do painting
3. Magazine of school (c) Good Handwriting
4. Sharanjeet Kaur (d) Nikke-Nikke Tare.
Answer:
1. (b)
2. (c)
3. (d)
4. (a).

Short Answer Type Questions

Question 1.
How is brotherhood created?
Answer:
We have a lot of needs in our life. That is why we establish relations with others. Our needs create brother hood.

Question 2.
Which mottoes were given in the rally took out at the village level?
Answer:
Human values, pure air, sports, cleanliness, Education, Saving water etc.

Question 3.
Whom name was given by Tanya of the school magazine?
Answer:
She told its name ‘Sanj Vadaiay’.

Question 4.
About whom were the poems of Tanya and Arun?
Answer:
About mother, soldier uncle, kulfi, butterfly etc.

Question 5.
Give one motto about leaving the drugs.
Answer:
Awake people, leave drugs.

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 10 ਠੋਸ ਅਕਾਰਾਂ ਦਾ ਚਿਤਰਨ Ex 10.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 10 ਠੋਸ ਅਕਾਰਾਂ ਦਾ ਚਿਤਰਨ Exercise 10.2

ਪ੍ਰਸ਼ਨ 1.
ਇਕ ਨਗਰ ਦੇ ਲਈ ਦਿੱਤੇ ਹੋਏ ਨਕਸ਼ੇ ਨੂੰ ਦੇਖੋ | ਹੇਠਾਂ ਲਿਖੇ ਪ੍ਰਸ਼ਨਾਂ ਦੇ ਉੱਤਰ ਦਿਉ :

(a) ਇਸ ਨਕਸ਼ੇ ਵਿਚ ਇਸ ਤਰ੍ਹਾਂ ਰੰਗ ਭਰੋ :
ਨੀਲਾ-ਪਾਣੀ, ਲਾਲ-ਫਾਇਰ ਸਟੇਸ਼ਨ, ਸੰਤਰੀ| ਲਾਇਬਰੇਰੀ, ਪੀਲਾ-ਸਕੂਲ, ਹਰਾ-ਪਾਰਕ, ਗੁਲਾਬੀ-ਕਾਲਜ, ਬੈਂਗਨੀ-ਹਸਪਤਾਲ, ਭੂਰਾ-ਕਬਰਸਤਾਨ ।
(b) ਸੜਕ C ਅਤੇ ਨਹਿਰੁ ਰੋਡ ਦੇ ਕੱਟਣ ਵਾਲੀ ਥਾਂ ਤੇ ਇਕ ਹਰਾ ‘X’ ਅਤੇ ਗਾਂਧੀ ਰੋਡ ਅਤੇ ਸੜਕ A ਤੇ ਕੱਟਣ ਵਾਲੀ ਥਾਂ ਤੇ ਇਕ ਹਰਾ ‘Y ਖਿੱਚੋ ।
(c) ਲਾਇਬਰੇਰੀ ਤੋਂ ਬੱਸ ਅੱਡੇ ਤੱਕ ਇਕ ਛੋਟਾ ਸੜਕ ਮਾਰਗ ਲਾਲ ਰੰਗ ਨਾਲ ਖਿੱਚੋ ।
(d) ਕਿਹੜਾ ਜ਼ਿਆਦਾ ਪੂਰਬ ਦਿਸ਼ਾ ਵਿਚ ਹੈ : ਸਿਟੀ ਪਾਰਕ ਜਾਂ ਬਜ਼ਾਰ ?
(e) ਕਿਹੜਾ ਜ਼ਿਆਦਾ ਦੱਖਣ ਵਿਚ ਹੈ : ਪ੍ਰਾਇਮਰੀ ਸਕੂਲ ਜਾਂ ਸੀਨੀਅਰ ਸੈਕੰਡਰੀ ਸਕੂਲ ॥
ਹੱਲ:
ਆਪ ਕੋਸ਼ਿਸ਼ ਕਰੋ ।

ਪ੍ਰਸ਼ਨ 2.
ਢੁੱਕਵੇਂ ਪੈਮਾਨੇ ਅਤੇ ਵੱਖ-ਵੱਖ ਵਸਤੁਆਂ ਦੇ ਲਈ ਸੰਕੇਤਾਂ ਦਾ ਪ੍ਰਯੋਗ ਕਰਦੇ ਹੋਏ, ਆਪਣੀ ਜਮਾਤ ਦੇ ਕਮਰੇ ਦਾ ਇਕ ਨਕਸ਼ਾ ਖਿੱਚੋ ।
ਹੱਲ:
ਆਪ ਕੋਸ਼ਿਸ਼ ਕਰੋ ।

ਪ੍ਰਸ਼ਨ 3.
ਢੁੱਕਵੇਂ ਪੈਮਾਨੇ ਅਤੇ ਵੱਖ-ਵੱਖ ਵਿਸ਼ੇਸ਼ਤਾਵਾਂ ਵਸਤੂਆਂ) ਜਿਸ ਤਰ੍ਹਾਂ ਕਿ-ਖੇਡ ਦਾ ਮੈਦਾਨ, ਮੁੱਖ ਭਵਨ, ਬਗੀਚਾ ਆਦਿ ਦੇ ਲਈ ਸੰਕੇਤਾਂ ਦਾ ਪ੍ਰਯੋਗ ਕਰਦੇ ਹੋਏ, ਆਪਣੇ ਸਕੂਲ ਦੇ ਵਿਹੜੇ (Compound) ਦਾ ਇਕ ਨਕਸ਼ਾ ਖਿੱਚੋ ।
ਹੱਲ:
ਆਪ ਕੋਸ਼ਿਸ਼ ਕਰੋ ।

ਪ੍ਰਸ਼ਨ 4.
ਆਪਣੇ ਮਿੱਤਰ ਦੇ ਮਾਰਗ ਦਰਸ਼ਨ ਦੇ ਲਈ ਇਕ ਨਕਸ਼ਾ ਖਿੱਚੋ ਜਿਸ ਨਾਲ ਉਹ ਤੁਹਾਡੇ ਘਰ ਬਿਨ੍ਹਾਂ ਕਿਸੇ ਮੁਸ਼ਕਿਲ ਨਾਲ ਪਹੁੰਚ ਜਾਵੇ ।
ਹੱਲ:
ਆਪ ਕੋਸ਼ਿਸ਼ ਕਰੋ ।

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 10 ਠੋਸ ਅਕਾਰਾਂ ਦਾ ਚਿਤਰਨ Ex 10.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 10 ਠੋਸ ਅਕਾਰਾਂ ਦਾ ਚਿਤਰਨ Exercise 10.1

ਪ੍ਰਸ਼ਨ 1.
ਦਿੱਤੇ ਹੋਏ ਹਰੇਕ ਠੋਸ ਦੇ ਲਈ, ਦੋ ਦ੍ਰਿਸ਼ ਦਿੱਤੇ ਗਏ ਹਨ । ਹਰੇਕ ਠੋਸ ਦੇ ਲਈ ਸੰਗਤ, ਉੱਪਰ ਤੋਂ ਦ੍ਰਿਸ਼ ਅਤੇ ਸਾਹਮਣੇ ਤੋਂ ਦਿਸ਼ ਦਾ ਮਿਲਾਣ ਕਰੋ । ਇਸ ਵਿਚੋਂ ਇਕ ਤੁਹਾਡੇ ਲਈ ਕੀਤਾ ਗਿਆ ਹੈ ।


ਹੱਲ:
(a) → (iii) → (iv)
(b) → (i) → (v)
(c) → (iv) → (ii)
(d) → (v) → (iii)
(e) → (ii) → (i)

ਪ੍ਰਸ਼ਨ 2.
ਦਿੱਤੇ ਗਏ ਹਰੇਕ ਠੋਸ ਦੇ ਲਈ, ਤਿੰਨ ਦ੍ਰਿਸ਼ ਦਿੱਤੇ ਗਏ ਹਨ । ਹਰੇਕ ਠੋਸ ਦੇ ਲਈ ਸੰਗਤ, ਉੱਪਰ ਤੋਂ ਦ੍ਰਿਸ਼, ਸਾਹਮਣੇ ਤੋਂ ਦ੍ਰਿਸ਼ ਅਤੇ ਇੱਕ ਪਾਸੇ ਦੇ ਦ੍ਰਿਸ਼ ਦੀ ਪਹਿਚਾਣ ਕਰੋ ।


