MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8

Assume π = \(\frac{22}{7}\), unless stated otherwise.

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Question 1.
Find the volume of a sphere whose radius is

(i) 7 cm
(ii) 0.63 m

Solution:
(i) Here, radius (r) = 7 cm
∴ Volume of the sphere
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8 img-1
Thus, the required volume is 1.05 m3 (approx.)

Question 2.
Find the amount of water displaced by a solid spherical ball of diameter

(i) 28 cm
(ii) 0.21 m

Solution:
(i) Diameter of the ball = 28 cm
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8 img-2

Question 3.
The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8,9 g per cm3.
Solution:
d = 4.2 cm
⇒ r = 2.1 cm
Density (D) = 8.9 gm/cm3
Volume of metallic ball = \(\frac{4}{3}\) x \(\frac{22}{7}\) x 2.1 x 2.1 x 2.1 = 38.808 cm3
Mass = D x V
= 8.9 x 38.808
= 345.3912 gm.

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Question 4.
The diameter of the moon is approximately one – fourth of the diameter of the earth. What fraction of the volume of the earth is volume of the moon?
Solution:
Let d and d be the diameter of moon and earth respectively.
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8 img-3

Question 5.
How many liters of milk can hemispherical bowl of diameter 10 J cm hold?
Solution:
d = 10.5 cm
r = 5.25 cm
Volume of the hemisphere = \(\frac{2}{3}\) x \(\frac{22}{7}\) x 5.25 x 5.25 x 0.25
= 303.18 cm3
= 0.303 l

Question 6.
A hemispherical tank is made up of an iron sheet 1cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
Solution:
t = 1 cm
r1 = 1 m = 100 cm
r2 = r1 + t = 100 + 1 = 101 cm
Outer volume of tank (V2) = \(\frac{2}{3}\) πr22
Inner volume of tank (V1) = \(\frac{2}{3}\) πr13
Volume of iron = Outer volume – inner volume
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8 img-4
= 0.06348 ml

Question 7.
Find the volume of a sphere whose surface area is 154 cm2.
Solution:
Surface area = 154 cm2
Surface area of sphere = 4πr2
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8 img-5

Question 8.
A dome of a building is in the from of a hemisphere. From inside, it was White – washed at the cost of ₹ 498.96. If the cost of white-washing is ₹ 2.00 per square meter, find the

(i) inside surface area of the dome.
(ii) volume of the air inside the dome.

Solution:
(i) Cost = ₹ 498.96
Rate = ₹ 2 per m2
Inside surface area = \(\frac{498.96}{2}\) = 249.48 m2
Inside curved surface area = 2πr2
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8 img-6

Question 9.
Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S’. Find the

(i) radius r’ of the new sphere
(ii) ratio of S and S’.

Solution:
Let V and be the volume of old and new sphere respectively
(i) Volume of new sphere = 27 x volume of old sphere
V1 = 27 x V
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8 img-7

Question 10.
A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule?
Solution:
d = 3.5 mm
r = 1.75 mm
Volume of medicine needed to fill the capsule
= \(\frac{4}{3}\)πr3
= \(\frac{4}{3}\) x \(\frac{22}{7}\) x 1.75 x 1.75 x 1.75
= 22.458 mm3
= 22.46 mm3 (Approx.)

MP Board Class 9th Maths Solutions

MP Board Class 9th General English Grammar Translation

MP Board Class 9th General English Grammar Translation

Continuous Tenses

(1) Present Continuous Tense Structure-am/is/are+Verb+ing+Object etc.

(A) Affirmative Sentences

(i) मैं खाना रहा हूँ।
I am eating food.

(ii) हम नावें तैरा रहे हैं।
We are floating boats.

(iii) रीना बैडमिंटन खेल रही है।
Reena is playing badminton.

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(B) Negative Sentences

(i) तुम सुन नहीं रहे हो।
You are not listening.

(ii) वह खाना नहीं पका रही है।
She is not cooking food.

(iii) वे हँस नहीं रहे हैं।
They are not laughing.

(C) Interrogative Sentences

(i) क्या वे खेल रहे हैं?
Are they playing?

(ii) राम क्या कर रहा है?
What is Ram doing?

(iii) आप क्यों रो रहे हैं?
Why are you crying?

(iv) क्या वो आ रहा है?
Is he coming?

(2) Past Continuous Tense
Structure-Subject + was/were + Verb + ing + object etc.

(A) Affirmative Sentences

(i) मैं चित्र बना रहा था।
I was drawing picture.

(ii) वे सो रहे थे।
They were sleeping.

(iii) वह दौड़ रही थी।
She was running.

(B) Negative Sentences

(i) पानी नहीं बरस रहा था।
It was not raining.

(ii) मैं चिल्ला नहीं रहा था।
I was not shouting.

(iii) गाड़ी चल नहीं रही थी।
Țhe vehicle was not moving.

(C) Interrogative Sentences

(i) तुम कहाँ जा रहे थे?
Where were you going?

(ii) शीला क्यों हँस रही थीं?
Why was Sheela laughing?

(iii) वे क्या कर रहे थे?
What were they doing?

(3) Future Continuous Tense

Structure-Subject + shall/will + be + Verb + ing + object etc.

