Prasanna

MP Board Class 8th General English Solutions Essay Writing

1. Any Indian Festival
Or
Diwali

India is a land of festivals. We mainly celebrate festivals for fun and joy. We celebrate Holi, Diwali, Dusshera, Raksha Bandhan and many other festivals. Diwali is my favorite festival. It is the festival of lights. It is so called because people light candles and lamps. It is celebrated because Lord Ram had come Lack from banishment after killing Ravana. People of Ayodhya and illuminated the city.

Before this day we clean and whitewash our houses. We worship Goddess Laxmi on this day. We decorate our houses. Children play with fire crackers. We exchange sweets with our relatives and friends. Some people enjoy in their own way by drinking and gambling. Sometimes children get hurt by crackers. So we should take proper care while celebrating Diwali.

कठिन शब्द –

• festival = त्योहार
• light = जलान
• worship = पूजा करना
• banishment = अज्ञातवास।
• whitewash = सफेदी करना
• decorate = सजाना
• crackers = पटाखे
• celebrate = मनाना।

2. My Hobby

An activity which pleases us and which we do just to please ourselves in our free time is called a hobby. Stamp collecting, listening to music, drawing and painting, gardening are some of the hobbies.. • My hobby is drawing and painting. I am interested in drawing landscapes and human figures and painting them. When I travel by train, I see beautiful landscapes outside the window.

When I sit in peace, I recall those scenes, and draw them. At some places I get the subject matter as floating clouds, rivers, hills, fields and green trees. At evening I paint the scenery of the setting sun. I get a satisfaction when I complete a good landscape. In my opinion painting makes the nature a companion of the artist. He forgets the world and his worries for a while.

कठिन शब्द –

• Landscape = नयनगेचन प्रदेश
• floating = तैरते हुए
• Companion = साथी
• Worries = परेशानियाँ

3. My School

I read in Senior Model School, Bhopal. It is situated in a peaceful environment as it is far from | the city. It has a red building with fifteen rooms. It has a big hall, a library, store room, games and sports room, clerks room and principal’s room. My school has a big play ground where cricket, hockey, football and other games are played. The name of my Principal is Mr. S.D. Sharma. He is a learned person.

There are 35 teachers in my school. All the teachers are well qualified The library of our school is well managed. We can read magazines and newspapers there. Annual functions are held in our school. There is a scheme of holding debate on every Saturday in my school. Sometimes picnics and tours are arranged in my school. All the children come in proper uniform to the school. I love my school very much.

कठिन शब्द –

• Peaceful environment = शान्त वातावरण
• situated = स्थित
• well qualified = सुयोग्य
• Debate = वाद – विवाद
• Magazines = पत्रिकाएँ

4. Wonders of Science

Today Science is the life of human beings. It is the age of science. All our luxuries, comforts are the gifts of science.
Electricity is the most useful gift of science. It gives us light. Heaters, fans, coolers, refrigerators, computers etc. all work on electricity. It also runs machines and trains. Many new methods in the field of surgery and medicines have been possible because of science. We have conquered death and disease to a great extent.

Plastic surgery can transform the face. Science has made man reach the moon. Fast means of transport and communication help us to reach distant places in a short time. On the other hand science is a bad master. Atom bombs, hydrogen bombs and missiles are the products of science. If science is used as a servant, it is useful but if it becomes our master, it is very dangerous.”

कठिन शब्द –

• luxuries = भोगविलास
• Surgery = शल्यशास्त्र
• conquered = जीतना
• transform = बदलना।

5. Importance of Trees

We cannot imagine life without trees. Trees . are one of the most important creations of God. Trees are essential part of our lives. They help us in several ways. They produce oxygen in the presence of sunlight which is important for our survival and take in carbon di oxdie making the environment pure. We get wood from trees for making furniture, houses and paper. They provide us food to eat. Trees act as home for many animals and birds. Some trees have medicinal value like tulsi, neem, eucalyptus etc. Trees maintain the ecological balance of nature and bring rain through transpiration. They make the environment pollution free. So we should try our level best to preserve trees.

कठिन शब्द –

• essential = जरूरी
• environment = वातावरण
• ecological = स्थिति विज्ञान का
• balance = सन्तुलन
• Transpiration = वाष्पोत्सर्जन
• pollution = दूषित
• Preserve = रक्षा

6. The Independence Day

Celebrations In Your School Our country got freedom on 15th August, 1947. Britishers quieted India on this day. Therefore, this day is known as Independence Day. It is our National festival. It is celebrated all over India. In schools and colleges, it is celebrated with great pomp and show. It is celebrated in my school. The school building is decorated nicely. We reach school at 7 a.m. in proper uniform. Principal hoists the flag.

Then we all sing the national anthem. After that some, cultural programme is presented and then the teachers deliver speeches to teach us to be faithful to our country. In the end, the principal delivers a speech thanking the audience, teachers and the taught .We come back home with the laddoos given to us with the feeling of patriotism.

कठिन शब्द –

• quit= छोड़कर जाना
• pomp and show – = ठाठबाट
• national anthem = राष्ट्रीय गान
• patriotism = देशभक्ति

7. Annual Day Celebrations in Your School

I study in Deep Vidya Mandir. Our school holds each year an annual function on its foundation day. The prizes are given away in this function to the students who perform well in various fields as academics, sports, cultural activities etc. Our Principal invited the Director of Education to preside over the function. He came in time. Our school scouts gave him guard of honor and staff members received him at the gate.

First of all, he was welcomed with garland and principal read the annual report of the school. After few cultural activities, prize distribution was started. The Director gave away the prizes. He was very happy with school affairs, teachers and Principal. The Principal thanked the Director. In the end, a feast was arranged and we came back to our homes happily.

कठिन शब्द –

• annual function = सालाना कार्यक्रम
• foundation = स्थापना
• academics = शिक्षा सम्बन्धी।
• preside = अध्यक्षता
• garland = फूल माला
• affairs = कार्य
• feast = पार्टी

8. Kalpana Chawla

Kalpana Chawla was the first Indian woman astronaut. She was born on July 1, 1961 in Karnal, Haryana. She had always dreamt about flying when she was a child. She was a strict vegetarian and had hobbies like reading, flying, hiking and bird watching. She did her schooling from Karnal, then She joined Punjab Engineering College, Chandigarh. For further education she went to U.S.A.

She joined NASA in 1995 and was selected for her first flight in 1996. Her first space mission was STS – 87 on 19th Nov., 1997. Her next mission was STS – 107, which took off on 16th January, 2003. It performed eighty experiments but unfortunately 16 minutes prior to landing, the spacecraft perished on 1st February, 2003. She is remembered by the whole world. She was awarded many medals of honor after her death in India and abroad as well.