ਹੱਲ:
(a) (i) → ਸਾਹਮਣੇ
(ii) → ਇਕ ਪਾਸੇ ਦਾ ਦ੍ਰਿਸ਼
(iii) → ਉੱਪਰ

(b) (i) → ਇਕ ਪਾਸੇ ਦਾ ਦ੍ਰਿਸ਼
(ii) → ਸਾਹਮਣੇ
(iii) → ਉੱਪਰ

(c) (i) → ਸਾਹਮਣੇ
(ii) → ਇਕ ਪਾਸੇ ਦਾ ਦ੍ਰਿਸ਼
(iii) → ਉੱਪਰ

(d) (i) → ਸਾਹਮਣੇ
(ii) → ਇਕ ਪਾਸੇ ਦਾ ਦ੍ਰਿਸ਼
(iii) → ਉੱਪਰ

ਪ੍ਰਸ਼ਨ 3.
ਦਿੱਤੇ ਹੋਏ ਹਰੇਕ ਠੋਸ ਦੇ ਲਈ, ਉੱਪਰ ਤੋਂ ਦਿਸ਼, ਸਾਹਮਣੇ ਤੋਂ ਦ੍ਰਿਸ਼ ਅਤੇ ਇਕ ਪਾਸੇ ਦੇ ਦ੍ਰਿਸ਼ ਦੀ ਪਹਿਚਾਣ ਕਰੋ :


ਹੱਲ:
(a) (i) → ਉੱਪਰ
(ii) → ਸਾਹਮਣੇ
(iii) → ਇਕ ਪਾਸੇ

(b) (i) → ਇਕ ਪਾਸੇ
(ii) → ਸਾਹਮਣੇ
(iii) → ਉੱਪਰ

(c) (i) → ਉੱਪਰ
(ii) → ਸਾਹਮਣੇ
(iii) → ਇਕ ਪਾਸੇ

(d) (i) → ਇਕ ਪਾਸੇ
(ii) → ਸਾਹਮਣੇ
(iii) → ਉੱਪਰ

(e) (i) → ਸਾਹਮਣੇ
(ii) → ਉੱਪਰ
(iii) → ਇਕ ਪਾਸੇ

ਪ੍ਰਸ਼ਨ. 4.
ਦਿੱਤੀਆਂ ਹੋਈਆਂ ਵਸਤੂਆਂ ਦੇ, ਸਾਹਮਣੇ ਤੋਂ ਦ੍ਰਿਸ਼, ਇਕ ਪਾਸੇ ਦੇ ਦ੍ਰਿਸ਼ ਅਤੇ ਉੱਪਰ ਦੇ ਦ੍ਰਿਸ਼ ਖਿੱਚੋ :

ਹੱਲ:

Punjab State Board PSEB 5th Class Welcome Life Book Solutions Chapter 1 Health and Cleanliness Textbook Exercise Questions and Answers.

PSEB Solutions for Class 5 Welcome Life Chapter 1 Health and Cleanliness

Welcome Life Guide for Class 5 PSEB Health and Cleanliness Textbook Questions and Answers

(A) Germs and Diseases

Activity – 1
Make all the students of the class stand in a circle Put talcum powder on the hand of one student. Tell that student to shake his hand with the next child.In this way let this process go on till all the students have done the handshake. Now tell them to hold their book, pen pencil, etc. with that hand. Explain to the students that as the talcum powder reached all the students by a handshake and then to the things they touched. Similarly, the germs spread from one person to the other through hands.

Fill in the blanks:
1. Germs often spread through …………………………………. (eyes/hands)
2. Use …………………………………. while coughing and sneezing, (hands/handkerchief)
3. Wash your hands properly with …………………………………. after toilet, (soap/soil)
4. Germs spread from animals to food by …………………………………. (touching/eating)
Answer:
1. hands
2. handkerchief
3. soap
4. touching.

Sukhdeep has kept a dog at home. He plays with the dog every day. Suddenly he fell ill and went to the doctor. The doctor told him the cause of his sickness. Choose the correct cause of his sickness:

Keeping a dog at home [ ]
Playing with the dog [ ]
Not washing hands after playing with the dog [ ]
None of the above [ ]
Answer:
Not washing hands after playing with the dog.

Let’s test understanding:

1. How do germs spread?
(a) by touching
(b) by coughing and sneezing
(c) by air
(d) by all of these
Answer:
(d) All of the above.

2. What is the prime cure to save ourselves from germs?
(a) not going outside
(b) to cover the nose
(c) not to go close to anyone
(d) cleanliness
Answer:
(d) Cleanliness.

3. Which of these diseases is not caused by germs?
(a) diarrhea
(b) cold
(c) night blindness
(d) T.B.
Answer:
(c) Blindness.

4. Where do the germs live?
(a) in the air
(b) in the water
(c) in the soil
(d) everywhere
Answer:
(d) Everywhere.

(b) Air, Water, Food and Health

Once air and water were sharing their joys and sorrows with each other. Brother water, “What happened? Why are you looking sad ?” Water kept silent as if he could not find words to share his grief.” “What can he do, poor fellow. His grief is big”, said the food lying in the plate nearby. “Man has made it dirty and poisonous with garbage and chemicals”. Really, sister air, “I have lost my quality. I used to be clean and holy, cold and tasty also. Recall how vast my body was!

It has contracted due to unnecessary flow.” “True”, said the air, “My condition is the same as yours. My purity has also been lost due to the smoke of vehicles and factories. I am worried about man’s future. For how long will I be able to fill freshness in his lungs. The element that supports the human’s breath has become much lesser in me the before.” “It’s true, sister air,” said the food. Even my condition is not too good. My taste and nutrients are also decreasing due to toxicity and insecticides in water. I am worried that man is falling prey to terrible diseases after consuming me. I don’t know why man is not getting it?

He is himself falling prey due to his negligence and greedy thinking towards us. He has forgotten that Heath is Treasure.”

Activity – 1

Role play of the story

Answer:
Do it yourself

Activity – 2

Air, water and food are much worriec about their deteriorated condition. Can you suggest any solution?

Answer:
Air : Due to the smoke of vehicles and factories, the purity of air is being destroyed.
Water : Man has poisoned water with garbage and chemicals. Wastage of water leads to a shortage of drinkable water.
Food : The nutrients of food are also | being destroyed due to poisonous water and pesticides.

Activity – 3

Let’s prepare – Banners and slogans for organising an awareness rally regading air and water pollution.
Answer:
Do it yourself.

Explain On the basis of the story explain which content has increased and which has decreased in food due to it’s deteriorated condition.

Answer:

Increased	Decreased
1. Poisonous food is increased. 2. Pesticides are increased.	1. Nutrients are decreased. 2. Taste is decreased.

To reduce air pollution which option is correct?

Answer:
We should walk on foot for near distance, go on cycle for less distance and on motorcycle/scooter for more distance. We should make more use of public transport like a bus. We should do carpooling also. We should make less use of petrol and diesel.

Let’s Evaluate:

1. Pollution which thing causes the worst effect on the human body?
(a) air
(b) water
(c) food
(d) all of these
Answer:
(d) All of the above.

2. What is damaged by the polluted (poisonous) air?
(a) nutrients of food
(b) lungs
(c) factories
(d) water
Answer:
(b) Lungs

(c) Cleanliness

For the teacher: On the basis of this mind map, different areas of cleanliness are to be discussed with the students for a better understanding of the relation between good health and cleanliness and to inspire them to keep the cleanliness.

Activity – 1
Fill in the blanks :

Answer:

Activity – 2

Germ Race

a) To make the children understand that when we step out of our clean surroundings, we come in the grip of germs and germs spread very fast. The teacher should prepare a flash card with the cooperation of students with the word germs written on it. The teacher will take all the students to the playground.

A circle will be made with the word clean written in it. Out of the whole class, 2 students will be separated and flashcards with the word germs written will be put around their necks. Those two students will become germs and the rest of the class will become hands. Students, who have become hands will be made to stand in the clean circle. When the game starts, the students who have become hands will come out of the circle and start running and then the teacher will ask the students, who have become germs to hold hands and run to catch the students who have become hands. The students, who would be caught by the germ students will start running with them while holding their hands. In this way, the number of germs will increase and the number of hands will decrease. In the end, all the hands will be caught by the germs.