(A) Affirmative Sentences

(i) पानी बरस रहा होगा।
It will be raining.

(ii) हम खेल रहे होंगे।
We shall be playing.

(iii) वह पत्र लिख रहा होगा।
He will be writing a letter.

(B) Negative Sentences

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(i) वे नहीं आ रहे होंगे।
They will not be coming.

(ii) वह पढ़ नहीं रहा होगा।
He will not be reading.

(iii) मैं खाना नहीं खा रहा हूँगा।
I shall not be eating food.

(C) Interrogative Sentences

(i) वह कैसे खेल रहा होगा?
How will he be playing?

(ii) कौन सो रहा होगा?
Who will be sleeping?

(iii) क्या वह पढ़ रहा होगा?
Will he be playing?

Indefinite Tense

(4) Present Indefinite Tense

(A) Affirmative Sentences Structure -Subject +Verb I/Verb I +s, es, ies + Object

(i) मैं पुस्तक पढ़ता हूँ।
I read the book.

(ii) हम बस को रोकते हैं।
We stop the bus.

(iii) तुम फल लाते हो।
You bring fruit.

(iv) मोहन कानपुर में रहता है।
Mohan lives in Kanpur.

(B) Negative Sentences
Structure-Subject + do not/does not + Verb I + Object

(i) मैं वहाँ नहीं जाता हूँ।
I do not go there.

(ii) तुम कहानी नहीं कहते हो।
You do not tell a story.

(iii) वह यहाँ नहीं आता है।
He does not come here.

(C) Interrogative Sentences
Structure-Do Does + Subject + (not) Verb I + Object etc.?

(i) क्या मैं झूठ बोलता हूँ?
Do I tell a lie?

(ii) क्या तुम मुझे जानते हो?
Do you know me?

(iii) क्या वह पतंग उड़ाता है?
Does he fly kite?

(5) Past Indefinite Tense

(A) Affirmative Sentences Structure-Subject + Verb II + Object etc.

(i) मैंने एक लाल पक्षी देखा।
I saw a red bird.

(ii) हमने टीवी खरीदा।
We bought a TV.

(iii) शाहजहाँ ने ताजमहल बनवाया।
Shahjahan got the Taj Mahal built.

(iv) रहीम ने हॉकी खेली।
Rahim played hockey.

(v) तुमने कार चलाई।
You drove the car.

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(B) Negative Sentences
Structure-Subject + did not + Verb I+ Object etc.

(i) मैंने फल नहीं खाये।
I did not eat fruits.

(ii) तुमने हिन्दी का अध्ययन नहीं किया।
You did not study Hindi.

(iii) हमने कपड़े नहीं सुखाये।
We did not dry the clothes.

(C) Interrogative Sentences
Structure-Did + Subject +(not) Verb I + Object etc.?

(i) क्या मैंने तुमसे कभी झगड़ा किया?
Did I ever quarrel with you?

(ii) क्या तुमने फीस चुकाई?
Did you pay the fee?

(ii) क्या शीला ने फूल नहीं सूंघे?
Did Sheela not smell flowers?

(6) Future Indefinite Tense

Structure-Subject + shall/will + Verb I + Object etc. .

(i) मैं एक पत्र लिखूगा।
I shall write a letter.

(ii) हम कल झाँसी जायेंगे।
We shall go to Jhansi tomorrow.

(iii) हम अगले वर्ष नैनीताल जायेंगे।
We shall go to Nainital next year.

(iv) तुम यहाँ नहीं बैठोगे।
You will not sit here.

(v) क्या आप मेरी मदद करेंगे?
Will you help me?

(7) Present Perfect Tense

Structure -Subject + have/has + Verb III + Object etc.

(i) मैंने यह पुस्तक पढ़ ली है।
I have read this book.

(ii) दिनेश ने यह चित्र देखा नहीं है।
Dinesh has not seen this picture.

(iii) सूर्य अस्त हो चुका है।
The sun has set.

(iv) क्या वे भोपाल गये हैं?
Have they gone to Bhopal?

(v) क्या तुमने पत्र लिख लिया है?
Have you written your letter?

(8) Present Perfect Continuous

Tense Structure- Subject + have been/has been + Verb + ing + Object for/since + Time

(i) मैं दो दिन से बुखार से पीड़ित हूँ।
I have been suffering from fever for two days.

(ii) हम इस विद्यालय में तीन वर्ष से पढ़ रहे हैं।
We have been reading in this school for three years.

(iii) तुम तीन बजे से ताश खेल रहे हो।
You have been playing cards since 3 O’clock.

(iv) वे दो घण्टे से फुटबाल खेल रहे हैं।
They have been playing football for two hours.

Miscellaneous
विविध

(i) नेहरू जी महान पुरुष थे।
Nehruji was a great man.

(ii) क्या तुम मेरे मित्र हो?
Are you my friend?.

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(iii) तुम्हारा क्या नाम है?
What is your name?

(iv) वह राजेश का भाई है।
He is Rajesh’s brother.

(v) तुम मेरे मित्र नहीं हो।
You are not my friend.

(vi) वहाँ जाओ। Go there.

