Laxmi

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Auxiliaries Verbs

A phrasal verb is a verb that is made up of a main verb together with an adverb or a preposition or both, to create a completely new meaning.

• Modals are special verbs which behave irregularly in English.
• These verbs perform several important functions in the formation of sentences.
• They have multiple uses that need to be understood for efficient use of the English language both for written and spoken purposes.

Modals Are Used In/To

• Indicate Tenses
• Frame Questions
• Short answers
• Question Tag
• Active & Passive Voice
• Direct & Indirect speech Negatives

Here Are Some Characteristics Of Modal Verbs :

• They never change their form. You can’t add “s”, “ed”, “ing”…
• They are always followed by an infinitive without “to” (i.e. the bare infinitive.)
• They are used to indicate modality allow speakers to express certainty, possibility, willingness, obligation, necessity, ability etc.,

Examples Of Modal Verbs
Here Is A List Of Modals With Examples:

Exercise
(i) Fill in the blanks with appropriate modal auxiliary verbs.
1. My grandmother is eighty-five, but she _________ still read and write without glasses
Answer:
can

2. _________ I come with you?
Answer:
Shall

3. _________ you help me with the housework, please?
Answer:
Could

4. There was a time when I _________ stay up very late.
Answer:
used to

5. you _________ lose any more weight. You are already slim.
Answer:
need not

6. we _________ not make the first move.
Answer:
must

7. It is snowing outside so I _________ stay at home.
Answer:
should

8. I _________ get you a shawl from Kashmir.
Answer:
shall

9. _________ you mind if I borrowed your car?
Answer:
Would

10. _________ you take care of my dog for a day?
Answer:
Can I Could

11. Our country _________ become a super power by 2025.
Answer:
may

12. She _________ sell her home because she needs money.
Answer:
might

13. _________ we visit Ajanta and Ellora?
Answer:
Shall

14. _________ you come with us?
Answer:
Will

15. The Captain said, ‘Players _________ assemble at the ground at 4 P.M.’
Answer:
must

16. I _________ not be unfair to him.
Answer:
should

17. We _________ do all the work for the common good.
Answer:
ought to

18. You _________ tell the truth.
Answer:
should

19. Excuse me _________ you tell me where the bus station is?
Answer:
can

20. She _________ play the flute and the guitar.
Answer:
can

21. When we were younger, we _________ watch movies all afternoon!
Answer:
used to

22. If you want to camp in the park, you _________ to pay for a permit first.
Answer:
need

23. He _________ go inside, or he will get a terrible sunburn!
Answer:
should

24. He _________ stop drinking so much coffee, or he will make himself sick!
Answer:
must

25. He _________ bring the food very soon.
Answer:
will

26. We _________ definitely win the championship game.
Answer:
must

27. I _________ rather have a cup of tea.
Answer:
would

28. You _________ stop eating pizzas because it is bad for you.
Answer:
should

29. _________ I sit down now?
Answer:
Mav

30. I _________ go now
Answer:
must

31. I _________ tell the truth to the teacher.
Answer:
ought to

32. _________ you pass me the ketchup?
Answer:
Could

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Non-finite verbs (Gerund, Infinitives, Participles)

A non-finite verb (also known as a verbal) is the term used to describe a verb that does not indicate tense. The non-finite verbs are called gerunds, infinitives, and participles.

• Finite verb : A verb that indicates tense and changes according to the subject
• Non-Finite verb : A verb that does not indicate tense and does not change according to the subject

Finite verb
Finite verbs change tense and number according to the subject.

• Arun invited Suresh to his daughter’s birthday.
• Her friends presented the girl with a toy.
• His friend presented a watch.

Non-finite verbs
Non-finite verbs have no subject and do not change according to the tense or number.

Non-finite verbs are broadly classified as follows:
i. Gerunds 1. Viking Is a healthy habit (Present participle used as a noun)
ii. Infinitive 2. I like to walk early in the morning. (lo infinitive)
iii. Present participle 3. These are my walking shoes. (Present participle used as an adjective)
iv. Past participle 4. Having walked a long distance I felt tired

Infinitives and Gerunds
The infinitive is often called as ‘to verb’. It functions as a subject or object.
SUBJECT : (e.g.) To swim is a good exercise. – Subject
OBJECT : (e.g.) I like to swim – Object

Infinitives may be used without to and we call such infinitives plain infinitives or bare infinitives.
(e.g.) She made me do my project.
We use plain/bare infinitives with these models.

shall will do did would make need
may might could must let dare see

The infinitive may function as a subject, direct object, subject complement, adjective, or adverb in a sentence. Although an infinitive is easy to locate because of the to+verb form, deciding what function it has in a sentence depends on the meaning.