कठिन शब्द –

• astronaut = अन्तरिक्ष यात्री
• unfortunately = दुर्भाग्यपूर्ण
• perished = नष्ट हो जाना
• abroad = दूसरे देशा, विदेश

9. A Visit to Kanha Kisli

Kanha Kisli is a beautiful National Park situated in Mandla district near Jabalpur in M.P. It came into existence in 1955. It attracts wildlife lovers and tourists in thousands during the peak season. There one can enjoy natural scenery, jungle life, wild animals and birds. The most attractive creature is the tiger. There one can find blackbucks, cheetals, deer, stag and more than twenty species of mammals. There are about 200 species of birds in Kanha Kisli. Water birds can be seen near pools. Common birds like fowls, doves, hawks, eagles, pigeons, flycatchers and woodpeckers are found in abundance. Kanha Kisli is a favourite picnic spot. I enjoyed my visit there very much.

कठिन शब्द –

• existence = अस्तित्व
• attractive = आकर्षक
• abundance = बहुतायत

10. Importance of Computer

The first computer was built by Charles Babbage in 19th Century. It is being improved everyday. Earlier it was used to carry long calculations and print the results but now it is used in almost every walk of life. Computer can provide answers to complicated problems in a flash in which a man would take days or even months. It has a memory also. It can store information and use it later. Computers are used in railway stations for reservation of tickets.

It is used in offices, hospitals, for maintaining records. It is also used for billing in shops. In banks and post office also, the whole work is done on computers. Computer can be compared to human brain. It can solve problems much faster and more accurately than the human brain. It can be used to play games like chess and translate words from one language to another. But it can’t take decisions or think up new ideas. That is where it cannot compete with human brain.

कठिन शब्द –

• complicated = कठिन
• flash = क्षण 42
• translate = अनुवाद
• compete = बराबरी करन

11. Water and Air Pollution

Pollution means to make impure. The air we breathe in is polluted by means of transport. Factories, with chimneys throwing out smoke into air is the chief source of air pollution. Automobiles are the second largest polluters of the environment. With the increase of vehicles the air pollution is increasing. Air pollution not only affects human beings, it is also injurious to plants, trees and animals.

Air pollution is not the only serious problem facing mankind. Water pollution’s is also causing concern to man. The waste product from factories, thousands of liters of sewage are poured into rivers. People throw left overs of meals in lakes and ponds. In seas also fuels, minerals, food and forest products are thrown to make it polluted. To reduce the air and water pollution the government is taking necessary steps and the public should also help the government.

कठिन शब्द –

• Pollution = दूषित करना
• transport = एक जगह से दूसरी जगह ले जाना
• automobiles = मोटर गाड़ी
• minerals = खनिज
• injurious = हानिकारक
• concern= चिन्ता का विषय।

MP Board Class 8th English Solutions

MP Board Class 9th Maths Solutions Chapter 4 Linear Equations in Two Variables Ex 4.1

Question 1.
The cost of notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Solution:
Let cost of pen be ₹ x and cost of a notebook be ₹ y
y = 2x
y – 2x = 0.

Question 2.
Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

1. 2x + 3y = 9.3\(\overline { 5 } \)
2. x – \(\frac{y}{5}\) – 10 = 0
3. -2x + 3y = 6
4. x = 3y
5. 2x = – 5y
6. 3x + 2 = 0
7. y – 2 = 0
8. 5 = 2x

Solution:
1. 2x + 3y = 9.3\(\overline { 5 } \)
2x + 3y – 9.3\(\overline { 5 } \) = 0
a = 2, b = 3, c = – 9.3\(\overline { 5 } \)

2. x – \(\frac{y}{5}\) – 10 = 0
a = 1, b = – \(\frac{1}{5}\), c = – 10

3. -2x + 3y = 6
– 2x + 3y – 6 = 0
a = – 2, b = 3, c = – 6

4. x = 3y
1. x – 3y + 0 = 0
a – 1, b = – 3, c = 0

5. 2x = – 5y
2x + 5y + 0 = 0
a = 2, b = 5, c = 0

6. 3x + 2 = 0
3x + 0y + 2 = 0
a = 3, b = 0, c = 2

7. y – 2 = 0
0x + y – 2 = 0
a = 0, b = 1, c = – 2

8. 5 = 2x
– 2x + 0y + 5 = 0
a = – 2, b = 0, c = 5

Solution of a Linear Equation:
Consider a Linear equation x + 2y = 6
Let x = 2 and y = 2.
Then L.H.S. of the equation = x + 2y = 2 + 2 x 2 = 6
and R.H.S. of the equation = 6 (given)
i.e., LHS. = R.H.S. for x = 2 and y = 2.
Therefore, x = 2 and y = 2 i.e., (2, 2) is the solution of the given equation x + 2y = 6.
Any pair of values of x and y which satisfies the given equation is called a solution of the equation. A linear equation in two variables has infinitely many solutions.

Note:
To find the solution of an equation, assure a value of one of the variable and calculate the value of second variable from the given equation.

MP Board Class 9th Maths Solutions

MP Board Class 8th Special English Grammar Active and Passive Voice

Memory Chart

Active से Passive Voice में बदलने के नियम –

1. Active Voice के Subject को Passive Voice में Subject बना दिया जाता है।
2. Active Voice के Subject को Passive Voice में Object बना देते हैं और उसको पूर्व रखा जाता है।
3. Passive Voice के Main Verb को सदैव Third Form में प्रयोग किया जाता है।
4. Main Verb से पहले Tense के अनुसार सहायक क्रिया लगाई जाती है।

1. Present Indefinite Tense
नियमः Verb की Third form से पूर्व is, are or am लगाया जाता है।

Exercise
Change the Voice:

1. We take milk.
2. He reads his books.
3. He does not help me.
4. Do you like her?
5. They do not help me.

2. Present Continuous Tense
Rule: Verb की Third form से पूर्व is being, am being, are being लगाया जाता है।

Exercise
Change the Voice:

1. Raj is doing his home-work.
2. The boys are dong their sums.
3. The women are not buying vegetables.
4. Are you chasing the dog?
5. Who is wasting the time?

3. Present Perfect Tense
Rule: Verb की Third form से पूर्व has been या have been रखा जाता है।

Exercise
Change the Voice:

1. This man has killed a dog.
2. Rajesh has not plucked mangoes.
3. I have not hurt any body.
4. These boys have not seen the Taj.
5. She has drown this picture.

4. Past Indefinite Tense
Rule: Verb की Third form से पूर्व was या were का प्रयोग किया जाता है।

Exercise
Change the Voice:

1. The farmer killed the snake.
2. The old man flew a kite.
3. They never helped any beggar.
4. I joined the two pieces of the rope.
5. Did he visit the historical place?

5. Past Continuous Tense
Rule: Verb की Third form से पहले was being या were being रखा जाता है।

Exercise
Change the Voice:

1. He was teaching his sister.
2. She was wasting her time.
3. Were they ploughing their fields?
4. Where were the boys hiding your books?
5. He was using a machine.

6. Past Perfect Tense
Rule: Verb की Third form से पूर्व had been लगा दिया जाता है।

Exercise
Change the Voice:

1. He had burnt his hand.
2. She had deceived me.
3. They had bought an apple.
4. Where had the washerman lost your clothes?
5. Who had plucked the flowers?