Exercise

Translate into English

1. ईश्वर तुम्हारी रक्षा करे।
2. मैंने तुम्हें कहाँ नहीं ढूँढा?
3. क्या हम सिनेमा देखने जा रहे हैं?
4. उसका भाई किस कक्षा में पढ़ता है?
5. शान्त रहो।
6. ईश्वर तुम्हें लम्बी उम्र प्रदान करें।
7. मैंने पानी नहीं पिया।
8. एक नाविक और तूफान से डरे !
9. क्या तुम तेज दौड़ सकते हो?
10. रवीन्द्रनाथ टैगोर को कौन नहीं जानता?
11. भिखारी इसी रास्ते से आता है।
12. आप चिरायु हों।
Answer:
1. May God protect you.
2. Where did I not look for you?
3. Are we going to see cinema?
4. In which class does his brother read?
5. Keep silence.
6. May God give you a long life.
7. I did not take water.
8. A sailor and afraid of storms !
9. Can you run fast?
10. Who does not know Rabindra Nath Tagore?
11. The beggar comes this way only:
12. May you live long.

Objective Type Questions

Choose the correct option and answer these questions :

1. All work and no play ……… Jack a dull boy.
(a) make
(b) making
(c) makes
(d) made.
Answer:
(a) make

2. The clothes of the beggar ………… torn.
(a) was
(b) are
(c) is
(d) am.
Answer:
(b) are

3. She ……….. consult the doctor at once.
(a) should
(b) must
(c) would
(d) may.
Answer:
(b) must

4. You ……….. speak the truth.
(a) should
(b) had to
(c) need
(d) shall.
Answer:
(b) had to

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5. ………. oil is a necessary article.
(a) a
(b) an
(c) the
(d) 0.
Answer:
(d) 0.

6. I want ………. flowers.
(a) some
(b) any
(c) much
(d) a litle.
Answer:
(a) some

7. She uses ………… eye glass to see the picture.
(a) a
(b) an
(c) the
(d) 0.
Answer:
(b) an

8. The old man is happy ………. me.
(a) by
(b) with
(c) for
(d) in.
Answer:
(b) with

9. I stayed with my uncle ………… two weeks.
(a) for
(b) in
(c) at
(d) form.
Answer:
(a) for

10. He went ………. a bus.
(a) by
(b) on
(c) in
(d) with.
Answer:
(c) in

11. Either he or his mother ………… coming.
(a) is
(b) are
(c) were
(d) 0.
Answer:
(a) is

12. You ……….. reach there on time.
(a) must
(b) should
(c) would
(d) 0.
Answer:
(a) must

13. The news ……….. not true.
(a) is
(b) are
(c) were
(d) 0.
Answer:
(a) is

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14. There is ………… rice in the plate.
(a) few
(b) some
(c) many
(d) much.
Answer:
(b) some

15. …….. of you will come.
(a) None
(b) No one
(c) Any
(d) Some.
Answer:
(a) None

MP Board Class 9th English Solutions

MP Board Class 9th General English Grammar Prepositions

MP Board Class 9th General English Grammar Prepositions

परिभाषा-जो शब्द वाक्य में किसी एक वस्तु का दूसरी
वस्तु से संबन्ध बतलाते हैं, Prepositions कहलाते हैं

A word used to show the relation of one thing to another in a sentence is a preposition.

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Relation Expressed by Prepositions

(1) Prepositions of Time – कुछ Prepositions समय सूचक होते हैं जैसे-
(i) He came at six.
(ii) I study for seven hours every day.
(iii) She is absent from class for three days.
(iv) They work from 10 to 4.

(2) Prepositions of Place – कुछ Prepositions स्थान सूचक होते हैं, जैसे
(i) He was born in America.
(ii) She was in her room.
(iii) They are coming home from school.
(iv) I stood before him.
(v) The ball is out of the circle.

(3) Prepositions of Movement- कुछ Prepositions गति सूचक/स्थान सूचक होते हैं, जैसे-

(i) He traveled by train.
(ii) I came by car.
(iii) He went there on his bike.
(iv) He travelled in my car.

Use of Some Other Preposition
(1)At, In : At छोटे स्थान के लिए प्रयोग किया जाता है। In, बड़े स्थान के लिए प्रयोग किया जाता है।

जैसे-
(i) He lives at Dholpur.
(ii) He lives in Madhya Pradesh.

(2) In, Into : In स्थिति को बताता है और Into गति का बोध कराता है।

जैसे-
(i) All the boys are in the class.
(ii) He dived into the river.

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(3) With, By : With — यन्त्र के साथ प्रयोग होता है और by कार्य करने वाले के साथ प्रयोग किया जाता है,

जैसे-
(i) We cut the apple with the knife.
(ii) The snake was killed by the farmer.

(4) Since, For : Since निश्चित समय के लिए (जैसे दिन का नाम या तिथि आदि) और for का प्रयोग समय की अवधि के लिए किया जाता है।

जैसे-
(i) He has been ill since Monday.
(ii). Raj Kumar has been absent for three days.

(5) Between, Among : Between दो व्यक्तियों तथा Among दो से अधिक व्यक्तियों के लिए प्रयोग किया जाता है।

जैसे-
(i) Divide these sweets between Raj and Ravi.
(ii) He divided his property among his four sons.

(6)On, Upon : On गतिहीन तथा upon गतिशीलता के लिए प्रयोग किया जाता है।

जैसे-
(i) The cat is on the mat.
(ii) The dog jumped upon the table.