(e.g.) To wait seemed foolish when decisive action was required, (subject)
(e.g.) Everyone wanted to go (direct object)
(e.g.) His ambition is to fly, (subject complement)
(e.g.) He lacked the strength to resist, (adjective)
(e.g.) We must study to learn, (adverb)

Gerunds

A gerund is an action word that ends in – ing but functions as a noun

Exercises
(i) Identify the finite and non-finite verbs in the following sentences.
1. I like (finite) to play (non-finite) with my puppy.
2. She works (finite) hard to pass (non-finite) the test.
3. Smoking (non-finite) is prohibited (finite) in the kitchen.
4. He went (finite) to the city to find (non-finite) work.
5. The boy saved (finite) the cat from the dogs.
6. The teacher asked (finite) the students to submit (non-finite) their assignments before they go (finite) home.

(ii) Identify the finite and non-finite verbs in the following sentences and state whether they are infinitives, participles or gerunds.
1. Singing (non-finite – gerund) is (finite verb) his pastime.
2. I like (finite verb) to read (non-finite).
3. It is (finite verb) easy to find (non-finite – infinitive) faults with others.
4. He went (finite verb) to work (non-finite – infinitive) in London.
5. She doesn’t like (finite verb) to do (non-finite – infinitive) anything.
6. I enjoy (finite verb) reading.

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Prepositional Phrases

A prepositional phrase is a modifying phrase consisting of a preposition and its object. Example prepositions: across, in, under, around, beneath, over, up, without etc.

A Prepositional phrase is a group of words that begin with a preposition and help to explain the relationship between two things.

• on the boat
• over the tree
• in the school

Example :
The present inside the big box is mine.

Exercises
Underline the prepositional phrase in each sentence below.

1. We walked op the stairs.
2. My mom took a walk around the block.
3. I looked under my bed.
4. The girl looked behind the door for her friend who was hiding.
5. Don’t leave without your coat.

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Clauses and Phrases

A clause is a group of words that contains both a subject and a predicate (or a verb). There are two types of clauses. They are independent clauses and dependent clauses.

Examples
1. Kalpana wants to buy a phone, but she does not have enough money.
(Independent Clause) (Independent Clause)

2. If you don’t study well, you won’t pass the exam.
(Dependent Clause) (Independent Clause)

3. Kavin bought a car which was too expensive.
(Independent Clause) (Dependent Clause)

4. San Jai is a talented player though he is out of form.
(Independent Clause) (Dependent Clause)

Independent Clauses also known as main clauses, are complete sentences. They can stand alone and express a complete thought.

Examples :

• I need a book.
• Mary prefers coffee.
• Ram is a good volleyball player.

Dependent Clauses also known as subordinate clauses contain a subject and a predicate, but they do not express a complete thought.

Examples:

• When it is raining
• Because you were late
• After you go to school

There are three main types of dependent clauses: adjective, adverb, and noun.

An adjective clause describes or gives more information about a noun—tells us which one, what kind, or how many.
Example :
The book that I left on the bus belongs to Mr. Baskar.

An adverb clause describes or gives more information about the verb—tells us when, where, how, to what extent, or under what condition something is happening.

Example :
She was happy because her father gave her a watch.
A noun clause takes the place of a noun in the sentence.

Example :
This is the best route that I know.

Phrases
A phrase is a group of words that forms a meaningful unit, but it is not a complete sentence. In other words, it does not have a subject or a verb.

• the black hat
• blown away
• in the wind

Example :
The red umbrella was blown away in the wind.

There are several kinds of phrases in the English language. Some of the common phrases are described below.

NOUN PHRASES
A Noun Phrase is a group of words made up of a noun and its modifiers.

• the white car
• my English teacher
• the book shop

Example :
The pink house is for sale.

VERB PHRASES
A Verb phrase is a group of words made up of a verb, helping verbs, and modifiers.

• ran quickly to catch
• filled with horror
• dedicated to

Example :
You have woken up everyone in the house.