7. Future Indefinite Tense
Rule: Verb की Third form से पूर्व will be या shall be लगा दिया जाता है।

Exercise
Change the Voice:

1. I shall snub him.
2. We shall obey you.
3. The servant will clean the room.
4. They will not eat these mangoes.
5. Will you meet him?

8. Future Perfect Tense
Rule: क्रिया की Third form से पूर्व will have been या shall have been रखा जाता है।

Exercise
Change the Voice:

1. The labourers will have their work.
2. They will have watered their fields.
3. The priest will have worshipped Shankar.
4. The teacher will have taught me.
5. Will the miser have sold his shop?

9. Imperative Sentences
Rule: Verb की Third form से पूर्व let be लगाया जाता है अथवा should be लगाया जाता है। यदि Please का प्रयोग भी किया गया हो तो should के स्थान पर you are requested लगा दिया जाता है।

Exercise
Change the Voice:

1. Do it now.
2. Serve your parents.
3. Give a rupee to the beggar.
4. Never waste your time.
5. Come to me and show your teeth.
6. Bring your book.
7. Let me help this patient.
8. Please sit down.

MP Board Class 8th English Solutions

MP Board Class 8th Special English Grammar Time and Tense

(A) Time and Tence

1. Look at these sentences:
Kapil plays cricket.
Kapil played cricket.
Kapil ivill play cricket.

इन वाक्यों में plays, played तथा will play verbs हैं।

1. plays present tense है तथा इससे present time का बोध होता है।
2. played past tense है तथा इससे past time का बोध होता है।
3. will play future tense है (किंतु modern grammarians इसे present tense कहते हैं) तथा इससे future time का बोध होता है।

इन वाक्यों से पता चलता है कि present, past तथा future tense क्रमशः present, past तथा future time का बोध कराते हैं।

By Tense we understand the correspondence between the form of the verb and our concept of time (past, present and future).

किंतु Time और Tense दोनों एक नहीं हैं। Time एक universal concept है, किंतु Tense का संबंध verb से होता है।
Time को हम तीन भागों में बाँटते हैं:
Past Time, Present Time, Furture Time
अब time और tense के संबंध को देखें:

(B) Kinds of Tense

(C) Verb Forms
English Grammar में Verb का असली रूप present tense तथा plural number माना जाता है। Verb के पाँच रूप होते हैं।

Examples Worked Out

Fill in the blanks with the suitable forms of the verbs given in brackets:

1. The sun (shine) by day. – The sun shines by day.
2. Two and two (make) four. – Two and two make/makes four.
3. I (see) him last Monday. – I saw him last Monday.
4. He will do it if you (pay) him. – He will do it if you pay him.
5. She (be) born in 1965. – She was born in 1965.
6. I (live) here since 1980. – I have been living here since 1980.
7. Tom (arrive) last night. – Tom arrived last night.
8. Since when you know) him? – Since when have you known him?
9. I never (see) the Taj. – I have never seen the Taj.
10. The earth (move) round the sun. – The earth moves round the sun.
11. He (write) a letter now. – He is writing a letter now.
12. Did you (sleep) well? – Did you sleep well?
13. I (pass) the exam. in 1980. – I passed the exam. in 1980.
14. Honesty (be) the best policy. – Honesty is the best policy.
15. Onions (smell). – Onions smell.
16. We (see) him the other day. – We saw him the other day.
17. I (not see) him so far. – I haven’t seen him so far.
18. She (read) a book at present. – She is reading a book at present.
19. He (go) out an hour ago. – He went out an hour ago.
20. Horse (be) animals). – Horses are animals.

Exercise

Re-write the following sentences in the tenses indicated in brackets:
Examples: (i) He comes very early. (into simple past)
= He came very early.
(ii) You ride a bicycle. (into simple future)
You will ride a bicycle.

1. He comes very early. (into simple past)
2. You ride a bicycle. (into simple future)
3. He will say ‘no’. (into simple present)
4. It begins to rain. (into present perfect)
5. Soma made tea. (into future continuous)
6. We heard his speech. (into present perfect)
7. They go to the cinema. (into present continuous)
8. Boys play cricket here. (into present perfect continuous)
9. She comes here on Sundays. (into simple future)
10. I am going to have a bath. (into past continuous)
11. Did he like tea? (into simple present)
12. Moti has thrown the ball. (into past perfect)
13. He writes a long letter. (into present continuous)
14. They drove a car. (into simple future)
15. I thank him for his help. (into future continuous)
16. We waited here for long. (into present perfect continuous)
17. Mr. Sinha teaches us Hindi. (into simple past)
18. She has a sweet voice. (into simple future)
19. He does his work honestly.(into present perfect)

MP Board Class 8th English Solutions

MP Board Class 8th Special English Grammar Clause

1. Look at these sentences:
I shouted and he ran up.
I called her but she gave no answer.
(i) प्रथम वाक्य में I shouted और he ran up में एक-एक subject और एक-एक finite verb हैं।
(ii) उसी प्रकार दूसरे वाक्य में I called her तथा she gave no answer में भी एक-एक subject और एक-एक finite verb हैं।
(iii) इस प्रकार प्रत्येक subject+verb वाले अंश को clause कहते हैं।
(iv) ऊपर के वाक्यों में and तथा but से दोनों clauses को जोड़ा गया है।
clause शब्दों के उस समूह को कहते हैं जो किसी वाक्य का अंश (part) हो और जिसमें एक Subject और एक Finite verb हो।

Kinds of Clauses

Clause मूलतः तीन प्रकार के होते हैं –
(i) Main clause या Principal clause
(ii) Subordinate clause या Dependent clause
(iii) Co-ordinate clause

Main Clauses

2. Look at these sentences:
This is the pen which I like.
Sunday is the day when I am least busy.

(i) इन वाक्यों में This is the pen/Sunday is the day – Main clauses हैं। Main clause it Principal clause या Independent clause भी कहा जाता है।
जो Clause स्वस्तः पूर्ण अर्थ रहता है, और किसी अन्य clause पर आश्रित नहीं रहता, उसे main या principal clause कहते हैं।

Subordinate Clauses

3. Look at these sentences:
I do it because I like it.
I hoped that was true.
Don’t talk while she is singing.
He must stay where he is.