(7) In, Within : In समय की अवधि की समाप्ति का बोध कराता है और Within समय की अवधि के भीतर का बोध कराता है।

जैसे-
(i) I shall come back in a week. (सप्ताह की समाप्ति पर)
(ii) I shall come within a week. (एक सप्ताह समाप्त होने से पूर्व)

(8) Below, Beneath : Below पद के सन्दर्भ में और Beneath स्थान के सन्दर्भ में प्रयोग किया जाता है।

जैसे-
(i) Your brother is below my rank.
(ii) The lion sat beneath a tree.

(9) Beside, Besides : Beside का अर्थ है-पास और Besides का अर्थ है-अतिरिक्त।।

(i) The boys stood beside the teacher’s.chair.
(ii) Besides the Principal, other teachers spoke in the prayer assembly.

(10) With, Without : With का अर्थ है-साथ और Without का अर्थ बिना (रहित)

जैसे-
(i) Come to me with your brother.
(ii) Come to the field without anything.

Exercise-1
Fill in the blanks with the words given in brackets :

1. Hari has been playing …………………….. two hours. (for, since)
2. He is angry …………………….. me. (to, with)
3. The lion jumped …………………….. the deer. (on, upon)
4. I live …………………….. Kolkata. (in, at)
5. They reached the Bhil village …………………….. 9 O’clock. (in, at)
6. Gita was sitting …………………….. me. (beside, besides)
7. Your sister is angry …………………….. you. (with, from)
8. She cannot finish this work …………………….. time. (on, at, in)
9. Your letter is full …………………….. mistakes. (of, with, from)
10. I knocked thrice …………………….. the door. (at, on)
Answer:
1. for,
2. with,
3. upon,
4. in,
5. at,
6. beside,
7. with,
8. in,
9. of,
10. at.

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Exercise-2

Fill in the blanks with suitable prepositions :
1. Lincoln was born ………… Thursday.
2. He went ………… the hill.
3. He lives ………. Bombay.
4. Yesterday Mohan fell ………… the well.
5. Suman and Rajesh went to see the marble rocks ………… Jabalpur.
6. The teacher was angry ………… Rahul.
7. Look ………… this picture.
8. He met me …………15th August.
9. I don’t want ………… take it back.
10. Put your signature ………… ink
Answer:
1. on,
2. up,
3. in,
4. into,
5. in,
6. with,
7. at,
8. on,
9. to,
10. in.

Exercise-3

Fill in the blanks with at, for, on, or, in :
1. The hunter aimed ………… the lion.
2. They were waiting ………… the station the train.
3. She is looking ………… a job.
4. The girl is sleeping …. the chair ….. an hour.
5. Rita always comes ………… time.
Answer:
1. at,
2. at, for
3. for,
4. on, for,
5. on.

MP Board Class 9th English Solutions

MP Board Class 9th General English Grammar Punctuation

MP Board Class 9th General English Grammar Punctuation

Punctuation का अर्थ होता है किसी वाक्य में Full stop, comma आदि विराम चिह्न का प्रयोग करना। इसके प्रयोग इस प्रकार हैं
(1) Full Stop (.) -हिंदी के पूर्ण विराम (1) के स्थान पर अंग्रेजी में fullstop (.) प्रयोग है-

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(a) Affirmative, Negative और Imperative वाक्यों के अन्त में
(i) She is a girl.
(ii) She is not coming.
(iii) Please come here.

(b) Abbreviation (संक्षिप्त शब्दों) तथा नामें के प्रारम्भ में अन्त में-
M.A., A.P.J. Abdul Kalam.

(2) Comma (,)-Comma (अर्द्ध विराम) pot sem निम्न दशाओं में होता है
(i) एक ही Part of Speech के कई शब्दों के अलग करने के लिए, जैसे –
He can read, write and sing well.

(ii) And से जोड़े गये एक से अधिक शब्द समूहों को अलग करने के लिए,जैसे-
The minister addressed all, men and women, old and young.

(iii) Yes और No के बाद, जैसे-
(a) Yes, I shall do it.
(b) No, I can’t go there.

(iv) Reported Speech के शेष वाक्य को अलग करने के लिए, जैसे-
He said, “The sun rises in the East.” –

(v) Noun और Phrase in apposition को अलग करने के लिए, जैसे- Milton, the great poet, was blind.

(vi) दिन, दिनांक या वर्ष को पृथक करने के लिए, जैसे-
Monday, 6th June, 2006.

(3) Question Mark (?)—प्रश्नवाचक वाक्यों के अन्त में लगाया जाता है, जैसे-
What is your name?

(4) Exclamation Mark (!)—इस चिह्न का प्रयोग

(i) Interjection (विस्मयादिबोधक) शब्दों के बाद होता है, जैसे-
Oh ! Alas! Hurrah !

(ii) उन वाक्यों के अन्त में भी होता है जो गहन संवेग व्यक्त करते हैं, जैसे-
What a beautiful picture !

(5) Inverted Commas (“….”)-Direct Speech में किसी के द्वारा कहे गये यथार्थ शब्दों को शेष वाक्य से अलग करने के लिए Inverted commas का प्रयोग होता है, जैसे-
He said, “I shall win.”