Exercises
(i) Choose either phrase or clause from the group of words.
1. He works hard every day. (Clause / Phrase)
Answer:
Clause

2. After a good day. (Clause / Phrase)
Answer:
Phrase

3. If I need to call you. (Clause / Phrase)
Answer:
Clause

4. In a dark and dangerous hallway. (Clause / Phrase)
Answer:
Phrase

5. Before the next light. (Clause / Phrase)
Answer:
Phrase

6. Because it’s the right thing to do. (Clause / Phrase)
Answer:
Clause

7. As quickly as possible. (Clause / Phrase)
Answer:
Phrase

8. This car’s not working. (Clause / Phrase)
Answer:
Clause

9. Working for himself. (Clause / Phrase)
Answer:
Phrase

10. Whenever it gets cold. (Clause / Phrase)
Answer:
Clause

Choose either Dependent or Independent for the group of words.
1. Because it’s the best solution. (Independent / Dependent)
Answer:
Dependent

2. Working at this job is a lot of fun. (Independent / Dependent)
Answer:
Independent

3. It doesn’t really interest me. (Independent / Dependent)
Answer:
Independent

4. I should have given her a ride. (Independent / Dependent)
Answer:
Independent

5. After the movie is over. (Independent / Dependent)
Answer:
Dependent

6. If he ever calls. (Independent / Dependent)
Answer:
Dependent

7. Whenever I have the time. (Independent / Dependent)
Answer:
Dependent

8. There could be a problem. (Independent / Dependent)
Answer:
Independent

9. Since the last time they visited. (Independent / Dependent)
Answer:
Dependent

10. Whenever it gets cold (Independent / Dependent)
Answer:
Dependent

Students can Download Maths Chapter 2 Algebra Ex 2.5 Questions and Answers, Notes Pdf, Samacheer Kalvi 8th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 2 Chapter 2 Algebra Ex 2.5

Miscellaneous Practice Problems

Question 1.
The sum of three numbers is 58. The second numberis three times of two-fifth of the first number and the third number is 6 less than the first number. Find the three numbers.
Solution:
Here what we know
a + b + c = 58 (sum of three numbers is 58)
Let the first number be ‘x’
b = a + 3 (the second number is three times of \(\frac{1}{2}\) of the first number)
b = 3 x \(\frac{2}{5}\)x = \(\frac{6}{5}\)x
Third number = x – 6
Sum of the numbers is given as 58.
∴ x + \(\frac{6}{5}\)x + (x – 6) = 58
Multiplying by 5 throughout, we get
5 × x + 6x + 5 × (x – 6) = 58 x 5
5x + 6x + 5x – 30 = 290
∴ 16x = 290 + 30
∴ 16x = 320
∴ x = \(\frac{320}{16}\)x = 20
Answer:
1st number =20
2nd number = 3 x \(\frac{2}{5}\) x 20 = 24
3rd number = 24 – 6 = 14

Question 2.
In triangle ABC, the measure of ∠B is two third the measure of ∠A. The measure of ∠C is 20° more than the measure of ∠A. Find the measures of the three angles.
Solution:
Let angle ∠A be a°
Given that ∠B = \(\frac{2}{3}\) x ∠A = \(\frac{2}{3}\)a
& given ∠C = ∠A + 20 = a + 20
Since A, B & C are angles of a triangle, they add up to 180° (∆ property)
∠A + ∠B + ∠C = 180°
a + \(\frac{2}{3}\) a + a + 20 = 180°
\(\frac{3a+2a+3a}{3}\) + 20 = 180°
\(\frac{8a}{3}\) = 180 – 20 = 160°

∠C = 80°

Question 3.
Two equal sides of an isosceles triangle are 5y – 2 and 4y + 9 units. The third side is 2y + 5 units. Find y and the perimeter of the triangle.
Solution:
Given that 5y – 2 & 4y + 9 are the equal sides of an isosceles triangle.
The 2 sides are equal

∴ 5y – 4y = 9 + 2 (by transposing)
∴ y = 11
∴ 1st side = 5y – 2 = 5 x 11-2 = 55 – 2 = 53
2nd side = 53
3rd side = 2y + 5 = 2 x 11 + 5 = 22 + 5 = 27
Perimeter is the sum of all 3 sides
∴ P = 53 + 53 + 27 = 133 units

Question 4.
In the given figure, angle XOZ and angle ZOY form a linear pair. Find the value of x.