Break the germs circle

Activity : Make a list of the areas in your school and home which need to be cleaned and also suggest the ways to clean

Place	Suggestion

Answer:

Place	Suggestion
1. Toilet	To clean after throwing more water and using phenyl.
2. Yard	To sweep
3. Library	To clean benches, chairs, books etc. with duster.

Explain
What all comes under personal hygiene?
Answer:
Cleanliness of body, cleanliness of face and cleanliness of clothes are included in personal cleanliness.

Activity: I am Cleanliness. I want to live everywhere but I will stay there only where you want to keep me. Where do you want to keep me? And tell about those places where I am and where I am not?

Answer:
I would like to keep cleanliness at all places. For example: at home, at school, in streets, at parks, at bus stand etc. Mostly there is less cleanliness at parks, bus stand, railway station, toilets, streets etc.

True or False

1. It Is the responsibility of the government to keep cleanliness.
2. It is easy to keep cleanliness than to do it.
3. We remain healthy while keeping cleanliness.

Answer:

1. (✗)
2. (✓)
3. (✓)

Let’s test understanding :

1. From where should cleanliness begin?
(a) from our home
(b) from our neighborhood
(c) from our surroundings
(d) from yourself
Answer:
(c) From ourselves.

2. Whyshouldwedocleaning?
(a) for beauty and cleanliness
(b) to remain healthy
(c) to get rid of dirt.
(d) all of the above
Answer:
(d) all of the above

(d) Preeti is very sensible (Poem)

Preeti is very sensible as
she knows how important it is
to brush and bathe every day.
If there is tooth decay,
it will be difficult to chew the
corn and sugarcane.

Preeti is very sensible as
she knows, how important it is
to wear clean clothes after bathing.
If we fall sick with sweat, smell and germs
then we wi 11 have to eat bitter med icine
and get the injections.

Preeti is very sensible as
she knows how important it is
to make the house clean and beautiful.
If the garbage is not put in the bin,
flies will spread cholera and mosquito
will spread malaria.

Preeti is very sensible as
she knows how important it is
to sweep the street.
If the surroundings are not kept clean
then the whole garbage will re-enter
the house with feet.

Preeti is very sensible as
she knows how important it is
to adopt good habits of eating
If we kept on eating uncovered food
with dirty hands,
health will be spoilt and
we will have to regret.

Preeti is very sensible as
she knows how important it is
to eat fruits, salad and green vegetables.
By eating outside and having cold drink,
the eyesight will become weak
and we will have to wear spectacles.

Preeti is very sensible
as she remembers
what her grandmother had told
Think about the things timely,
As time once passed cannot be recalled.

Activity – 1
Discussion: Is Preeti really sensible? if yes then why?
Answer:
Do it yourself

Activity – 2
Make a list of Preeti’s good habits
Answer:

• Brushing teeth every day,
• bathing,
• Wearing clean clothes,
• to clean the house,
• to throw the garbage in the dustbin,
• to sweep the streets,
• Good food habits,
• Not eating food with dirty hands,
• Eating green vegetables, fruits and salad etc.

Activity – 3
Preeti has to prepare a speech on good healthy habits. Help her write the speech

Let’s test understanding

1. Why is Preeti sensible?
(a) Her age is more
(b) She drinks milk
(c) She is beautiful
(d) She has the knowledge of good habits
Answer:
(d) She has the knowledge of good habits.

2. What happens by wearing dirty clothes?
(a) It stinks
(b) germs spread
(c) we get disease
(d) all of these
Answer:
(d) All of the above.

PSEB 5th Class Welcome Life Guide Health and Cleanliness Important Questions and Answers

Multiple Choice Questions :

Question 1.
Which diseases are caught by germs?
(a) Cold
(b) Cholera
(c) Dysentery
(d) All of the above.
Answer:
(d) All of the above.

Question 2.
Which are the public places?
(a) Bus stand
(b) Railway Station
(c) Park
(d) All of the above.
Answer:
(d) All of the above.

Question 3.
Which is the personal clean – Iiness?
(a) Of body
(b) Of face
(c) Of clothes
(d) All of the above.
Answer:
(d) All of the above.

Question 4.
Which of the following is not right?
(a) We should not eat naked eatables from the market.
(b) There is no need to take bath daily.
(c) We should brush our teeth twice daily.
(d) We should keep our surroun – dings clean.
Answer:
(b) There is no need to take bath daily.

Question 5.
What is not included in cleaning the face?
(a) Cleanliness of eyes
(b) Cleanliness of nose
(c) Cleanliness of ears
(d) Cutting of nails.
Answer:
(d) Cutting of nails.

Fill in the blanks :

1. We suffer from illness, cold and ………………………. cough through
2. After passing stool, we should wash our hands properly with ……………………… .
3. Man has made the water dirty and poisonous with dirt and ……………………… .
4. We remain ………………………. while keeping cleanliness.
Answer:
1. germs
2. soap
3. chemicals
4. healthy.

Tick Right (✓) or Wrong (✗) :
1. The germs reach our nails and hands with different methods through dirty surroundings.
2. Cleanliness of clothes is included in the cleanliness of house.
3. Due to poisonous water, the taste and nutrients of food are being destroyed.
Answer:
1. ✓
2. ✗
3. ✓

Mind Mapping :

Match the following :

1. Cleanliness of ears (a) Bus Stand
2. Cleanliness of toilets (b) Washing with soap
3. Hair (c) With wet cloth
4. Public places (d) With Phenyl.
Answer:
1. (c)
2. (d)
3. (b)
4. (a).

Short Answer Type Questions

Question 1.
Give two reasons to spread germs.
Answer:
Germs can spread from ill person’s stool to other persons through close link. They can also spread while cooking and eating with dirty hands.

Question 2.
Which diseases are caught by germs?
Answer:
Dysentery, Cholera, Typhoid, Measles, Cough etc.

Question 3.
What are the rules of cleanliness?
Answer:
Wash hands before cooking and eating food, after cleaning nose, after passing stool and after touching raw food.

Question 4.
Which clothes are cleaned?
Answer:
The clothes which we wear and mattresses are cleaned.

Question 5.
Who is responsible for keeping cleanliness?
Answer:
All are responsible for keeping cleanliness.

Question 6.
What will happen if the garbage is not thrown in the dustbin?
Answer:
Cholera can be caught by flies and malaria can be caught by mosquitoes.

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 9 ਬੀਜਗਣਿਤਕ ਵਿਅੰਜਕ ਅਤੇ ਤਤਸਮਕ InText Questions and Answers.

PSEB 8th Class Maths Solutions Chapter 9 ਬੀਜਗਣਿਤਕ ਵਿਅੰਜਕ ਅਤੇ ਤਤਸਮਕ InText Questions

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਇਕ ਚਲ ਵਾਲੇ ਅਤੇ ਦੋ ਚਲਾਂ ਵਾਲੇ ਵਿਅੰਜਕਾਂ ਦੀਆਂ ਪੰਜ-ਪੰਜ ਉਦਾਹਰਨਾਂ ਦਿਓ ।
ਹੱਲ:
ਇਕ ਚਲ ਵਾਲੇ ਵਿਅੰਜਕਾਂ ਦੀਆਂ ਉਦਾਹਰਨਾਂ :
(i) 4x² – 4x + 5
(ii) 9x
(iii) – 6x³
(iv) 2x⁵ + 3x² + 4x
(v) 5a² + 6a + 3
ਦੋ ਚਲਾਂ ਵਾਲੇ ਵਿਅੰਜਕਾਂ ਦੀਆਂ ਉਦਾਹਰਨਾਂ :
(i) 5xy + \(\frac{5}{11}\)xy²
(ii) \(-\frac{7}{10}\)ab + \(\frac{1}{3}\)ab²
(iii) 7xy + 5x²y + 3xy²
(iv) 3xy
(v) – 8xy + 9x²y.