MP Board Solutions

(6) Apostrophe (‘) इसका प्रयोग होता है, जैसे-
(i) अक्षरों के लोप को प्रकट करने के लिए-
Don’t, can’t, won’t, didn’t.

(ii) Possessive case बनाने के लिए
Sita’s doll.

(iii) अक्षरों तथा संख्याओं को बहुवचन बनाने के लिए….
Add three 4’s and two 3’s.

(7) Capital Letters—इनका प्रयोग निम्न होता है
(i) वाक्य के प्रथम शब्द का प्रथम अक्षर लिखने के लिए-
He is my brother.

(ii) Proper Nouns और उससे बने हुए Adjectives
के प्रथम अक्षर को लिखने के लिए-
Asha, Delhi, Indian.

(iii) Pronoun I को लिखने के लिए
I am a teacher.

(iv) God, Almighty, Lord शब्दों के प्रथम अक्षर लिखने के लिए

MP Board Solutions

Exercise-1
Punctuate the following sentences :
1. Gaurav said the teacher scolded me.
2. my mother and I went to the market.
3. Kanyakumari is surrounded by the Indian ocean the bay of Bengal and Arabian sea
4. I like to eat apples grapes and guavas what do you like said he
5. it is the best book I have ever read.
Answer:
1. Gaurav said, “The teacher scolded me.”
2. My mother and I went to the market.
3. Kanyakumari is surrounded by the Indian Ocean, the Bay of Bengal and Arabian Sea.
4. “I like to eat apples, grapes and guavas. What do you like?”, said he.
5. It is the best book I have ever read.

MP Board Class 9th English Solutions

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7

Assume π = \(\frac{22}{7}\), unless stated otherwise.

MP Board Solutions

Question 1.
Find the volume of the right circular cone with

  1. radius 6 cm, height 7 cm
  2. radius 3.5 cm, height 12 cm.

Solution:
1. Here, radius of the cone r = 6 cm
height (h) = 7 cm
Volume = \(\frac{1}{3}\) x πr2h
= \(\frac{1}{3}\) x \(\frac{22}{7}\) x 6 x 6 x 7 cm3
= 22 x 2 x 6 cm3
= 264 cm3

2. Here, radius of the cone (r) ;
= 3.5 cm = \(\frac{35}{10}\) cm
Height (h) = 12 m
Volume of the cone
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7 img-1

Question 2.
Find the capacity in litres of a conical vessel with

  1. radius 7 cm, slant height 25 cm
  2. height 12 cm, slant height 13 cm

Solution:
1. Here, r = 7 and l = 25 cm
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7 img-2
Thus, the required capacity of the conical vessel is 1.232 l.

2. Here, height (h) – 12 cm and l = 13 cm
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7 img-3
Thus, the required capacity of the conical vessel is \(\frac{11}{35}\) l.

Question 3.
The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of the base. (Use 71 = 3.14)
Solution:
Here, height of the cone (h) = 15 cm
Volume of the cone (v) = 1570 cm3
Let the radius of the base be ‘r’ cm.
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7 img-4

Question 4.
If the volume of a right circular cone of height 9 cm is 48 JI cm3, find the diameter of its base.
Solution:
Volume of cone = \(\frac{1}{3}\) πr2h
\(\frac{1}{3}\) x πr2 x 9 = 48π
r2 = \(\frac{48π}{9π}\) x 3
r2 = 16
r = 4 cm
Diameter = 2 x 4 = 8 cm

MP Board Solutions

Question 5.
A conical pit of top diameter 3,5 m is 12 m deep. What is its capacity in kilolitres?
Solution:
d = 3.5 m
r = 1.75 m
h = 12m
Volume of the pit = \(\frac{1}{3}\) x \(\frac{22}{7}\) x 1. 75 x 1.75 x 12
= 38.5 m3 = 38.5 kl (1 kl= 1 m3)

Question 6.
The volume of a right circular cone is 9856 cm3. If the diameter of the base 28 cm, find.

(i) height of the cone.
(ii) slant height of the cone.
(iii) curved surface area of the cone.

Solution:
V = 9856 cm2
d =28 cm
r = 14 cm
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7 img-5

Question 7.
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the sides 12 cm. Find the volume of the solid 30 obtained.
Solution:
h = 12cm
r = 5cm
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7 img-6
Volume of solid, V1 = \(\frac{1}{3}\)πr2h
= \(\frac{1}{3}\) x π x 5 x 5 x 12
= 100π cm3

Question 8.
If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.
Solution:
h = 5 cm
r = 12 cm
Volume of solid, V2 = \(\frac{1}{3}\) x π x 12 x 12 x 5
= 240π
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7 img-7

MP Board Solutions

Question 9.
A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be by covered canvas to protect it from rain. Find the area of the canvas required.
Solution:
d = 10.5 m ⇒ r = 5.25 m
h = 3m
Volume of heap of wheat = \(\frac{1}{3}\) x \(\frac{22}{7}\) x 5.25 x 5.25 x 3
= 86.625 m3
l2 = 32 + (5.25)2
l = \(\sqrt{9+27.56}\) = \(\sqrt{36.56}\) = 6.04 cm
Area of canvas required = CSA of cone –
= \(\frac{22}{7}\) x 5.25 x 6.04 = 99.66 m2

MP Board Class 9th Maths Solutions

MP Board Class 9th General English Grammar Clauses

MP Board Class 9th General English Grammar Clauses

जब किसी sentence में एक subject और एक predicate (अर्थात् एक ही verb) हो तो वह simple sentence कहलाता है
Example Subject + Predicate (verb + other words)
Harish is playing football.