Solution:
Since ∠XOZ & ∠ZOY form a linear pair,
by property, we have their sum to be 180°
∴ ∠XOZ + ∠ZOY = 180°
3x – 2 + 5x + 6 = 180°
8x + 4 = 180 = 8x = 180 – 4
∴ 8x = 176 ⇒ x = \(\frac{176}{8}\) ⇒ x = 22°
XOZ = 3x – 2 = 3 x 22 – 2 = 66 – 2 = 64°
YOZ = 5x + 6 = 5 x 22 + 6
= 110 + 6 = 116

Question 5.
Draw a graph for the following data:

Does the graph represent a linear relation?
Solution:
Graph between side of square & area

When we plot the graph, we observe that it is not a linear relation.

Challenging Problems

Question 6.
Three consecutive integers, when taken in increasing order and multiplied by 2, 3 and 4 respectively, total up to 74. Find the three numbers.
Solution:
Let the 3 consecutive integers be ‘x’, ’x + 1 & ‘x + 2’
Given that when multiplied by 2, 3 & 4 respectively & added up, we get 74

Simplifying the equation, we get
2x + 3x + 3 + 4x + 8 = 74
9x + 11 = 74
9x = 63 ⇒ x = \(\frac{63}{9}\) = 7
First number = 7
Second numbers = x + 1
Third numbers = x + 2
∴ The numbers are 7, 8 & 9

Question 7.
331 students went on a field trip. Six buses were filled to capacity and 7 students had to travel in a van. How many students were there in each bus?
Solution:
Let the number of students in each bus be ‘x’
number of students in 6 buses = 6 × x = 6x
Apart from 6 buses, 7 students went in van
A total number of students is 331
∴ 6x + 7 = 331
∴ 6x = 331 – 7 = 324
∴ x = \(\frac{324}{6}\) = 54
∴ There are 54 students in each bus.

Question 8.
A mobile vendor has 22 items, some which are pencils and others are ball pens. On a particular day, he is able to sell the pencils and ball pens. Pencils are sold for ₹ 15 each and ball pens are sold at ₹ 20 each. If the total sale amount with the vendor is ₹ 380, how many pencils did he sell?
Solution:
Let vendor have ‘p’ number of pencils & ‘b’ number of ball pens
Given that total number of items is 22
∴ p + b = 22
Pencils are sold for ₹ 15 each & ball pens for ₹ 20 each
total sale amount = 15 x p + 20 x b
= 15p + 20b which is given to be 380.
∴ 15p + 20b = 380
Dividing by 5 throughout,
\(\frac{15p}{5}\) + \(\frac{20b}{5}\) = \(\frac{380}{5}\)
⇒ 3p + 4b = 76
Multiplying equation (1) by 3 we get
3 x 7 + 3 x b = 22 x 3
⇒ 3p + 3b = 66
Equation (2) – (3) gives

∴ b = 10
∴ p = 12
He sold 12 pencils

Question 9.
Draw the graph of the lines y = x, y = 2x, y = 3x and y = 5x on the same graph sheet. Is there anything special that you find in these graphs?
Solution:

1. y = x
2. y = 2x
3. y = 3x
4. y = 5x

1. y = x
When x = 1, y = 1
x = 2, y = 2
x = 3, y = 2

2. y = 2x
When x = 1, y = 2
X = 2, y = 4
X = 3, y = 6

3. y = 3x
when x = 1, y = 3
x = 2, y = 6
x = 3, y = 9

4. y = 5x
When x = 1, y = 5
x = 2, y = 10
x = 3, y = 15

When we plot the alijpve points & join the points to form line, we notice that the lines become progressively steeper. In other words, the slope keeps increasing.

Question 10.
Consider the number of angles of a convex polygon and the number of sides of that polygon. Tabulate as follows:

Use this draw a graph illustrating the relations hip between the number of angles and the number of sides of a polygon.
Solution:
Angles:

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Prepositional Verbs

Some verbs are usually followed by prepositions before the object of the verb.

Examples:
i. The kids the hilarious antics of the clown.
Answer:
laughed at

ii. Fathima stay at a hotel, when she visited Mumbai.
Answer:
planned to

iii. I have pressing matters to in Kolkata.
Answer:
attend to

iv. I the healing power of a mother’s touch.
Answer:
believe in

v. She was so happy in life that she could not more.
Answer:
ask for

vi. The elderly couple their pets as they do for their children.
Answer:
care for

vii. I everything you’ve said.
Answer:
agree with

Exercises
(i) Frame sentences using the prepositional verbs given in the box.