(i) ऊपर के वाक्यों में टेढ़े अक्षरों में लिखे हुए clauses Subordinate clauses हैं।
जो Clause अपने अर्थ की पूर्णता के लिए Main Clause या अन्य Clause पर आश्रित रहता है उसे Subordinate (या Dependent) Clause कहते हैं।

(i) निम्नलिखित Conjunctions से शुरू होने वाले clauses Subordinate clauses होते हैं: as, because, since, before, till, after, while, when, if, unless, though, although, lest, in order that, as soon as provided, that, as if, that, whether, which, where, why, how, as much as, according as, than इत्यादि

Co-ordinate Clauses

4. Look at these sentences:
Govern your passion or they will govern you. (2 clauses joined by or)
I came, I saw, I conquered. (3 clauses separated by comnas)
To err is human : to forgive; divine. (2 clauses separated by a semicolon)
(i) जो clauses एक ही rank या order (सामान महत्त्व) के होते हैं. Co-ordinate clauses कहलाते हैं।
(ii) ये साधारणः Co-ordinate conjunctions and, or but इत्यादि द्वारा जुड़े रहते हैं या कभी-कभी conjuctions के बदले comma या semi-colon का प्रयोग किया जाता है।
(iii) मुख्य Co-ordinating conjunctions निम्नलिखित हैं; and, but, or, still, yet, as well as, both….and, either ….or, however, neither….nor, neither, nor, otherwise, else, for, so, not only….but also, nevertheless इत्यादि।

Compound Sentence

1. Look at these sentences:
God made the country – Simple sentence
Man made the town – Simple sentence
(i) यदि इन दो Simple sentences को किसी conjunction से जोड़ दें तो इनमें प्रत्येक को clause कह सकते हैं। जैसे:
God made the country and man made the town. इस वाक्य में दो clauses हैं और यह Compound sentence है:
(i) God made the country.
(ii) (and) man made the town.

Use of Co-ordinating Conjunctions

आगे कुछ Co-ordinating conjunctions का list और उनसे शुरू होने वाले compound sentences के उदाहरण दिए जा रहे हैं:
and : Man discovered fire and learnt to cook.
but : We knocked at the door, but no one answered.
or : Hurry up or you will be late.
Yet : He is poor, yet he is happy.
still : The best doctors are attending on him, still he is not out of danger.
for : The only lady does not go out in the winter, for she feels the cold a great deal.
so : The man had a stomach pain, so we took him to a doctor.
otherwise : You should better go now, otherwise you will miss your train.
either…or : You may either stay in the hostel or stay at home.
not only…bot also : The enemy not only captured the city, but aslo killed several soldiers.
as well as : He was punished as well as fined.
therefore : He is laborious, therefore he will succeed.
neither…nor : The old man could neither read nor write.
nor : He cannot speak, nor can he write.
else : Walk quickly, else he will overtake you.
nevertheless : I did my best, nevertheless I failed.

Complex Sentence

1. Look at these sentences :
I know the reason why he was so angry.
That is the house that I would like to buy.
(i) ऊपर के वाक्यों में I know the reason तथा That is the house Main clauses हैं।
(ii) इन्हीं वाक्यों में why he was so angry तथा that I would like to by subordinate clauses हैं।
(iii) Subordinate clauses why तथा that से शुरू हुए है। Why तथा that Subordinate conjunctions हैं।
ऊपर के दोनों वाक्य Complex sentences हैं।

जिस वाक्य में एक Main clause (या Principal clause) और एक या एक से अधिक Subordinate clauses रहें उसे Complex Sentence कहते हैं।

MP Board Class 8th English Solutions

MP Board Class 8th Special English Grammar Transformation

Look at these sentences:

(i) स्तम्भ A के नीचे दिए गए वाक्यों तथा ठीक उनके सामने स्तम्भ B में दिए गए वाक्यों को देखें, अर्थ की दृष्टि से दोनों समान हैं।
(ii) किन्तु एक ही बात को हम दो तरह से कह सकते हैं और तब वाक्यों के words तथा word-order भी अलग-अलग हो सकते हैं।

अतः, हम कह सकते हैं कि किसी वाक्य के meaning को अक्षुण्ण रखते हुए उसके form (रूप) को बदला जा सकता है। अंग्रेजी व्याकरण में इसे Transformation कहते हैं। Transformation का अर्थ होता है-रूप-परिवर्तन An To transform a sentence is to re-write it to change its form without any change of meaning.

अंग्रेजी में वाक्यों के मुख्यतः निम्नलिखित forms हो सकते हैं:
(a) Statement या Assertive (affirmative or negative)
(ii) Question या Interrogative
(iii) Desires या Imperative and Optative तथा
(iv) Exclamations.

(b) Voice : Active and Passive

(c) (i) Simpel
(ii) Complex
(iii) Double and Multiple (Compound).

(d) Direct and Indirect (Narration).
Voice तथा Narration के विषय में आप पढ़ चुके हैं। यहाँ हम Transformation की अन्य विधियों पर एक-एक कर विचार करेंगे।

(a) Transforming interrogative into assertive

Look at these sentences:

Interrogative sentence में पहले verb तब subject रहता है, किन्तु assertive sentence में subject + verb का word-order रहता है। Interrogative sentence को assertive में बदलने के लिए:

1. Verb + subject के word-order के बदले वाक्य में subject + verb का word-order लगाते हैं;
2. Interrogative mark की जगह full stop देते हैं;
3. यदि interrogative sentence में not नहीं रहे तो assertive में not लगाते हैं, पर यदि interrogative में not हो तो assertive में not का प्रयोग नहीं करते हैं।
4. कुछ ऐसे interrogative sentences होते हैं जो अर्थ के अनुसार assertive होते हैं, उन्हें rhetorical questions कहते हैं। ऐसे वाक्यों को अर्थ के अनुसार assertive में बदलते हैं। जैसे –

Isn’t India a big country?
India is a big country.

(b) Transforming assertive sentences into interrogative

Look at these sentences:

Assertive sentence को interrogative बनाने के लिए:

1. सबसे पहले assertive sentence के subject + verb के शब्द-क्रम को verb + subject के शब्द-क्रम में बदलें :
2. फिर full stop की जगह question mark लगाएँ; तथा
3. अगर assertive sentence में not नहीं हो तो interrogative में not लगाएँ अगर assertive में not हो तो interrogative में इसका प्रयोग नहीं करें।

(c) Transforming exclamatory sentence into assertive

Look at these sentences:

Exclamatory sentence को assertive में बदलने के लिए :

1. सब से पहले subject + verb का शब्द क्रम करें;
2. लुप्त शब्दों को जोड़ दो; What a lovely rose ! = What a lovely rose it is!
3. अगर exclamation how, what, such आदि से प्रारम्भ हो तो very या great + adjective या उपयुक्त adjectiv + noun का प्रयोग करें;
4. अगर exclamation o that, would that, if I were, if only, alas that से प्रारम्भ हो तो assertive वाक्य में I wish, I earnestly desir, I am sad आदि का प्रयोग करें;
5. Exclamation के चिह्न के स्थान पर full stop का प्रयोग करना चाहिए।

(d) Transforming affirmative sentences into negative

1. Look at these sentences:

Affirmative से negative बनाने के लिए कभी-कभी no/not तथा अन्य नकारात्मक भाव व्यक्त करने वाले शब्दों का प्रयोग किया जाता है। जैसे : doubtful = not sure; always = never; as soon as = no sooner than; all = none; cruel = not kind आदि। कभी-कभी affirmative ध्वनि वाले शब्दों की जगह negative ध्वनि वाले विपरीतार्थक शब्दों के प्रयोग से भी काम चल जाता है।

2. Look at these sentences:

कभी-कभी affirmative से negative बनाने के लिए double negative (negative + negative) की आवश्यकता पड़ती है। आप जानते हैं कि double negative = affirmative.