Simple sentences जब जुड़कर complex sentences बन जाते हैं तो clauses कहलाते हैं

Complex Sentence-This is the picture which was drawn by me.
Simple sentences को किसी conjunction (योजक शब्द) से जोड़कर Complex sentence बनाया जाता है

MP Board Solutions

Clauses दो प्रकार के होते हैं-

  1. Principal Clause व
  2. Subordinate Clause.

I love him because he is my son.
I love him वाक्य अपने आप में पुर्ण है अत: यह Principal clause है because he is my son को अकेले नहीं लिखा जा सकता पुरे अर्थ के लिए यह I love him पर निर्भर है अत : यह subordinate clause है

Subordinate Clause तीन प्रकार के होते हैं

  1. Noun Clause
  2. Adverb Clause
  3. Adjective Clause.

Adverb Clauses
Adverb clauses are clauses that function as an adverb.
Adverb clauses किसी verb, Adverb या की विशेषता बताते हैं adjective की विशेषता बताते हैं।

आपके पाठ्यक्रम में दो प्रकार के रखे Adverb clauses गये हैं

(1) Adverb Clauses of Time.
(2) Adverb Clauses of Condition.

(1) Adverb Clauses of Time (i) We will leave.
We finish our lunch.
Answer:
As soon as we finish our lunch we will leave.

(ii) We will go out.
The rain stops.
Answer:
We will go out when the rain stops.

(iii) Don’t shout…
She is studying.
Answer:
Don’t shout while she is studying.

(iv) Father called me.
I was taking food.
Answer:
Father called me when I was taking food.

(v) A stone hit me.
I was coming out.
Answer:
As I was coming out, a stone hit me.

Exercise-1
Join the following sentences to make an adverb clause with the help of conjunctions given :
1. The sun rises. (As soon as)
He takes bath.

2. I had been living there. (Since)
He took birth.

3. There is unity in the country. (As long as)
We shall remain strong.

4. We reached the station. (Before)
The train had arrived.

5. She found a coin.
She was cleaning the floor. (While)

6. He came here.
I rushed to see him. (No sooner ….than)

7. The girl won’t go away. You tell her to go. (until)
Answer:
1. As soon as he takes bath, the sun rises.
2. I had been living there since he took birth.
3. As long as there is unity in the country we shall remain strong.
4. We reached the station before the train arrived.
5. She found a coin while she was cleaning the floor.
6. No sooner did he come here, than I rushed to see him. 7. The girl won’t go away until you tell her to go.

(2) Adverb Clause of Condition
जब एक simple sentence दूसरे simple sentence से इस तरह जुड़े कि जुड़कर वह उस sentence की verb की शर्त
हो तो वह Adverb clause of condition Emin कहलाता है

MP Board Solutions

यह if, in case, unless, if not, suppose, provided इत्यादि से जुड़ते हैं।

(i) Mohan comes.
I shall go.
Answer:
If Mohan comes, I shall go.

(ii) You are honest..
People will not respect you.
Answer:
If you are not honest, people will not respect you.

(iii) I like tea.
It is hot.
Answer:
I like tea provided it is hot.

(iv) We won’t pay.
He sends the bill again.
Answer:
Unless he sends the bill again, we won’t pay.

(v) I forget.
Please remind it to me.
Answer:
In case I forget, please remind it to me.

Exercise-1
Combine the sentences :
1. Take your teacher’s advice. I am not available. (In case) 2. The judge will not believe. You prove it. (Unless)
3. I will not come. It is too cold.
4. I shall forgive him. He say sorry. (provided)
5. I will go. You accompany me.
Answer:
1. In case I am not available take your teacher’s advice.
2. Unless you prove it, the judge will not believe.
3. If it is too cold, I will not come.
4. I shall forgive him provided he says sorry.
5. I will go if you accompany me.

Relative Clauses
Or
Adjective Clauses

जब एक Simple sentence दूसरे में जुड़कर उसके किसी Noun की विशेषता बतलाता है तो वह Adjective या Relative clause कहलाता है ये दो प्रकार के होते हैं-

(1) Defining or Restrictive Relative Clause जब कोई Clause किसी Noun को qualify इस तरह करे कि वह उस Noun को identify करने के लिए अनिवार्य हो जाए तब उसे Restrictive Clause कहेंगे।

As-The man who lives next door has just retired.

(2) Non-Defining or Non-Restrictive Clause – किन्तु जब Adjective Clause उसके Noun को identify करने हेतु आवश्यक न हो, किन्तु एक अतिरिक्त जानकारी के रूप में सम्बद्ध हो तो वह Non-Defining Clause कहलाता है। जैसे

(i) Mr. Sharma, who lives next door, has just retired.
(ii) Suresh, who was wearing red shirt, has disappeared.