1. Parents ________ their children whole-heartedly.
Answer:
care for

2. He ________ his father’s forgiveness.
Answer:
asked for

3. I don’t ________ you.
Answer:
agree with

4. Don’t ________ him.
Answer:
laugh at

5. I ________ God.
Answer:
believe in

Choose the correct phrase to complete the sentence.
1. ________ Pongal, we have long holidays.
(a) In spite of (b) Even though (c) On account of

2. My father knows Hindi ________ English.
(a) in addition to (b) on account of (c) in case of

3. ________ her poor health, she did not attend the meeting.
(a) Because of (b) In spite of (c) In the event of

4. ________ walking fast, he missed the train.
(a) In the event of (b) On account of (c) In spite of

5. ________ his riches, he is not happy.
(a) Because of (b) In spite of (c) Owing to

6. ________ the book, I returned it to the library.
(a) Having read (b) Having been reading (c) Having reading

7. ________ his hard work, Mani will pass.
(a) On account of (b) In spite of (c) In the event of

8. ________ it rained, the teams continued to play the match.
(a) In the event of (b) On account of (c) Even though
Answer:
(c) Even though

9. The flights were delayed ________ thick fog.
(a) despite (b) even though (c) due to
Answer:
(c) due to

10. The Kabadi match continued ________ heavy rains.
(a) in the event of (b) in spite of (c) because of

(iii) Given below is a picture of a carnival. Complete filling in the blanks with appropriate prepositions.

Fairs and festivals form an integral part of the culture of Tamil Nadu. They are an excellent platform to promote and preserve the vibrant art and culture of the Tamils.

A thiruvizha is a source of excitement and thrill for villagers. The village thoroughfare wears a festival look, as the open spaces are cleaned, spruced up and decorated (a) ________ colorful streamers.

People throng the premises (b) ________ catch a glimpse (c) ________ their village deity (d) ________ a magnificently decorated chariot, and pay their respects. There is a big crowd (e) ________the food stalls that serve free piping hot sakkarai pongal (sweet pongal), lemon rice and curd rice.

People (f) ________ nearby villages and towns display their wares attractively, and call out loudly (g) ________ the people (h) ________ buy their wares. Cotton candy, cut raw mangoes smothered (i) ________ salt and chilly powder, boiled groundnuts, murukku, sweets, buttermilk, etc are sold. Men, women, grandmas, grandpas, and little children, dressed (j) ________ their best clothes, enjoy the Thiruvizha greatly.

You can hear the shrieks (k) ________ happy children enjoying the rides on Ferris wheels and carousels, elders looking (l) ________ each other with smiles on their faces.

The entire day is spent (m) ________ fun and gaiety. All the village people irrespective of their age, look forward (n) ________ the thiruvizha every year.
Answers:
(a) with (b) to (c) of (d) on (e) in (f) from (g) to (h) to (i) with (j) in (k) of (l) at (m) in (n) to

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Preposition

Prepositions are short words (on, in, to) that usually stand in front of nouns (sometimes also in front of gerund verbs).

There are hardly any rules as to when to use which preposition. The only way to learn prepositions is looking them up in a dictionary, reading a lot in English and learning useful phrases by heart.

The following table contains rules for some of the most frequently used prepositions in English:

Prepositions – Place Position And Direction

Other Important Prepositions

List Of Prepositions
While there are only about 150 prepositions in the English language, these words are among the most important. Without them, the sentences we speak, read, and write would be difficult to understand. The following list of prepositions is not a complete one, however, it is among the most comprehensive lists of prepositions available anywhere.

Exercises
(i) Fill the gap with the correct prepositions.
1. We live Chennai.
Answer:
in

2. Would you like to go the library?
Answer:
to

3. No, thanks. I was the library yesterday.
Answer:
at

4. We are going a holiday next week.
Answer:
on

5. There is a bridge the river.
Answer:
across

6. The train Chennai Madurai is the station.
Answer:
from, to, in

7. my wall, there are many picture postcards.
Answer:
on

8. Who is the person in this picture?
Answer:
in

9. Come the hall, we shall watch TV.
Answer:
into

10. Elgin lies 530 meters sea level.
Answer:
above

11. The bone was the dog.
Answer:
for

12. We are going on vacation August.
Answer:
on, in

13. Please put the vase the table.
Answer:
on

14. received a present Janaki.
Answer:
from

15. School begins Monday.
Answer:
on

(ii) Complete the exercise with appropriate prepositions.
1. Compare your answers your partner.
Answer:
with