ਪ੍ਰਸ਼ਨ 2.
x, x – 4, 2x + 1, 3x – 2 ਨੂੰ ਸੰਖਿਆ ਰੇਖਾ ‘ਤੇ ਦਰਸਾਉ ।
ਹੱਲ:
x
ਸੰਖਿਆ ਰੇਖਾ ਉੱਤੇ ਚਲ x ਦੀ ਸਥਿਤੀ X ਹੈ ।

x – 4
ਸੰਖਿਆ ਰੇਖਾ ਉੱਤੇ x – 4 ਦਾ ਮੁੱਲ X ਦੇ ਖੱਬੇ ਪਾਸੇ ਵੱਲ 4 ਇਕਾਈ ਦੀ ਦੂਰੀ ਉੱਤੇ ਬਿੰਦੂ P ਦੇ ਦੁਆਰਾ ਦਰਸਾਇਆ ਜਾਂਦਾ ਹੈ ।

2x + 1
ਸੰਖਿਆ ਰੇਖਾ ਉੱਤੇ 2 ਦੀ ਸਥਿਤੀ ਬਿੰਦੂ A ਉੱਤੇ ਹੋਵੇਗੀ ।
ਮੂਲ ਬਿੰਦੂ ਤੋਂ 8 ਦੀ ਦੂਰੀ X ਦੀ ਦੂਰੀ ਤੋਂ ਦੁੱਗਣੀ ਹੋਵੇਗੀ । 2x + 1 ਦੀ ਸਥਿਤੀ B, A ਦੇ ਸੱਜੇ ਪਾਸੇ 1 ਇਕਾਈ ਦੀ ਦੂਰੀ ਤੇ ਹੋਵੇਗੀ ।

3x – 2
ਸੰਖਿਆ ਰੇਖਾ ਉੱਤੇ 31 ਦੀ ਸਥਿਤੀ ਬਿੰਦੂ B ਉੱਤੇ ਹੋਵੇਗੀ ।
ਲ ਬਿੰਦੂ ਤੋਂ B ਦੀ ਦੁਰੀ ਦੀ ਦੁਰੀ ਤੋਂ ਤਿਗੁਨੀ ਹੋਵੇਗੀ । 3x – 2 ਦੀ ਸਥਿਤੀ P ਦੀ ਸਥਿਤੀ B ਦੇ ਖੱਬੇ ਪਾਸੇ 2 ਇਕਾਈ ਦੀ ਦੂਰੀ ਤੇ ਹੋਵੇਗੀ ।

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਵਿਅੰਜਕ x²y² – 10x²y + 5xy² – 20 ਦੇ ਹਰੇਕ ਪਦ ਦੇ ਗੁਣਜ ਪਹਿਚਾਣੋ ।
ਹੱਲ:
x²y² ਦਾ ਗੁਣਜ 1 ਹੈ ।
x²y ਦਾ ਗੁਣਜ – 10 ਹੈ ।
xy² ਦਾ ਗੁਣਜ 5 ਹੈ ।
ਅਚਲ ਪਦ- 20 ਹੈ ।

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਹੇਠਾਂ ਲਿਖੇ ਬਹੁਪਦਾਂ ਨੂੰ ਇਕ ਪਦੀ, ਦੋ ਪਦੀ ਅਤੇ ਤਿੰਨ ਪਦੀ ਦੇ ਰੂਪ ਵਿਚ ਵਰਗੀਕਰਨ ਕਰੋ :
– z + 5, x + y + z, x + y + z + 100, ab – ac, 17.
ਹੱਲ:
ਇਕ ਪਦੀ : 17
ਦੋ ਪਦੀ : – z + 5, ab – ac
ਤਿੰਨਪਦੀ : x + y + z
ਬਹੁਪਦ : x + y + z + 100.

ਪ੍ਰਸ਼ਨ 2.
ਬਣਾਓ :
(a) ਤਿੰਨ ਇਸ ਤਰ੍ਹਾਂ ਦੇ ਦੋ ਪਦੀ ਜਿਸ ਵਿਚ ਕੇਵਲ ਇਕ ਚਲ x ਹੋਵੇ ।
(b) ਤਿੰਨ ਇਸ ਤਰ੍ਹਾਂ ਦੇ ਦੋ ਪਦੀ ਜਿਸ ਵਿੱਚ x ਅਤੇ y ਚਲ ਹੋਣ ।
(c) ਤਿੰਨ ਇਕ ਪਦੀ ਜਿਸ ਵਿਚ x ਅਤੇ y ਚਲ ਹੋਣ ।
(d) ਚਾਰ ਜਾਂ ਜ਼ਿਆਦਾ ਪਦਾਂ ਵਾਲੇ 2 ਬਹੁਪਦ ।
ਹੱਲ:
(a) ਦੋ ਪਦੀ ਜਿਸ ਵਿਚ ਕੇਵਲ ਇਕ ਚਰ x ਹੋਵੇ
(i) 3x² + 5x
(ii) 6x³ + 2x
(iii) 9x + 4x³

(b) ਦੋ ਪਦੀ ਜਿਸ ਵਿਚ 1 ਅਤੇ y ਚ ਹੋਵੇ :
(i) 3x²y + 4xy
(ii) 9xy + 6xy²
(iii) 5xy + 8x²y

(c) ਇਕ ਪਦੀ ਜਿਸ ਵਿਚ 1 ਅਤੇ y ਹੋਵੇ :
(i) 4x²y
(ii) 5xy²
(iii) 3xy

(d) ਚਾਰ ਅਤੇ ਜ਼ਿਆਦਾ ਪਦਾਂ ਵਾਲੇ ਬਹੁਪਦ :
(i) a + b + c + d
(ii) 2x³ + 5x² + 3x + 18
(iii) 3x² + 4xy + y² + y + x + 9.

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਹੇਠਾਂ ਲਿਖਿਆਂ ਵਿਚ ਹਰੇਕ ਦੇ ਦੋ ਸਮਾਨ ਪਦ ਲਿਖੋ :
(i) 7xy
(ii) 4 mn²
(iii) 2l.
ਹੱਲ:
(i) 7xy ਦੇ ਸਮਾਨ ਪਦ :
3xy, 9xy ਆਦਿ ।

(ii) 4mn² ਦੇ ਸਮਾਨ ਪਦ :
9mn², mnv ਆਦਿ ।

(iii) 2l ਦੇ ਸਮਾਨ ਪਦ :
6l, 9l, 5l ਆਦਿ ।

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
4x × 5y × 7z ਪਤਾ ਕਰੋ ।
ਸਭ ਤੋਂ ਪਹਿਲਾਂ 4 × 5y ਪਤਾ ਕਰੋ ਅਤੇ ਫਿਰ ਉਸ ਨੂੰ 7z ਨਾਲ ਗੁਣਾ ਕਰੋ, ਜਾਂ
ਪਹਿਲਾਂ 5y × 7z ਪਤਾ ਕਰੋ, ਅਤੇ ਇਸ ਨੂੰ 4 ਨਾਲ ਗੁਣਾ ਕਰੋ ।
ਕੀ ਨਤੀਜਾ ਇਕੋ ਜਿਹਾ ਹੋਵੇਗਾ ? ਤੁਸੀਂ ਕੀ ਵਿਚਾਰ ਕਰ ਸਕਦੇ ਹੋ ?
ਕੀ ਗੁਣਾ ਕਰਦੇ ਸਮੇਂ ਕ੍ਰਮ ਦਾ ਮਹੱਤਵ ਹੈ ?
ਹੱਲ:
4x × 5y × 7z
= (4x × 5y) × 7z
= [(4 × 5) × (xy}} × 7z
= 20xy × 7z = (20 × 7)
(xy) (z) = 140xyz
= 4x × 5y × 7z
= 4x × (5y × 7z)
= 4x × (5 × 7) (yz)
= 4x × 35yz
= (4 × 35) (xyz)
= 140 xyz
ਨਹੀਂ, ਗੁਣਾ ਕਰਦੇ ਸਮੇਂ ਕੁਮ ਨਤੀਜੇ ਨੂੰ ਪਰਿਵਰਤਿਤ ਨਹੀਂ ਕਰਦਾ ।
ਦੋਨੋਂ ਸਥਿਤੀਆਂ ਵਿਚ ਨਤੀਜਾ ਸਮਾਨ ਹੈ ।

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਗੁਣਨਫਲ ਪਤਾ ਕਰੋ :
(i) 2x (3x + 5xy)
(ii) a²(2ab – 5c).
ਹੱਲ:
(i) (2x) × (3x + 5xy)
= (2x) × (3x) + (2x) × (5xy)
= 6x² + 10x²y.
(ii) a²(2ab – 5c) = a² × 2ab – a² × 5c.
= 2a³b – 5a²c.