(e) Transforming negative sentences into affirmative

Look at these sentences:

Negative से affirmative बनाने की प्रक्रिया affirmative से negative बनाने की प्रक्रिया के ठीक विपरीत है। जैसे: not always = sometimes; no one = everyone; not good = bad; not kind = cruel; not getting help = helpless; no sooner than = as soon as आदि।

(f) Transforming simple sentences into double or compound sentences :

Look at these sentences:

1. Simple sentence में एक ही principal clause रहता है, किन्तु double sentence में दो;
2. And, but, still, yet, or, both ________ and, not only ______ but also, otherwise, either _______ or आदि द्वारा जोड़कर simple से double sentence बनाया जाता है।

(g) “Transforming double or compound sentences into simple sentences.

Look at these sentences:

Double sentence को simple में बदलने के लिए :

1. Double sentence के finite verb को participle (verb + ing) में बदल दिया जाता है; या
2. अवश्यक्तानुसार उस जगह to, for, after, by, unless, owing to, in spite of आदि का प्रयोग किया जाता है।

(h) Transforming simple sentences into complex sentences

Look at these sentences:

1. Simple sentence में एक principal clause रहता है, किन्तु complex sentence में एक principal clause तथा कम-से-कम एक subordinate clause (noun, adjective या adverb clause) अवश्य रहता है।
2. अतः, simple sentence से complex sentence में बदलने के लिए simple sentence के किसी एक word or phrase (शब्द समूह) को लेकर noun, adjective या adverb clause में who, whom, whose, that, which, when, why, where, unless, till, so ……….. that इत्यादि की सहायता से बदल दें।

(i) Transforming complex sentences into simple sentences

Look at these sentences:

Complex sentence को simple sentence बनाने की कला simple से complex बनाने की कला के ठीक विपरीत है, अर्थात simple sentence में noun, adverb या adjective clause के भाव को एक शब्द या शब्दसमूह (phrase) में व्यक्त करना चाहिए।

(j) Transforming double sentences into complex sentences

Look at these sentences:

Co-ordinate main clause के स्थान पर subordinate clause का प्रयोग कर Double sentence को complex में बदला जा सकता है।

(k) Transforming complex sentences into double sentences

Look at these sentences:

MP Board Class 8th English Solutions

MP Board Class 9th Maths Solutions Chapter 2 Polynomials Ex 2.3

Question 1.
Find the remainder when x³ + 3x³ + 3x + 1 is divided by

1. x + 1
2. x – \(\frac{1}{2}\)
3. x
4. x + π
5. 5 + 2x.

Solution:
Let p(x) = x³ + 3x² + 3x + 1

1. x + 1
x + 1 = 0
x = – 1
Remainder
= p(- 1)= (- 1)³ + 3 (- 1)² + 3 (-1) +1
= – 1 + 3 – 3 + 1 = 0.

2. x – \(\frac{1}{2}\) = 0
x =π
When p(x) is divided by ( x – \(\frac{1}{2}\)) the remainder is P(\(\frac{1}{2}\))

3. x = 0
When p(x) is divided by x, the remainder is p(0).
p(0) = (0) + 3(0)² + 3(0) + 1
= 0 + 0 + 0 + 1 = 1

4. x + π = 0
x = – π
When p(x) is divided by (x + π), the remainder is p(- π) p(- K) = (- π)³ + 3 (- π)² + 3 (- π) + 1
= – π³ + 3π² – 3π + 1

5. 5 + 2x = 0 x = \(\frac{-5}{2}\)
When p(x) is divided by (5 + 2x), the remainder is p(\(\frac{-5}{2}\))

Question 2.
Find the remainder when x³ – ax² + 6x – a is divided by x – a.
Solution:
Let p(x) = x² – ax² + 6x – 1
x – a = 0
x = a
Remainder = (a)³ – a(a)² + 6(a) – a
= a² – a² + 6a – a
= 5a.

Question 3.
Check whether 7 + 3x is a factor of 3x³ + 7x.
Solution:
p(x) = 3x³ + 7x
7 + 3X = 0

(7 + 3x) is not a factor of p(x).

Factorization of Polynomials:

Factor Theorem:
Let p{x) be any polynomial of degree equal to or greater than 1 and ‘a’ be any real number such that –

1. If p(a) = 0, then (x – a) is a factor of p(x)
2. If (x – a) is a factor then p(a) = 0

Proof:
Let p(x) be a polynomial of degree ≥ 1 and be a real number.

1. If p(a) = 0, then (x – a) is a factor of p(x)
Suppose q(x) be the quotient when p(x) is divided by (x – a). By remainder theorem, remainder = p(a).
P(x) = (x – a) x q(x) + p(a)
p(x) = (x – a) x q(x) (∴ p(a) = 0, given)
= (x – a) is a factor of p(x).

2. If (x – a) is a factor then p(a) = 0
=> p(x) when divided by (x – a) gives remainder = 0 …(i)
But by remainder theorem
When p(x) is divided by (x – a), remainder = p(a) …(ii)
From (i) and (ii), we get
p(a) = 0 Proved.

MP Board Class 9th Maths Solutions

MP Board Class 8th Special English Grammar Prepositions

A Preposition is a word placed before a noun or a pronoun to show its relation to some other word in the sentence; as:

1. He is true to his word.
2. They boy fell into the pit.

Chief Prepositions: At, on, in, to, by, with, for, from, out, of, up, under, upon, about, before, behind, between, beneath, within, without etc.

Use of Some Prepositions

1. At. In: At छोटे स्थान के लिए और in बड़े स्थान के लिए प्रयोग किया जाता है:
जैसे –
1. He lives at Najaf Garh.
2. We live in India.

2. In, Into: In स्थिति का बोध कराता है, परन्तु Into गति प्रकट करता है; जैसे –
1. The boys are in the class room.
2. We went into the class room.

3. With, By: With यन्त्र के साथ और By कार्य करने वाले के लिए प्रयोग किया जाता है; जैसे –
1. He cut the apple with a sharp knife.
2. The snake was killed by the farmer.

4. Since, For: Since निश्चित समय के लिए और For समय की अवधि के लिए प्रयोग किया जाता है; जैसे –
1. She has been knitting since morning.
2. Ram has been sick for two days.

5. Between, Among: Between दो आदमियों या वस्तुओं के लिए प्रयोग किया जाता है Among दो से अधिक के लिए; जैसे –
1. Divide these fruits between Mohini and Radha.
2. The man divided his property among his four sons.

6. On, Upon: On गतिहीन वस्तुओं की ओर और Upon गतिशील की ओर संकेत करता है; जैसे –
1. The mother is on the roof.
2. The dog jumped upon the table.

7. In, Within: In का तात्पर्य समय की समाप्ति पर, जबकि Within का तात्पर्य है समय की अवधि के अन्दर। (अर्थात् निश्चित समय के पूर्व) जैसे –
1. I shall come back in a week. (एक सप्ताह की समाप्ति पर)
2. I shall come back within a week. (एक सप्ताह समाप्त होने से पूर्व)

8. Below, Beneath: Below से पद का पता चलता है, जबकि Beneath स्थान का बोध कराता है। जैसे –
1. He is below me in rank.
2. The lion is sleeping beneath a tree.