2. This key holder is very special me.
Answer:
for

3. Apples and oranges are the same box.
Answer:
in

4. Write me soon.
Answer:
to

5. Have you got a piece paper?
Answer:
of

6. What’s the calculator for? It is my exam.
Answer:
for

7. I’m tall black hair and brown eyes.
Answer:
with

8. We have a house a big backyard.

9. I come a big family.
Answer:
with

10. Match the pictures the names.
Answer:
from

11. Is your house the country?
Answer:
with

12. Guess what I have my hand?
Answer:
in

13. I have to color pens. what you?
Answer:
about

(iii) Fill in the prepositions.
1. The cat hid the door.
(a) behind (b) under (c) on
Answer:
(a) behind

2. Mv uncle will visit me May.
(a) at (b) in (c) on
Answer:
(b) in

3. Wait there I come.
(a) behind (b) until (c) near
Answer:
(b) until

4. Hang the charts the wall.
(a) in (b) on (c) by
Answer:
(b) on

5. I have been practicing morning.
(a) by (b) for (c) since
Answer:
(c) since

6. The baby has been sleeping for a long time.
(a) for (b) since (c) at
Answer:
(a) for

7. The work will be over this evening.
(a) on (b) by (c) in
Answer:
(b) by

8. We could not get help anyone.
(a) from (b) till (c) in
Answer:
(a) from

9. The ladder is placed the wall.
(a) on (b) upon (c) against
Answer:
(c) against

10. The people stood the road to watch the procession go by.
(a) across (b) along (c) on
Answer:
(b) along

Students can Download Maths Chapter 3 Algebra Additional Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 3 Algebra Additional Questions

Additional Questions and Answers

Exercise 3.1

Question 1.
Simplify the following and write the answer in Exponential form.
(i) 3² × 3⁴ × 3⁸
(ii) 6¹⁵ ÷ 6¹⁰
(iii) a³ × a²
(iv) 7^x × 7²
(v) (5²)³ ÷ 5³
Solution:
(i) 3² × 3⁴ × 3² = 3²⁺⁴⁺⁸ = 3¹⁴ [∵ a^m × aⁿ = a^m+n]
So 3² × 3⁴ × 3² = 3¹⁴
(ii) 6¹⁵ ÷ 6¹⁰ = 6^15-10 = 6⁵ [∵ a^m × aⁿ = a^m-n]
(iii) a³ × a² = a³⁺² = a⁵
(iv) 7^x × 7² = 7^x+2
(v) (5²)³ ÷ 5³ = 5^2×3 ÷ 5³ = 5⁶ ÷ 5³ [∵ (a^m)ⁿ = a^m×n]

Question 2.
Express the following as a product of factors only in exponential form
(i) 108 × 192
(ii) 270
(iii) 729 × 64
(iv) 768
Solution:
(i) 108 × 192
108 = 2 × 2 × 3 × 3 × 3
192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

∴ 108 × 192 = (2 × 2 × 3 × 3 × 3) ×
(2 × 2 × 2 × 2 × 2 × 2 × 3)
= 2⁸ × 3⁴
Thus 108 × 192 = 2⁸ × 3⁴

(ii) 270
We have 270 = 2 × 3 × 3 × 3 × 5

= 2¹ × 3³ × 5¹
= 2 × 3³ × 5
So 270 = 2 × 3³ × 5

(iii) 729 × 64
729 = 3 × 3 × 3 × 3 × 3 × 3
64 = 2 × 2 × 2 × 2 × 2 × 2

729 × 64 = (3 × 3 × 3 × 3 × 3 × 3)
× (2 × 2 × 2 × 2 × 2 × 2)
= 3⁶ × 2⁶
∴ 729 × 64 = 3⁶ × 2⁶

(iv) 768
We have 768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

= 2⁸ × 3¹
= 2⁸ × 3
Thus 768 = 2⁸ × 3

Question 3.
Identify the greater number, wherever possible in each of the following.
(i) 5³ or 3⁵
(ii) 2⁸ or 8²
(iii) 100² or 2¹⁰⁰⁰
(iv) 2¹⁰ or 10²
Solution:
(i) 5³ or 3⁵ 5³ = 5 × 5 × 5 = 125
3⁵ = 3 × 3 × 3 × 3 × 3 = 243
243 > 125 ∴ 3⁵ > 5³