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
(4p² + 5p + 7) × 3p ਦਾ ਗੁਣਨਫਲ ਪਤਾ ਕਰੋ ।
ਹੱਲ:
(4p² + 5p + 7) × 3p = 4p² × 3p + 5p × 3p + 7 × 3p
= 12p³ + 15p² + 21p

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
ਤਤਸਮਕ (I) ਵਿਚ b ਦੇ ਸਥਾਨ ‘ਤੇ – b ਰੱਖੋ । ਕੀ ਤੁਹਾਨੂੰ ਤਤਸਮਕ (II) ਪ੍ਰਾਪਤ ਹੁੰਦੀ ਹੈ ?
ਹੱਲ:
ਤਤਸਮਕ (I) ਹੈ :
(a + b)² = a² + 2ab + b²
ਇਸ ਵਿੱਚ b ਦੇ ਸਥਾਨ ਉੱਤੇ -b ਰੱਖਣ ਤੇ, ਸਾਨੂੰ ਪ੍ਰਾਪਤ ਹੁੰਦਾ ਹੈ :
[a +(-b)]² = a² + 2a(-b) + (-b)²
ਜੋ (a – b)² = a² – 2ab + b
ਜੋ ਕਿ ਤਤਸਮਕ (II) ਹੈ ।
ਇਸ ਲਈ ਤਤਸਮਕ (I) ਵਿਚ b ਦੇ ਸਥਾਨ ਉੱਤੇ b. ਰੱਖਣ ਤੇ ਸਾਨੂੰ ਤਤਸਮਕ (II) ਪ੍ਰਾਪਤ ਹੁੰਦਾ ਹੈ :

ਕੋਸ਼ਿਸ਼ ਕਰੋ :

ਪ੍ਰਸ਼ਨ 1.
a = 2, b = 3, x= 5 ਦੇ ਲਈ ਤਤਸਮਕ (IV) ਦੀ ਪੜਤਾਲ ਕਰੋ ।
ਹੱਲ:
ਤਤਸਮਕ (IV) ਹੈ।
(x + a) (x + b) = x² + (a + b)x + ab
L.H.S. = (x + a) (x + b)
= (5 + 2) (5 + 3)
= (7) (8)
= 56
ਅਤੇ R.H.S. = x² + (a + b) x + ab
= (5)² + (2 + 3) 5 + 2 × 3
= 25 + 6 × 5 + 6
= 25 + 25 + 6
= 56
∴ L.H.S. = R.H.S. = 56.
ਇਸ ਲਈ ਤਤਸਮਕ ਦੇ ਕੋਣਾਂ ਪੱਖਾਂ ਦੇ ਮੁੱਲ a = 2, b = 3, x = 5 ਦੇ ਲਈ ਸਮਾਨ ਹੈ ।

ਪ੍ਰਸ਼ਨ 2.
ਤਤਸਮਕ (IV) ਵਿਚ a = b ਲੈਣ ‘ਤੇ, ਤੁਸੀਂ ਕੀ ਪ੍ਰਾਪਤ ਕਰਦੇ ਹੋ ? ਕੀ ਇਹ ਤਤਸਮਕ (I) ਨਾਲ ਸੰਬੰਧਿਤ ਹੈ ?
ਹੱਲ:
ਤਤਸਮਕ (IV) ਹੈ :
(x + a) (x + b) = x² + (a + b)x + ab
ਇਸ ਵਿਚ a = b ਲੈਣ ਤੇ ਅਸੀਂ ਪ੍ਰਾਪਤ ਕਰਦੇ ਹਾਂ :
(x + a) (x + a) = x² + (a + a) x + a.a
⇒ (x + a)² = x² + 2ax + a²
ਹਾਂ, ਇਹ ਤਤਸਮਕ (I) ਨਾਲ ਸੰਬੰਧਿਤ ਹੈ ।

ਪ੍ਰਸ਼ਨ 3.
ਤਤਸਮਕ (IV) ਵਿਚ a = – c ਅਤੇ b = – c ਲੈਣ ਤੇ, ਤੁਸੀਂ ਕੀ ਪ੍ਰਾਪਤ ਕਰਦੇ ਹੋ ? ਕੀ ਇਹ ਤਤਸਮਕ (II) ਨਾਲ ਸੰਬੰਧਿਤ ਹੈ ?
ਹੱਲ:
ਤਤਸਮਕ (IV) ਹੈ :
(x + a) (x + b) = x² + (a + b)x + ab
ਇਸ ਵਿਚ a = – c ਅਤੇ b = – c ਲੈਣ ਤੇ, ਅਸੀਂ ਪ੍ਰਾਪਤ ਕਰਦੇ ਹਾਂ :
[x + (-c)] [x + (-c)] = x² + [- c) +(-c)]x +(-c) (-c)
⇒ (x – c) (x – c) = x² + (-2c)x + c²
⇒ (x – c)² = x² – 2cx + c²
ਹਾਂ, ਇਹ ਤਤਸਮਕ (II) ਨਾਲ ਸੰਬੰਧਿਤ ਹੈ ।

ਪ੍ਰਸ਼ਨ 4.
ਤਤਸਮਕ (IV) ਵਿਚ b = – a ਲਵੋ । ਤੁਸੀਂ ਕੀ ਪ੍ਰਾਪਤ ਕਰਦੇ ਹੋ ? ਕੀ ਇਹ ਤਤਸਮਕ (III) ਨਾਲ ਸੰਬੰਧਿਤ ਹੈ ?
ਹੱਲ:
ਤਤਸਮਕ (IV) ਹੈ :
(x + a) (x + b) = x² + (a + b)x + ab
ਇਸ ਵਿਚ b = – a ਲੈਣ ਤੇ, ਅਸੀਂ ਪ੍ਰਾਪਤ ਕਰਦੇ ਹਾਂ :
(x + a) [x + (-a)] = x² + [a + (-a)]x + a. (-a)
⇒ (x + a) (x – a) = x² + (a – a)x – a²
⇒ (x + a) (x – a) = x² – a²
ਹਾਂ, ਇਹ ਤਤਸਮਕ (III) ਨਾਲ ਸੰਬੰਧਿਤ ਹੈ ।

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 9 ਬੀਜਗਣਿਤਕ ਵਿਅੰਜਕ ਅਤੇ ਤਤਸਮਕ Ex 9.5 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 9 ਬੀਜਗਣਿਤਕ ਵਿਅੰਜਕ ਅਤੇ ਤਤਸਮਕ Exercise 9.5

1. ਹੇਠਾਂ ਲਿਖੇ ਗੁਣਨਫਲਾਂ ਵਿਚੋਂ ਹਰੇਕ ਨੂੰ ਪ੍ਰਾਪਤ ਕਰਨ ਦੇ ਲਈ ਢੁੱਕਵੇਂ ਤਤਸਮਕ ਦਾ ਉਪਯੋਗ ਕਰੋ :

ਪ੍ਰਸ਼ਨ (i).
(x + 3) (x + 3)
ਹੱਲ:
(x + 3) (x + 3) = (x + 3)²
(a + b)² = a² + 2ab + b²
a = x, b = 3
∴ (x + 3)² = (x)² + 2(x) (3) + (3)²
= x² + 6x + 9.

ਪ੍ਰਸ਼ਨ (ii).
(2y + 5) (2y + 5)
ਹੱਲ:
(2y + 5) (2y + 5) = (2y + 5)²
(a + b)² = a² + 2ab + b²
a = 2y, b = 5
∴ (2y + 5)² = (2y)² + 2 (2y) (5) + (5)²
= 4y² + 20y + 25

ਪ੍ਰਸ਼ਨ (iii).
(2a – 7) (2a – 7)
ਹੱਲ:
(2a – 7) (2a – 7) = (2a – 7)²
(a – b)² = a² – 2ab + b²
a = 2a, b = 7
∴ (2a – 7)² = (2a)² – 2(2a) (7) + (7)²
= 4a² – 28a + 49.

ਪ੍ਰਸ਼ਨ (iv).
(3a – \(\frac{1}{2}\))(3a – \(\frac{1}{2}\))
ਹੱਲ:
(3a – \(\frac{1}{2}\))(3a – \(\frac{1}{2}\)) = (3a – \(\frac{1}{2}\))²
(a – b)² = a² – 2ab + b²
a = 3a, b = \(\frac{1}{2}\)
∴ (3a – \(\frac{1}{2}\))² = (3a)² – 2(3a)(\(\frac{1}{2}\)) + (\(\frac{1}{2}\))²
= 9a² – 3a + \(\frac{1}{4}\)

ਪ੍ਰਸ਼ਨ (v).
(1.1m – 0.4) (1.1m + 0.4)
ਹੱਲ:
(1.1m – 0.4) (1.1m + 0.4)
(a + b) (a – b) = a² – b²
a = 1.1m, b = 0.4
∴ (1.1m – 0.4) (1.1m + 0.4) = (1.1m)² – (0.4)²
= 1.21m² – 0.16.