(नोट-Non-defining Clause के पूर्व व पश्चात् Commas का प्रयोग किया जाता है।)

Relative Pronouns
Adjective Clauses के साथ Relative Pronouns योजक का कार्य करते हैं।
Who = जो, जिसने
Whom = जिसे, जिसको
Which = जो, जिसने
Whose = जिसका, जिसकी इत्यादि का प्रयोग होता है।
That = जो, जिसने।

अन्य योजक:
Relative adverbs-when, where, why, how. Others-same…..as, such……as etc.

Examples
(i) This is the time.
We must act now.
Answer:
This is the time when we must act.

(ii) The news is not true.
Sohan brought this news.
Answer:
The news that Mohan brought is not true.

(iii) The place is dirty.
You are sitting there.
Answer:
The place where you are sitting is dirty.

MP Board Solutions

(iv) The lady is beautiful.
The lady is wearing a red saree.”
Answer:
The lady, who is wearing a red saree, is beautiful.

Exercise-1
Combine the sentences :
1. The book is mine.
The book is lying on the table. (which)
2. The boy was very stupid.
The boy was sitting next to me. (who)
3. The man has just gone out. You want to see the man. (whom)
4. Blessed is the man. His cares are few. (whose)
5. The car came first in the race.
The car was driven by a foreigner. (that)
6. The time is not known.
When does he come here?
Answer:
1. The book which is lying on the table is mine.
2. The boy who was sitting next to me was very stupid.
3. The man whom you want to see has just gone out.
4. Blessed is the man whose cares are few.
5. The car that was driven by a foreigner came first in the race.
6. The time when he comes here is not known.

Noun Clauses
वे Clauses जो Noun का कार्य करते हैं, Noun Clause कहलाते हैं ये निम्न कार्य करते हैं-
(1) Subject of a verb.
(2) The object of a transitive verb.
(3) The complement of a verb.
(4) The object of a preposition.

(1) Subject of a Verb
जब कोई Clause किसी verb के subject का कार्य करता है तो Noun Clause कहलाता है जैसे

That he is ill is not true.
(i) What he says.
(ii) That is wrong.

These two sentences can be combined to form a complex sentence. What he says is wrong.

Exercise-1
Combine the sentences :
1. This was unfortunate.
We lost the opening match.

2. This is possible.
They might have misunderstood you.

3. This is doubtful.
Will they be able to get good grades?

4. This is not certain.
Will they be able to come with us?

5. This is a mystery.
Why did she go there alone?

6. He is ill.
It is not true.

7. When will he come?
This is uncertain.
Answer:
1. That we lost the opening match was unfortunate.
2. That they might have misunderstood you is possible.
3. Whether they will be able to get good grades is doubtful. 4. Whether they will be able to come with us is not certain. 5. Why she went there alone is a mystery.
6. That he is ill is not true.
7. When will he come is uncertain.

(2) Object of a Transitive Verb
जब कोई simple sentence दूसरे simple sentence से इस तरह जुड़ता है कि जुड़कर उस sentence की Finite Verb के Object का कार्य करे तो इस तरह Noun का कार्य करने के कारण Noun Clause कहलाता है

Transitive verb में sentence का structure होता है-

Subject—VerbObject
Object कोई Noun/Pronoun होता है।
अत: निम्न sentence में
I know …….. he is stupid.

Complex sentence in I know that he is stupid, इसमें I know Main clause व Object के रूप में जुड़ा that he is stupid-Noun clause है।

Exercise-1
Combine the following sentences :
1. They asked this.
Did we want to insure our luggage?
2. Do you know this?
When is the next train?
3. Can you tell me this?
Where have they gone?
4. Please remember this.
You have to attend the meeting.
5. We expect this.
The party will get absolute majority.
Answer:
1. They asked if we wanted to insure our luggage.
2. Do you know when the next train is?
3. Can you tell me where they have gone?
4. Please remember that you have to attend the meeting.
5. We expect that the party will get absolute majority.

(3) Complement of a Verb
जब कोई Clause किसी Verb के Complement का कार्य करता है तब उसे भी Noun Clause कहते हैं।

जब कोई sentence दूसरे simple sentence में इस तरह जुड़ता है कि जुड़कर उसकी incomplete verbs के Noun complement का कार्य करे तो इस तरह जुड़ा वाक्य Noun clause कहलाता है

MP Board Solutions

जैसे-
The problem is this
How can we reach there in time?
Answer:
The problem is how we can reach there in time.

Exercise-1
Combine the sentences making one of them a Noun clause complement of a verb.
1. It seems this.
He is worried.
2. His intention is this.
You should not sell the house.
3. The fact is this.
We cannot afford a holiday this year.
4. My opinion is this.
You have made a mistake.
5. His suggestion is this.
We should go for picnic.
Answer:
1. It seems that he is worried.
2. His intention is that you should not sell the house.
3. The fact is that we cannot afford a holiday this year.
4. My opinion is that you have made a mistake.
5. His suggestion is that we should go for picnic.

(4) Object of a Preposition :
जब कोई simple sentence दूसरे simple sentence में इस तरह जुड़ता है की जुड़कर उस sentence के किसी Preposition का Object बन जाए तो वह Noun Clause कहलाता है जैसे-
(i) They couldn’t agree about this.
Who should do the work?
Answer:
They couldn’t agree about who should do the work.