(ii) 2⁸ or 8² 2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
8² = 8 × 8 = 64
256 > 64 ∴ 2⁸ > 8²

(iii) 100² or 2¹⁰⁰⁰
We have 100² = 100 × 100 = 10000
2¹⁰⁰ = (2¹⁰)¹⁰ = (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)¹⁰
= (1024)¹⁰ = [(1024)²]⁵
= (1024 × 1024)⁵ = (1048576)⁵
Since 1048576 > 10000
(1048576)⁵ > 10000
i.e., (1048576) > 100²
(2¹⁰)¹⁰ > 100²
2¹⁰⁰ > 100²

(iv) 2¹⁰ or 10²
We have 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
10² = 10 × 10 = 100
Since1 1024 > 100
2¹⁰ > 10²

Exercise 3.2

Question 1.
Find the unit digit of the following exponential numbers.
(i) 255²²³
(ii) 8111¹⁰⁰⁰
(iii) 4866⁴³¹
Solution:
(i) 255²²³
Unit digit of base 255 is 5 and power is 223.
Thus the unit digit of 255²²³ is 5.

(ii) 8111¹⁰⁰⁰
Unit digit of base 8111 is 1 and power is 1000.
Thus the unit digit of 8111¹⁰⁰⁰ is 1.

(iii) 4866⁴³¹
Unit digit of base 4866 is 6 and power is 431.
Thus the unit digit of 4866⁴³¹ is 6.

Question 2.
Find the unit digit of the numbers
(i) 1844⁶⁷¹
(ii) 1564¹⁰⁰
Solution:
(i) 1844⁶⁷¹
Unit digit of base 1844 is 4 and the power is 671 (odd power)
Therefore unit digit of 1844⁶⁷¹ is 4

(ii) 1564¹⁰⁰
Unit digit of base 1564 is 4 and the power is 100 (even power)
Therefore unit digit of 1564¹⁰⁰ is 6.

Question 3.
Find the unit digit of the numbers
(i) 999²²²
(ii) 1549⁷⁷⁷
Solution:
(i) 999²²²
Unit digit of base 999 is 9 and the power is 222 (even power).
Therefore, unit digit of 999²²² is 1.

(ii) 1549⁷⁷⁷
Unit digit of base 1549 is 9 and the power is 777 (odd power).
Therefore, unit digit of 1549⁷⁷⁷ is 9.

Question 4.
Find the unit digit of 1549¹⁰¹ + 6541²⁰
Solution:
1549¹⁰¹ + 6541²⁰
In 1549¹⁰¹, the unit digit of base 1549 is 9 and power is 101 (odd power).
Therefore, unit digit of the 1549¹⁰¹ is 9.
In 6541²⁰, the unit digit of base 6541 is 1 and power is 20 (even power).
Therefore, unit digit of the 6541²⁰ is 1.
∴ Unit digit of 1549¹⁰¹ + 6541²⁰ is 9 + 1 = 10
∴ Unit digit of 1549¹⁰¹ + 6541²⁰ is 0.

Exercise 3.3

Question 1.
Find the degree of the following polynomials.
(i) x⁵ – x⁴ + 3
(ii) 2 – y⁵ – y³ + 2y⁸
(iii) 2
(iv) 5x³ + 4x² + 7x
(v) 4xy + 7x²y + 3xy³
Solution:
(i) x⁵ – x⁴ + 3
The terms of the given expression are x⁵, -x⁴, 3.
Degree of each of the terms : 5, 4, 0
Term with highest degree: x⁵
Therefore degree of the expression in 5.

(ii) 2 – y⁵ – y³ + 2y⁸
The terms of the given expression are 2, -y⁵ ,-y³, 2y⁸.
Degree of each of the terms : 0, 2, 3, 8.
Term with highest degree: 2y⁸
Therefore degree of the expression in 8.

(iii) 2
Degree of the constant term is 0.
∴ Degree of 2 is 0.

(iv) 5x³+ 4x² + 7x
The terms of the given expression are 5x³, 4x², 7x
Degree of each of the terms : 3, 2, 1
Term with highest degree: 5x³
Therefore degree of the expression in 3.

(v) 4xy + 7x²y + 3xy³
The terms of the given expression are 4xy , 7x²y, 3xy³
Degree of each of the terms : 2, 3, 4
Term with highest degree: 3xy³
Therefore degree of the expression in 4.