ਪ੍ਰਸ਼ਨ (vi).
(a² + b²) (-a² + b²)
ਹੱਲ:
(a² + b²) (-a² + b²) ⇒ (b² + a²) (b² – a²)
(a + b) (a – b) = a² – b²
a = b², b = a²
∴ (b² + a²) (b² – a²) = (b²)² – (a²)²
= b⁴ – a⁴.

ਪ੍ਰਸ਼ਨ (vii).
(6x – 7) (6x + 7)
ਹੱਲ:
(6x – 7) (6x + 7)
(a – b) (a + b) = a² – b²
a = 6x, b = 7
(6x – 7) (6x + 7) = (6x)² – (7)²
= 36x² – 49

ਪ੍ਰਸ਼ਨ (viii).
(-a + c) (-a + c)
ਹੱਲ:
(-a + c) (-a + c)
(c – a) (c – a) = (c – a)²
(a – b)² = a² – 2ab + b²
a = c, b = a
∴ (c – a)² = (c)² – 2 (c) (a) + (a)².
= c² – 2ac + a².

ਪ੍ਰਸ਼ਨ (ix).
(\(\frac{x}{2}\) + \(\frac{3y}{4}\))(\(\frac{x}{2}\) = \(\frac{3y}{4}\))
ਹੱਲ:
(\(\frac{x}{2}\) + \(\frac{3y}{4}\))(\(\frac{x}{2}\) + \(\frac{3y}{4}\)) = (\(\frac{x}{2}\) + \(\frac{3y}{4}\))²
(a + b)² = a² + 2ab + b²
a = \(\frac{x}{2}\), b = \(\frac{3y}{2}\)
∴ (\(\frac{x}{2}\) + \(\frac{3y}{4}\))² = (\(\frac{x}{2}\))² + 2(\(\frac{x}{2}\))(\(\frac{3y}{2}\)) + (\(\frac{3y}{2}\))²
= \(\frac{x^{2}}{4}\) + \(\frac{3xy}{2}\) + \(\frac{9y^{2}}{4}\)

ਪ੍ਰਸ਼ਨ (x).
(7a – 9b) (7a – 9b).
ਹੱਲ:
(7a – 9b) (7a – 9b) = (7a – 9b)²
(a – b)² = a² – 2ab + b²
a = 7a, b = 9b
(7a – 9b)² = (7a)² – 2 (7a) (9b) + (9b)²
= 49a² – 126ab + 81b²

2. ਹੇਠਾਂ ਲਿਖੇ ਗੁਣਨਫਲਾਂ ਨੂੰ ਪਤਾ ਕਰਨ ਦੇ ਲਈ, ਤਤਸਮਕ (x + a) (x + b) = x² + (a + b)x + ab ਦਾ ਉਪਯੋਗ ਕਰੋ ।

ਪ੍ਰਸ਼ਨ (i).
(x + 3) (x + 7).
ਹੱਲ:
(x + 3) (x + 7)
(x + a) (x + b) = x² + (a + b)x + ab
x = x, a = 3, b = 7
∴ (x + 3) (x + 7) = x² + (3 + 7) + (3) (7)
= x² + 10x + 21.

ਪ੍ਰਸ਼ਨ (ii).
(4x + 5) (4x + 1)
ਹੱਲ:
(4x + 5) (4x + 1)
(x + a) (x + b) = x² + (a + b)x + ab
x = 4x, a = 5, b = 1
∴ (4x + 5) (4x + 1) = (4x)² + (5 + 1) 4x + (5) (1)
= 16x² + ( 6) (4x) + 5
= 16x² + 24x + 5.

ਪ੍ਰਸ਼ਨ (iii).
(4x – 5) (4x – 1)
ਹੱਲ:
(4x – 5) (4x – 1)
(x + a) (x + b) = x² + (a + b)x + ab.
x = 4x, a = – 5, b = – 1
∴ (4x – 5) (4x – 1) = (4x)² + (-5 – 1)(4x) + (-5) (-1)
= 16x² + (-6) (4x) + 5
= 16x² – 24x + 5

ਪ੍ਰਸ਼ਨ (iv).
(4x + 5) (4x – 1)
ਹੱਲ:
(4x + 5) (4x – 1)
(x + a) (x + b) = x² + (a + b)x + ab.
x = 4x, a = 5, b = – 1
∴ (4x + 5) (4x – 1) = (4x)² + (5 – 1) 4x + (5) (-1)
= 16x² + (4) (4x) – 5
= 16x² + 16 – 5.

ਪ੍ਰਸ਼ਨ (v).
(2x + 5y) (2x + 3y)
ਹੱਲ:
(2x + 3y) (2x + 3y)
(x + a) (x + b) = x² + (a + b)x + ab
x = 2x, a = 5y, b = 3y
∴ (2x + 5y) (2x + 3y) = (2x)² + (5y + 3y)(2x) + (5y) (3y)
= 4x² + (8y)(2x) + 15y²
= 4x² + 6xy + 15y².

ਪ੍ਰਸ਼ਨ (vi).
(2a² + 9) (2a² + 5)
ਹੱਲ:
(2a² + 9) (2a² + 5)
(x + a) (x + b) = x² + (a + b) x + ab.
x = 2a², a = 9, b = 5
∴ (2a² + 9) (2a² + 5) = (2a²)² + (9 + 5)(2a²) + (9) (5)
= 4a² + (14) (2a²) + 45
= 4a⁴ + 28a² + 45.

ਪ੍ਰਸ਼ਨ (vii).
(xyz – 4) (xyz – 2).
ਹੱਲ:
(xyz – 4) (xyz – 2)
(x + a) (x + b) = x² + (a + b) x + ab.
x = xyz, a = – 4, b = -2
∴ (xyz – 4) (xyz – 2) = (xyz)² +(-4 – 2)xyz + (-4)(-2)
= x²y²z² – 6xyz + 8.

3. ਤਤਸਮਕਾਂ ਦਾ ਉਪਯੋਗ ਕਰਦੇ ਹੋਏ ਹੇਠਾਂ ਲਿਖੇ , ਵਰਗਾਂ ਨੂੰ ਪਤਾ ਕਰੋ :

ਪ੍ਰਸ਼ਨ (i).
(b – 7)²
ਹੱਲ:
(b – 7)²
(a – b)² = a² – 2ab + b²
a = b, b = 7
∴ (b – 7)² = (b)² – 2 (b) (7) + (7)²
= b² – 14b + 49
ਪੜਤਾਲ : (b – 7)² = (b – 7) (b – 7)
= b (b – 7) – 7 (b – 7)
= b² – 7b – 7b + 49
= b² – 14b + 49.
ਇਸ ਲਈ, ਇਹ ਸੱਚ ਹੈ ।

ਪ੍ਰਸ਼ਨ (ii).
(xy + 3z)²
ਹੱਲ:
(xy + 3z)²
(a + b)² = a² + 2ab + b²
a = xy, b = 3z
∴ (xy + 3z)² = (xy)² + 2 (xy) (3z) + (3z)²
= x²y² + 6xyz + 9z².
ਪੜਤਾਲ : (xy + 3z)² = (xy + 3z) (xy + 3z)
= xy(xy + 3z) + 3z (xy + 3z)
= x²y² + 3xyz + 3xyz + 9z²
= x²y² + 6xyz + 9z²
ਇਸ ਲਈ, ਇਹ ਸੱਚ ਹੈ ।

ਪ੍ਰਸ਼ਨ (iii).
(6x² – 5y)²
ਹੱਲ:
(6x² – 5y)²
(a – b)² = a² – 2ab + b²
a = 6x², b = 5y
∴ (6x² – 5y)² – 2(6x)² – 2(6x²) (5y) + (5y)²
= 36x⁴ – 60x²y + 25y
ਪੜਤਾਲ :
(6x² – 5y)² = (6x² – 5y) . (6x² – 5y)
= 6x²(6x² – 5y) – 5y (6x² – 5y)
= 36x⁴ – 30x²y – 30x²y + 25y²
= 36x⁴ – 60x²y + 25y²
ਇਸ ਲਈ, ਇਹ ਸੱਚ ਹੈ ।