9. Beside, Besides: Beside का अर्थ है पास और Besides का अर्थ है अतिरिक्त। जैसे –
1. She sat beside me.
2. Besides Raj, other boys came.

Exercise (1)

Fill in the blanks with suitable preposition selecting from those given in brackets:

1. I went to Bhopal _______ May. (on, in, at)
2. She bought this pen _______ ten rupees. (of, for in)
3. The monkey jumped _______ the river. (in, into, on)
4. He ran _______ the thief. (with, into, after)
5. We started _______ five _______ the morning (on, at, in)
6. He plucked an apple _______ the tree. (out, on, from)
7. The teacher beat him _______ a cane. (by, from, with)
8. He does not agree _______ me. (in, by, with)
9. Sita came _______ school (in, from, out)
10. The child fell _______ the well. (in, into, at)

Exercise (2)

Complete the following sentences by filling the suitable prepositions in the blanks :

1. I have not slept _______ yesterday.
2. He spoke _______ me _______ English.
3. She brought a doll _______ the market _______ two rupees.
4. The building was destroyed _______ fire.
5. You learn the poem _______ heart.
6. The furniture is made _______ wood.
7. Boys go to school _______ 10 o’cloek.
8. Raj lives _______ Calcutta
9. He lives _______ this building.
10. The game will begin 10 o’clock.

Fixed Prepositions

1. Afraid of : A cat is afraid of dogs.
2. Acquit of : The judge acquitted him of all the charges.
3. Assure of : I assure you of my help.
4. Aware of : Are you your faults of not aware.
5. Beg of : Gangu begged mercy of Hari.
6. Beware of : Beware of cheats.
7. Come of : Nanu and Nupur come of the family of writers.
8. Consist of: This book consists of three hundred pages.
9. Convict of : Jag Mohan was convicted of pick-pocketing.
10. Die of : Many men die of cholera every year.
11. Dispose of : I have disposed of my old scooter.
12. Enquire of : I enquired of him about his health.
13. Hope of : He has no hope of success.
14. Relieve of : This medicine will relieve you of your pain.
15. Taste of : This water tastes of salt.
16. Warn of : She warned me of the coming danger.
17. Abound in : This tank abounds in fish.
18. Arrive in : The Prime Minister will arrive in Delhi tomorrow.
19. Bask in : Let us bask in the sun.
20. Believe in : We should not believe in ghosts.
21. Call in : Please call in the doctor.
22. Confide in : I confide in my niece.
23. Consist in : Beauty consists in simplicity.
24. Deal in : Her father deals in sugar.
25. End in : All her efforts ended in smoke.
26. Fail in : She failed in her mission.
27. Fill in : Fill in the following blanks.
28. Give in : The enemy gave in at last.
29. Indulge in : Do not indulge in idle talks.
30. Interfere in : Do not interfere in other’s work.
31. Succeed in : You cannot succeed in the examination.
32. Trust in : Trust in God and do the right.
33. Aim at : The hunter aimed at the deer.
34. Angry at : Your father was angry at your misconduct.
35. Arrive at : You have arrived at the wrong decision.
36. Bark at : Dogs always bark at the strangers.
37. Catch at : A drowning man catches at a straw. ”
38. Grieve at : Do not grieve at your loss.
39. Grumble at : Do not grumble at your lot.
40. Knock at : Do not knock at my door.
41. Laugh at : Never laugh at the helpless.
42. Point at : The child pointed at the bird.
43. Wonder at : I wondered at the sight of the Taj.
44. Absent from : Sushma is absent from school today.
45. Abstain from : I abstain from smoking.
46. Differ from : My book differs from yours.
47. Escape from : The thief escaped from the police station.
48. Part from : The bride parted from her parents in tears.
49. Prevent from : The teacher prevented her from entering the classroom.
50. Protect from : The umbrella protects us from sun and shower.
51: Recover from : She has recovered from illness.
52. Ask for : He asked me for a loan of money.
53. Blame for : Do not blame anybody for your failure.
54. Care for : He does not care for my advice.
55. Die for: A soldier should be ready to die for his country.
56. Feel for : The rich should feel for the poor.
57. Fight for : We should fight for our rights.
58. Grieve for : Do not grieve for your parents.
59. Hope for : Always hope for the best.
60. Live for : We should fight for our country.
61. Long for : Do not long for a very long life.
62. Look for : I am looking for my lost purse.
63. Pay for : You will have to pay for your folly.
64. Pray for : Should I pray for your welfare.
65. Prepare for : We should be prepared for the worst.
66. Send for : Send for the doctor at once.
67. Take for : The police took him for a thief.
68. Wait for : I am waiting for my friend.
69. Agree with : I cannot agree with you.
70. Angry with : Do not be angry with me.
71. Begin with : The function began with a song.
72. Charge with : He has been charged with murder.
73. Compare with : Compare this apple with that.
74. Deal with : You should deal with all in a polite way.
75. Differ with : I differ with you on this point.
76. Disagree with : I disagree with you on this point.
77. Fight with : We must not fight with our neighbours.
78. Fill with : Fill this cup with tea.
79. Interfere with : Do not interfere with others.
80. Mix with : Do not mix with idlers.

MP Board Class 8th English Solutions

MP Board Class 8th Special English Grammar Direct and Indirect Narration

किसी व्यक्ति की कही हुई बात को हम दो प्रकार से लिखते हैं –

1. कहने वाले के मूल शब्दों में लिखना। इसे Direct Speech कहते हैं। ये शब्द सदैव Inverted Commas “…” में बन्द रहते हैं। जैसे –
Ram says, “I am going.”

2. कहने वाले की बात को अपने शब्दों में लिखना। इसे Indirect Speech कहते हैं। इसमें Reporting verb का comma तथा Inverted Commas “…” का लोप कर दिया जाता है। जैसे –
Ram says that he is going.

Two Parts of Direct Speeches

1. Inverted Commas से पूर्व वाला भाग जिससे वाक्य को आरम्भ करते हैं, इसे Reporting Verb कहते हैं। जैसे उपर्युक्त उदाहरण में Ram says Reporting verb है।

2. Inverted Commas के अन्दर लिखा हुआ कथन Reported Speech कहलाता है। जैसे उपुर्यक्त भाग में “I am going” Reported Speech है। Direct से Indirect बनाते समय Personal Pronouns का परिवर्तनः

नियम – Reported Speech में प्रयोग किये गए first person-I, my, me, we, us, our के Pronouns को Reporting Verb के Subject के Person के अनुसार बदल देते हैं। जैसे –

Direct : The teacher says, “I am writing a letter.”
Indirect: The teacher says that he is wiriting a letter.