Question 2.
State whether a given pair of terms in like or unlike terms.
(i) 1,100
(ii) -7x,\(\frac { 5 }{ 2 } \)x
(iii) 4m²p, 4mp²
(iv) 12xz, 12x²z²
Solution:
(i) 1, 100 is a pair of like terms. [∵ 1 = x⁰ and 100 = 100 x⁰]
(ii) -7x, \(\frac { 5 }{ 2 } \)x is a pair of like terms.
(iii) 4m²p, Amp is a pair of unlike terms.
(iv) 12xz, 12x²z² is a pair of unlike terms.

Question 3.
Subtract 5a² – 7ab + 5b² from 3ab – 2a² – 2b² and find the degree of the expression
Solution:
(i) We have (3ab – 2a² – 2b²) – (5a² – 7ab + 5b²)
= 3ab – 2a² – 2b² – 5a² + 7ab – 5b²
= (3ab + 7ab) + (- 2 – 5)a² + (- 2 – 5)b²
= 10 ab + (-7)a² + (-7)b²
= 10ab – 7a² – 7b²
Degree of the expression is 2.

Question 4.
Add x² – y² -1,y² – 1 – x², 1 – x² – y² and find the degree of the expression.
Solution:
We have (x² – y² – 1) + (y² – 1 – x²) + (1 – x² – y²)
= x² – y² – 1 + y² – 1 – x² + 1 – x² – y²
= (x² – x² – x²) + (-y² + y² – y²) + (- 1 – 1 + 1)
= (1 – 1 – 1)x² + (- 1 + 1 – 1)y² + ( – 2 + 1)
= (- 1) x² + (- 1)y² + (-1) = – x² – y² – 1
Degree of the expression is 2.

Question 5.
Find the degree of the terms
(i) x²
(ii) 4xyz
(iii) \(\frac{7 x^{2} y^{4}}{x y}\)
(iv) \(\frac{x^{2} \times y^{2}}{x \times y^{2}}\)
Solution:
We have
(i) x²
The exponent in x² is 2. ∴ Degree of the term is 2.

(ii) 4xyz
In 4xyz the sum of the powers of x, y and z as 3.

(iii) \(\frac{7 x^{2} y^{4}}{x y}\)
We have \(\frac{7 x^{2} y^{4}}{x y}\) = 7x^2-1 y^4-1 = 7x¹y³ [Since \(\frac{a^{m}}{a^{n}}\) = am-n]
In 7 x¹ y³ the sum of the poweres of x and y is 4(1 + 3 = 4)
Thus degree of the expression is 4.

(iv) \(\frac{x^{2} \times y^{2}}{x \times y^{2}}\)
We have \(\frac{x^{2} \times y^{2}}{x \times y^{2}}\) = x^2-1 y^2-2 = x¹ y⁰ = x¹ [∵ y⁰ = 1]
The exponent of the expression is 1.

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Vocabulary Anagrams

An Anagram is a word or a phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once.

Exercise
Write an anagram for the words given
1. Write an anagram for the word ‘ripples’.
Answer:
slipper

2. Write an anagram for the word ‘talks’.
Answer:
stalk

3. Write an anagram for the word ‘tough’.
Answer:
ought

4. Write an anagram for the word ‘trams’.
Answer:
smart

5. Write an anagram for the word ‘times’.
Answer:
items

6. Write an anagram for the word ‘there’.
Answer:
three

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Vocabulary Prefix / Suffix

Prefixes are added to the beginning of a root word while suffixes are added to the end.
Prefixes

Exercises
Write the root word for the suffixes.
1. Write the root word for the suffix ‘ment’
Answer:
immobile

2. Write the root word for the suffix ‘al’.
Answer:
unnatural

3. Write the root word for the suffix ‘ful’.
Answer:
ignoble

4. Write the root word for the suffix ‘less’.
Answer:
misplaced

5. Write the root word for the suffix ‘ive’.
Answer:
enclose, encircle

6. Write the root word for the suffix ‘ian’.
Answer:
irrelevant

Suffixes

Exercises
Write the root word for the suffixes.
1. Write the root word for the suffix ‘ment’.
Answer:
development

2. Write the root word for the suffix ‘al’.
Answer:
approval

3. Write the root word for the suffix ‘ful’.
Answer:
painful

4. Write the root word for the suffix ‘less’.
Answer:
careless

5. Write the root word for the suffix ‘ive’.
Answer:
attract

6. Write the root word for the suffix ‘ian’.
Answer:
electrician. musician