ਪ੍ਰਸ਼ਨ (iv).
(\(\frac{2}{3}\)m + \(\frac{3}{2}\)n)
ਹੱਲ:
(\(\frac{2}{3}\)m + \(\frac{3}{2}\)m)²
(a + b)² = a² + 2ab + b²
a = \(\frac{2}{3}\)m, b = \(\frac{3}{2}\)n
(\(\frac{2}{3}\)m + \(\frac{3}{2}\)m)² = (\(\frac{2}{3}\)m)² + 2(\(\frac{2}{3}\)m)(\(\frac{3}{2}\)n) + (\(\frac{3}{2}\)n)²
= \(\frac{4}{9}\)m² +2mn + \(\frac{9}{4}\)n²
ਪਤਾਲ :
(\(\frac{2}{3}\)m + \(\frac{3}{2}\)n)² = (\(\frac{2}{3}\)m + \(\frac{3}{2}\)n)(\(\frac{2}{3}\)m + \(\frac{3}{2}\)n)
= \(\frac{2}{3}\)m(\(\frac{2}{3}\)m + \(\frac{3}{2}\)n) + \(\frac{3}{2}\)n(\(\frac{2}{3}\)m + \(\frac{3}{2}\)n)
= \(\frac{4}{9}\)m² + mn + mn + \(\frac{9}{4}\)n²
= \(\frac{4}{9}\)m² + 2mn + \(\frac{9}{4}\)n²
ਇਸ ਲਈ, ਇਹ ਸੱਚ ਹੈ ।

ਪ੍ਰਸ਼ਨ (v).
(0.4p – 0.5q)²
ਹੱਲ:
(0.4p – 0.5q)²
(a – b)² = a² – 2ab + b²
a = 0.4p, b = 0.5 q
∴ (0.4p – 0.5q)² = (0.4p)² – 2 (0.4p)(0.5q) + (0.5q)²
= 0.16p² – 0.04pq + 025q²
ਪੜਤਾਲ :
(0.4p – 0.5q)²
= (0.4p – 0.5q) (0.4p – 0.5q)
= 0.4p (0.4p – 0.5q) – 0.5q (0.4p – 0.5q)
= 0.16p² – 0.02pq – 0.02pq + 0.25q²
= 0.16p² – 0.04pq + 0.25q²
ਇਸ ਲਈ, ਇਹ ਸੱਚ ਹੈ ।

ਪ੍ਰਸ਼ਨ (vi).
(2xy + 5y)².
ਹੱਲ:
(2xy +5y)²
(a + b)² = a² + 2ab + b²
a = 2xy, b = 5y
∴ (2xy + 5y)² = (2xy)² + 2 (2xy) (5y) + (5y)²
= 4x²y² + 20xy² + 25y²
ਪੜਤਾਲ :
(2xy + 5y)² = (2xy + 5y) (2ry + 5y)
= 2xy (2xy + 5y) + 5y (2xy + 5y)
= 4x²y² + 10xy² + 10xy² + 25y²
= 4x²y² + 20xy² + 25y²
ਇਸ ਲਈ, ਇਹ ਸੱਚ ਹੈ ।

4. ਸਰਲ ਕਰੋ :

ਪ੍ਰਸ਼ਨ (i).
(a² – b²)²
ਹੱਲ:
(a² – b²)²
(a – b)² = a² – 2ab + b²
a = a². b = b²
∴ (a² – b²)² = (a²)² – 2(a²) (b²) + (b²)²
= a⁴ – 2a²b² + b⁴.

ਪ੍ਰਸ਼ਨ (ii).
(2x + 5)² – (2x – 5)²
ਹੱਲ:
(2x + 5)² – (2x – 5)²
(a² – b²) = (a + b) (a – b)
a = (2x + 5), b = (2x – 5)
∴ (2x + 5)² – (2x – 5)² = (2x + 5 + 2x – 5)
(2x + 5 – 2x + 5)
= (4x) (10)
= 40x.

ਪ੍ਰਸ਼ਨ (iii).
(7m – 8n)² + (7m + 8n)²
ਹੱਲ:
(7m – 8n)² + (7m + 8n)²
(a – b)² = a² – 2ab + b²
(a + b)² = a² + 2ab + b²
∴ (7m – 8n)² + (7m + 8n)² = (7m)² – 2 (7m) (8n) + (8n)² + (7m)² + 2 (7m) (8n) + (8n)²
= 49m² – 112mn + 64n² + 49m² +112mn + 64n²
= 98m² + 128n².

ਪ੍ਰਸ਼ਨ (iv).
(4m + 5n)² + (5m + 4n)²
ਹੱਲ:
(4m + 5n)² + (5m + 4n)²
(a + b)² = a² + 2ab + b²
∴ (4m + 5n)² + (5m + 4n)² = (4m)² + 2(4m) (5n)+ (5n)² + (5m)² + 2 (5m) (4n) + (4n)²
= 16m² + 40mn + 25n² + 25m² + 40mn + 16n²
= 41m² + 80mn + 41n².

ਪ੍ਰਸ਼ਨ (v).
(2.5p + 1.5q)² – (1.5p – 2.5q)²
ਹੱਲ:
(2.5p – 1.5q)² – (1.5p – 2.5q)²
(a² – b²) = (a – b)(a + b)
a = (2.5p + 1.5q), b = (1.5p – 2.5q)
∴ (2.5p – 1.5q)² – (1.5p – 2.5q)² = [(2.5p – 1.5q) – (1.5p – 2.5q)][2.5p – 1.5q + 1.5p – 2.5q]
= (2.5p – 1.59 – 1.5p + 2.5q)(4p – 4q)
= (1p + 1q) (4p – 4q)
= p (4p – 4q) + q (4p – 4q)
= 4p² – 4pq + 4pq – 4q²
= 4p² – 4q².

ਪ੍ਰਸ਼ਨ (vi).
(ab + bc) – 2ab²c
ਹੱਲ:
(ab + bc)² – 2ab²c
= (ab)² + 2(ab) (bc) + (bc)² – 2ab²c
= a²b² + 2ab²c + b²c² – 2ab²c
= a²b² + b²c².

ਪ੍ਰਸ਼ਨ (vii).
(m² – n²m)² + 2m³n².
ਹੱਲ:
(m² – n²m)² + 2m³n²
= (m²)² – 2 (m²) (n²m) + (n²m)² + 2m³n²
= m⁴ – 2m³n² + n⁴m² + 2m³n²
= m⁴ + n⁴m²

5. ਦਰਸਾਉ ਕਿ :

ਪ੍ਰਸ਼ਨ (i).
(3x + 7)² – 84x = (3x – 7)²
ਹੱਲ:
(3x + 7)² – 84x = (3x – 7)²
L.H.S. = (3x + 7)² – 84x
[∵ (a + b)² = a² + 2ab + b²]
= (3x)² + 2(3x) (7) + (7)² – 84x
= 9x² + 42x + 49 – 84x
= 9x² – 42x + 49
= (3x)² – 2 (3x) (7) + (7)²
= (3x – 7)²
[∵ (a – b)² = a² – 2ab + b²]
= R.H.S.

ਪ੍ਰਸ਼ਨ (ii).
(9p – 5q)² + 180pq = (9p + 5q)²
ਹੱਲ:
(9p – 5q)² + 180pq = (9p + 5q)²
L.H.S. = (9p – 5q)² + 180pq
[∵ (a – b)² = a² – 2ab + b²
= (9p)² – 2(9p) (5q) + (5q)² + 180pq
= 81p² – 90pq + 25q² + 180pq
= 81p² + 90pq + 25q²
= (9p)² + 2 (9p) (5q) + (5q)².
[∵ (a + b)² = a² + 2ab + b²]
= (9p + 5q)²
= R.H.S.