उपयुक्त वाक्यों में वक्ता teacher, है,जिसने अपने लिए ‘I’ का प्रयोग किया है। Indirect Speech में teacher के third person के अनुसार subject बदलकर he हो गया है।
नियम – Reported Speech Second Person Pronouns के You, Your, Reporting Verb के Object के Person के अनुसार बदल देते हैं। जैसे –

Direct: You said to me, “You are an honest man.”
Indirect: You told me that I was an honest man.
Direct: He said to him, “You have helped me.”
Indirect: He told him that he had helped him.
Direct: He said, “You never helped me.”
Indirect: He said that he never helped him.
Direct: I said to you, “You are ill.”
Indirect: I told you that you were ill.
Direct: I said to him, “You killed a snake.”
Indirect: I told him that he had killed a snake.
Rule: Indirect Speech में बदलते समय Third Person के Pronouns में कोई परिवर्तन नहीं होता। जैसे –
Direct: He said, “He will go there.”
Indirect: He said that he would go there.
Direct: He said, “They will go there.”
Indirect: He said that they would go there.”

Change of Tenses

Rule: यदि Reporting Verb भूतकाल में हो तो Reported Speech की क्रिया नीचे लिखे नियमानुसार बदल जाती है –
Go, goes – is changed into went
is, are – is changed into was, were
has or have – is changed into had
has been or have been going – is changed into has been going
went – had gone
was or were going – is changed into had been going
will or shall – is changed into would or should
can – is changed into could
may – is changed into might
has and had – is changed into had
was and were – is changed into had been.

Change of Tenses

Assertive Sentences

Rule. यदि Reporting Verb Present या Future Tense में हो, तो Reported Speech के Verb का Tense नहीं बदलता।
Examples :
Direct : The boy says, “I am playing.”
Indicet : The boy says that he is playing.
Direct: Sita will say, “I write a letter.”
Indirect : Sita will say that she writes a letter.
Direct : The boy said, “I write a letter.”
Indirect : The boy said that he wrote a letter.
Direct : Hari said, “I am playing.”
Indirect : Hari said that he was playing.
Direct : The servant said, “I have swept the room.”
Indirect : The servant said that he had swept the room.
Direct : The boy said, “We have been playing for two hours.”
Indirect : The boys said that they had been playing for two hours.
Direct : The tailor said, “I pressed the clothes.”
Indirect : The tailor said that he had pressed the clothes.
Direct : My mother said, “I was cooking food.”
Indirect : My mother said that she had been cooking food.

Change of Auxiliary Verbs

Rule: of Reporting Verb में Auxiliary Verbs आये हैं, तो उनका परिवर्तन निम्न प्रकार से होगा।

Examples:
Direct: The boy said, “I am a good student.”
Indirect: The boy said that he was a good student.
Direct: Sita said, “I have a pen.”
Indirect: Sita said that she had a pen.
Direct: He said, “I do not go.”
Indirect: He said that he did not go.
Direct: He said, “I cannot go there.”
Indirect: He said that he could not go there.
Direct: I said to him, “I shall teach you.”
Indirect: I told him that I shall (would) teach him.

Exercise

Convert the following sentences into Indirect Speech:

1. I say, “I do my work daily.”
2. Hari says, “I am working hard for the examination.”
3. You say, “I know Ravi and his father.”
4. Gopal said, “I have done my work.”
5. She said, “I cannot learn the lesson so soon.”
6. Anil said, “I daily get up at four in the morning.”
7. My mother said to me, “I am cooking food for you.”
8. These boys said, “We have been playing since moring.”
9. Vinod said, “My brother plays cricket.”
10. The naughty girl said, “I have plucked flowers.”

Interrogative Sentences

Rule: जब प्रश्नवाचक वाक्यों को Direct से Indirect Speech में बदलते हैं, तो निम्नलिखित परिवर्तन किया जाता है –

1. Reporting Verb say अथवा tell को asked में बदल दिया जाता है।
2. यदि प्रशानवाचक वाक्य where, why, what, which, when, who आदि में से किसी एक से आरम्भ होता है, तो that या if का प्रयोग नहीं किया जाता है।
3. यदि वाक्य is, am, are, have, has, had, was, were, will, shall अथवा किसी अन्य सहायक क्रिया से आरम्भ होता है, तो Indirect Speech में if का प्रयोग नहीं किया जाता है।

Example:

A
Direct: He said to the beggar, “What do you want?”
Indirect: He asked the beggar what he wanted.
Direct: The teacher said to Mohan, “Why are you late for school today?”
Indirect: The teacher enquired of Mohan why he was late for the school that day.

В
Direct: I said to him, “Is your father at home?”
Indirect: I asked him if his father was at home.
Direct: The teacher said, “Hari did you bathe this morning?
Indirect: The teacher inquired of Hari if he had bathed that morning.
Direct: Harbans said to you, “Will you accompany me to Simla tomorrow?”
Indirect: Harbans asked you whether you would accompany him to Simla next day.

Exercise

Change the follwoing sentences into Indirect Speech:

1. You said to him, “What can I do for you?”
2. She said to Bimla, “Which school do you attend?”
3. I said to Hari, “How many boys are there in your class?”
4. He said to his friend, “When shall I call on you again?”
5. He said to me, “Where shall I wait for you?
6. Sohan said to Mohan, “Do you play foot-ball daily?”
7. The teacher said to the girl, “Have you done your home-work?”
8. She said to Bimla, “Does this book belong to you?”
9. He said to me, “Are you on speaking terms with your neighbour?”
10. Satish said, “Father, may I go to the picture today?”

Imperative Sentences

Rule: Imperative sentences में आदेश,आग्न्या,शिक्षा तथा प्रार्थना पायी जाती है, जैसे वाक्यों को Indirect मै बदलते समय Said to के स्थान पर ordered, advised, requested, proposed, forbade आदि शब्द लगाओ।
Rule: That का प्रयोग मत करो।
Rule: Verb के पूर्व To लगाओ। “Do not” को “not to” में बदल दो।

Examples:

A
Direct: The teacher said to Balbir, “Look at the black-board.”
Indirect: The teacher asked Balbir to look at the black-board.
Direct: He said to the servant, “Light the lamp atonce.”
Indirect: He ordered the servant to light the lamp atonce.
Direct: The general said to his men, “Stand at ease.”
Indirect: The general ordered his men to stand at ease.
Direct: He said to me, “Give me your knife.”
Indirect: He requesed me to give him my knife.
Direct: I said to him, “Please wait here for me till I return.”
Indirect: I requested him to wait there for me till I returned.
Direct: She said to her maid-servant, “Let the beggar come in.”
Indirect: She ordered her maid-servant to let the beggar come in.”
Direct: He said to his companions, “Let me go on with my work, please.”
Indirect: He requested his companions to let him go with his work.
Direct: He said, “Let us go out for a walk.”
Indirect: He proposed that they should go out for a walk.

Exercises

Change the following sentences into Indirect Speech:

1. I said to Raj, “Show me your new book.”
2. The teacher said to the boys, “Sit down and revise your lesson.”
3. The fox said to the crow, “Please sing me a song.”
4. He said to you, “Do attend my marriage.
5. Father said to me, “Respect your elders.”
6. I said to him, “Be quiet and listen to me.” (Use ‘urge’)
7. “Don’t do that again, or you will get into troubles,” said the old lady.
8. I said to my cousin, “Let us set out for Shimla tomorrow.”
9. Surender said, “Let this boy go out to play.”
10. Guru said to his disciples, “Do not mix with liars.”

Optative and Exclamatory Sentences

Rule: (i) Optative sentences में Reporting Verb के स्थान पर exclaimed with joy, sorrow, surprise आदि का प्रयोग किया जाता है। (ii) Optative Sentences में Reporting Verb के स्थान पर pray, wish आदि शब्दों का प्रयोग किया जाता है।

Examples:

Direct: She said, “May you live long, my daughter!”
Indirect: She wished that her daughter might live long.
Direct: He said to me, “May God bless you with a son!”
Indirect: He wished that God might bless me with a son.
Direct: Sohan said, “O that I were a rich man’s son.”
Indirect: Sohan wished that he were a rich man’s son.
Direct: Jagjit said, “What a terrible storm it is !”
Indirect: Jagjit exclaimed that is was a very terrible storm.
Direct: I said, “How fat he is !
Indirect: I exclaimed that he was very fat.
Direct: “Hurrah ! We are winning!” shouted the boys.
Indirect: The boys exclaimed with joy that they were winning.
Direct: Balbir said, “Alas! All my friends have deserted me.”
Indirect: Balbir exclaimed with sorrow that all his friends had deserted him.
Direct: Bimla said, “Alsa! How foolish I have been !”
Indirect: Bimla confessed with regret that she had been very foolish.
Direct: The Inspector said, “Bravo! Well played, Raj.”
Indirect: The Inspector applauded (or praised) Raj, saying that he had played well.
Direct: “Good night to you all,” said Harnam.
Indirect: Harnam wished them all good night.

Exercises

Change the following sentences into Indirect Speech:

1. They said to me, “May you be happy!”
2. I said to him, “May God help you in his matter !”
3. They said, “How sweetly the Cuckoo sings !”
4. He said to me, “May you succeed !”
5. She said, “Hurrah! I have won a prize in a lottery.”
6. You said, “Alas! I shall ‘fail.”
7. Hari cried, “O that I were dead !”
8. He said, “Alas! What a loss I have suffered !”
9. The man said, “What a fool I have been.”
10. He said, “Bravo! Well done, Ramu.”

MP Board Class 8th English Solutions

MP Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.3

Write the following in decimal form and say what kind of decimal expansion each has:

1. \(\frac{36}{100}\)
2. \(\frac{1}{11}\)
3. 4\(\frac{1}{8}\)
4. \(\frac{3}{13}\)
5. \(\frac{2}{11}\)
6. \(\frac{329}{400}\)

Solution:
1. \(\frac{36}{100}\)
\(\frac{36}{100}\) = 0.36
The decimal expansion is terminating.

2. \(\frac{1}{11}\)

The decimal expansion is non-terminating repeating.

3. 4\(\frac{1}{8}\)

The decimal expansion is terminating.

4. \(\frac{3}{13}\)

The decimal expansion is non-terminating repeating.

5. \(\frac{2}{11}\)

The decimal expansion is non-terminating repeating.

6. \(\frac{329}{400}\)

The decimal expansion is terminating.

Question 2.
You know that \(\frac{1}{7}\) = \(\overline { 0.142857 } \). Can vou predict what the decimal expansions of \(\frac{2}{7}\), \(\frac{3}{7}\), \(\frac{4}{7}\), \(\frac{5}{7}\), \(\frac{6}{7}\) are, without actually doing the long division? If so, how?
[Hint: Study the remainders while finding the value of \(\frac{1}{7}\) carefully.]
Solution:
\(\frac{1}{7}\) = \(\overline { 0.142857 } \)

Question 3.
Expressthe following in the form \(\frac{p}{q}\), wherep and q are integers and q ≠ 0.

1. \(0 . \overline{6}\)
2. \(0 . \overline{oo1}\)

Solution:
1. \(0 . \overline{6}\)
Let x = \(0 . \overline{6}\) …(i)
10x = \(6 . \overline{6}\)
[Multiplying (i) by 10 on both sides] …(ii)
Subtracting (i) from (ii). we get
9x = 6
x = \(\frac{6}{9}\) = \(\frac{2}{3}\)
∴ \(6 . \overline{6}\) = \(\frac{2}{3}\)

2. \(0 . \overline{oo1}\)
1000x = \(1 . \overline{001}\)
[Multiplying (i) by 1000] …(ii)
Subtracting (i) from (ii), we get
999x = 1
x = \(\frac{1}{999}\)
∴ \(0 . \overline{001}\) = \(\frac{1}{999}\)

Question 4.
Express 0.99999….. in the form \(\frac{p}{q}\). Are you surprised by vour answer? With your teacher and classmates, discuss why the answer make sense.
Solution:
0.99999 = \(0 . \overline{9}\)
Let x = 0.9 …(i)
10x = \(9 . \overline{9}\)
[Multiplying (i) by 10] …(ii)
Subtracting (i) from (ii), we get
9x = 9
x = \(\frac{9}{9}\)
∴ \(9 . \overline{9}\) = 1

Question 5.
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of \(\frac{1}{17}\)? Perform the division to check your answer.
Solution:
The maximum number of digits in the repeating block of digits in the decimal expansion \(\frac{1}{17}\) can be 16.
0. 05882352941176470588235294117647….

By Long Division, the number of digits in the repeating block of digits in the decimal expansion of = \(\frac{1}{17}\) = 16
∴ The answer is verified.

Question 6.
Look at several examples of rational numbers in the form \(\frac{p}{q}\) (q ≠ 0),where p and q are integers with no common factors other than 1 and having terminating decimal representation (expansions). Can you guess what property q must satisfy?
Solution:
Examples:

The property that q must satisfy is that the prime factorisation of q have only powers of 2 or powers of 5 or both.

Question 7.
Write three numbers whose decimal expansions are non – terminating non – recurring.
Solution:
0. 01001000100001……..,
0. 20200220002200002…….,
0. 003000300003

Question 8.
Find three different irrational numbers between the rational numbers \(\frac{5}{7}\) and \(\frac{9}{11}\).
Solution:
Irrational numbers between \(\frac{5}{7}\) and \(\frac{9}{11}\)
\(\frac{5}{7}\) = 0.71 and \(\frac{9}{11}\) = 0.81
Three irrational numbers between \(\frac{5}{7}\) and \(\frac{9}{11}\) are
0. 7201001000…
0. 7301001000…
0. 7401001000…

Question 9.
Classify the following numbers as rational or irrational:

1. \(\sqrt{23}\)
2. \(\sqrt{225}\)
3. 0. 3796
4. 7. 478478…
5. 1. 101001000100001…

Solution:

1. \(\sqrt{23}\) is an irrational number
2. \(\sqrt{225}\) = 15, a rational number
3. 0. 3796 is a rational number
4. 7. 478478….. is an irrational number
5. 1. 101001000100001… is an irrational number

MP Board Class 9th Maths Solutions