ਪ੍ਰਸ਼ਨ (iii).
(\(\frac{4}{3}\)m – \(\frac{3}{4}\)n)² + 2mn = \(\frac{16}{9}\)m² + \(\frac{9}{16}\)n²
ਹੱਲ:
(\(\frac{4}{3}\)m – \(\frac{3}{4}\)n)² + 2mn = \(\frac{16}{9}\)m² + \(\frac{9}{16}\)n²
L.H.S. = (\(\frac{4}{3}\)m – \(\frac{3}{4}\)m)² + 2mm
[∵ (a – b)² = a² – 2ab + b²]
= (\(\frac{4}{3}\)m)² – 2(\(\frac{4}{3}\)m)(\(\frac{3}{4}\)n) + (\(\frac{3}{4}\)n)² + 2mn
= \(\frac{16}{9}\)m² – 2mn + \(\frac{9}{16}\)n² + 2mn
= \(\frac{16}{9}\)m² + \(\frac{9}{16}\)n² = R.H.S.

ਪ੍ਰਸ਼ਨ (iv).
(4pq + 3q)² – (4pq – 3q)² = 48pq²
ਹੱਲ:
(4pq + 3q)² – (4pq – 3q)² = 48pq²
L.H.S. = (4pq + 3q)² – (4pq – 3q)²
a² – b² = (a + b)(a – b)
a = 4pq + 3q, b = 4pq – 3q
∴(4pq + 3q)² – (4pq – 3q)² = [(4pq + 3q) + (4pq – 3q)][(4pq + 3q) – (4pq – 3q)]
= (8pq) (4pq + 34 – 4pq + 3q)
= (8pq) (6q)
= 48pq² = R.H.S.

ਪ੍ਰਸ਼ਨ (v).
(a – b) (a + b) + (b – c)(b + c) + (c – a) (c + a) = 0
ਹੱਲ:
(a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0
L.H.S. = (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a)
= a² – b² + b² – c² + c² – a²
= 0
= R.H.S.

6. ਤਤਸਮਕਾਂ ਦੇ ਉਪਯੋਗ ਨਾਲ ਹੇਠਾਂ ਲਿਖਿਆਂ ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ :

ਪ੍ਰਸ਼ਨ (i).
(71)²
ਹੱਲ:
(71)²
= (70 + 1)²
[(a + b)² = a² + 2ab + b²]
= (70)² + 2 (70) (1) + (1)²
= 4900 + 140 + 1
= 5041.

ਪ੍ਰਸ਼ਨ (ii).
(99)²
ਹੱਲ:
(99)²
= (100 – 1)²
[(a – b)² = a² – 2ab + b²]
= (100)² – 2 (100) (1) + (1)²
= 10,000 – 200 +1
= 9801.

ਪ੍ਰਸ਼ਨ (iii).
(102)²
ਹੱਲ:
(102)²
= (100 + 2)²
[(a + b)² = a² + 2ab + b²]
= (100)² + 2 (100) (2) + (2)²
= 10,000 + 400 + 4
= 10404.

ਪ੍ਰਸ਼ਨ (iv).
(998)²
ਹੱਲ:
(998)²
= (1000 – 2)²
[(a – b)² = a² – 2ab + b²]
= (1000)² – 2 (1000) (2) + (2)²
= 1000000 – 4000 + 4
= 996004.

ਪ੍ਰਸ਼ਨ (v).
(5.2)²
ਹੱਲ:
(5.2)²
= (5 + 0.2)²
(a + b)² = a² + 2ab + b²
= (5)² + 2 (5) + (0.2) + (0.2)²
= 25 + 2 + 0.04
= 27.04.

ਪ੍ਰਸ਼ਨ (vi).
297 × 303
ਹੱਲ:
297 × 303
= (300 – 3) (300 + 3)
(a – b) (a + b) = a² – b²
a = 300, b = 3
∴ (300 – 3) (300 + 3) = (300)² – (3)²
= 90000 – 9
= 89991.

ਪ੍ਰਸ਼ਨ (vii).
78 × 82
ਹੱਲ:
78 × 82
= (80 – 2) (80 + 2)
(a – b)(a + b) = a² – b²
a = 80, b = 2
∴ (80 – 2) (80 + 2) = (80)² – (2)²
= 6400 – 4
= 6396.

ਪ੍ਰਸ਼ਨ (viii).
(8.9)²
ਹੱਲ:
(8.9)²
= (9 – 0.1)²
(a – b)² = a² – 2ab + b²
a = 9, b = 0.1
∴ (9 – 0.1)² = (9)² – 2 (9) (0.1) + (0.1)²
= 81 – 1.8 + 0.1
= 79.21.

ਪ੍ਰਸ਼ਨ (ix).
1.05 × 0.95.
ਹੱਲ:
1.05 × 0.95
= (1 + 0.05) (1 – 0.05)
(a – b) (a + b) = a² – b²
a = 1, b = 0.05
⇒ (1.05) (1 – 0.05) = (1)² – (0.05)²
= 1 – 0.0025
= 0.9975.

7. a² – b² = (a + b) (a – b) ਦਾ ਉਪਯੋਗ ਕਰਦੇ ਹੋਏ ਹੇਠਾਂ ਲਿਖਿਆਂ ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ :

ਪ੍ਰਸ਼ਨ (i).
(51)² – (49)²
ਹੱਲ:
(51)² – (49)²
a² – b² = (a + b) (a – b)
a = 51, b = 49
∴ (51)² – (49)² = (51 + 49) (51 – 49)
= (100) (2)
= 200.

ਪ੍ਰਸ਼ਨ (ii).
(1.02)² – (0.98)²
ਹੱਲ:
(1.02)² – (0.98)²
a² – b² = (a + b) (a – b)
a = 1.02, b = 0.98
∴ (1.02)² – (0.98)² = (1.02 + 0.98) (1.02 – 0.98)
= (2) (0.04)
= 0.08.

ਪ੍ਰਸ਼ਨ (iii).
(153)² – (147)²
ਹੱਲ:
(153)² – (147)²
a² – b² = (a + b) (a – b)
a = 153, b = 147
∴ (153)² – (147)² = (153 + 147) (153 – (147)
= (300) (6)
= 1800.

ਪ੍ਰਸ਼ਨ (iv).
(12.1)² – (7.9)².
ਹੱਲ:
(12.1)² – (7.9)²
a² – b² = (a + b) (a – b)
a = 12.1, b = 7.9
∴ (12.1)² – (7.9)² = (12.1 + 7.9) (12.1 – 7.9)
= (20) (4.2)
= 84.

8. (x + a) (x + b) = x² + (a + b)x + ab, ਦਾ ਉਪਯੋਗ ਕਰਦੇ ਹੋਏ, ਹੇਠਾਂ ਲਿਖਿਆਂ ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ :

ਪ੍ਰਸ਼ਨ (i).
103 × 104
ਹੱਲ:
103 × 104
⇒ (100 + 3) (100 + 4)
(x + a) (x + b) = x² + (a + b) x + ab
x = 100, a = 3, b = 4
(100 + 3) (100 + 4) = (100)² + (3 + 4) (100) + (3) (4)
= 10000 + (7) (100) + 12
= 10000 + 700 + 12
= 10712.

ਪ੍ਰਸ਼ਨ (ii).
5.1 × 5.2
ਹੱਲ:
5.1 × 5.2
⇒ (5 + 0.1) (5 + 0.2)
(x + a) (x + b) = x² + (a + b) x + ab
x = 5, a = 0.1, b = 0.2
= (5 + 0.1) (5 + 0.2)
= (5)² + (0.1 + 0.2)² + (0.1) (0.2)
= 25 + (0.3)5 + 0.02
= 25 + 1.5 + 0.02
26.52.

ਪ੍ਰਸ਼ਨ (iii).
103 × 98
ਹੱਲ:
103 × 98
(100 + 3) (100 – 2)
(x + a) (x + b) = x² + (a + b) x + ab
x = 100, a = 3, b = -2
(100 + 3) (100 – 2) = (100)² + (3 – 2)(100) + (3) (-2)
= 10000 + (1) (100) – 6
= 10000 + 100 – 6
= 10094.

ਪ੍ਰਸ਼ਨ (iv).
9.7 × 9.8.
ਹੱਲ:
9.7 × 9.8
(10 – 0.3) (10 – 0.2)
(x + a) (x + b) = x² + (a + b) x + ab
x = 10, a = -0.3, b = -0.2
∴ (10 – 0.3) (10 – 0.2) = (10)² + (-0.3 – 0.2) (10) + (0.3) (0.2)
= 100 + (-0.5) (10) + 0.06
= 100 – 5 + 0.06
= 95 + 0.06
= 95.06.