(ii) Have you decided upon this?
Where will you spend the holidays?
Answer:
Have you decided upon where you will spend the holidays?

(iii) Everything depends on this.
Does the train reach there in time?
Answer:
Everything depends on whether the train reaches there in time or not.

Exercise-1
Combine the following sentences.
1. I do not believe in his words.
He says the words.
2. He was punished for his misdeed.
He had done the misdeed.
3. I had drawn this conclusion from his words.
He said these words.
4. Pay attention to the teacher’s words.
The teacher says the words.
5. Be careful about the things.
You take things in your hands.
Answer:
1. I do not believe in what he says.
2. He was punished for what he had done.
3. I had drawn the conclusion from what he said.
4. Pay attention to what the teacher says.
5. Be careful about what you take in your hands.

MP Board Class 9th English Solutions

MP Board Class 9th Maths Solutions Chapter 14 Statistics Ex 14.1

MP Board Class 9th Maths Solutions Chapter 14 Statistics Ex 14.1

1. Give five examples of data that you can collect from your day – to – day life.
2. Classify the data in –

Question 1.
Above as primary or secondary data
Solution:
Do it yourself.

MP Board Solutions

Presentation of Data:
The data collected in original form is called raw data. These data are arranged in ascending or descending order. This arrangement is called array. The data are divided or grouped into classes in condensed form. This is known as presentation of data.

Range of Data:
The difference between highest and lowest value of data is called the range of data.

MP Board Class 9th Maths Solutions

MP Board Class 9th General English Grammar Determiners

MP Board Class 9th General English Grammar Determiners

Determiner is a word that comes before a noun and determines its number or quantity.
Determiner वह शब्द है जो किसी Noun से पूर्व प्रयोग किया जाता है व उसकी संख्या या मात्रा को निर्धारित करता है।

Commonly used determiners are-a, an, the, some, any, much, several, few, little, each, enough, every, both, all, either, neither, half, many, etc. – Uses of some determiners are given below.

MP Board Solutions

Any (कोई)
Any का प्रयोग countable व uncountable nouns के साथ Negative व Interrogative वाक्यों में किया जाता है।

जैसे-
(i) Father has not taken any food.
पिताजी ने कुछ भी नहीं खाया है।

(ii) I am not going anywhere.
मैं कहीं नहीं जा रहा हूँ।
(iii) There is not any milk in the pot.
बर्तन में कुछ भी दूध नहीं है।

(iv) Do you want any money?
क्या तुम्हें कुछ धन की आवश्यकता है?

Enough (पर्याप्त)
जब कोई वस्तु जरूरत या इससे थोड़ी ज्यादा संख्या या मात्रा में हो तो countable Runcountable दोनों के साथ इसका प्रयोग किया जाता है। जैसे

(i) You have taken enough food.
तुमने पर्याप्त भोजन कर लिया है।

(ii) Do you not have enough milk?
क्या तुम्हारे पास पर्याप्त दूध नहीं है?

(iii) Enough has been said by you on this matter.
तुम्हारे द्वारा इस मामले पर काफी कहा जा चुका है।

(iv) Father has not provided me enough money.
पिताजी ने मुझे पर्याप्त धन नहीं प्रदान किया है।

(v) Enough flowers have been plucked, now leave this work.
पर्याप्त फूल तोड़े जा चुके हैं, अब यह काम छोड़ दो।

Some (कुछ)

Some का प्रयोग countable व uncountable nouns से पूर्व Affirmative sentences में (Negative व Interrogative में नहीं) उस वस्तु के लिए किया जाता है जो Enough से कम किन्तु उसके बहुत कुछ पास होती है। जैसे-

(i) There is some milk in the pot.
बर्तन में थोड़ा दूध है।

(ii) He has given me some money to start my business.
उसने मुझे अपना व्यापार प्रारम्भ करने के लिए कुछ धन दिया है।

(iii) I have some books on this subject.
इस विषय पर मेरे पास कुछ पुस्तकें हैं।

(iv) The officer has received some complaints from people against the clerk.
ऑफिसर को क्लर्क के विरुद्ध कुछ शिकायतें प्राप्त

No (Not any) (कुछ नहीं)
No em countable singular, countable plural : और uncountable nouns के साथ किया जाता है। इसका उपयोग pronoun के समान नहीं किया जा सकता।

जैसे
(i) I have not read any book.
= I have read no book.

(ii) She did not bring any.copy.
= She brought no copy.

(iii) His brothers do not do anything.
= His brothers do nothing.

(iv) Your sister has not taken any rice.
= Your sister has taken no rice.

(v) Do you not play any game?
= Do you play no game?

MP Board Solutions

Many (कई)
कोई Countable noun जब पर्याप्त से ज्यादा मात्रा में होता है तब उससे पूर्व Many का प्रयोग किया जाता है। जैसे

(i) Many people will not agree to it.
कई व्यक्ति इसके लिए नहीं मानेंगे।

(ii) Sohan has written many books.
सोहन ने कई किताबें लिखी हैं।
(iii) Does she sell many clothes?.
क्या वह कई कपड़े बेचती है?

(iv) Many people do not know me.
कई लोग मुझे नहीं जानते हैं।

Much (ज्यादा)
Much का प्रयोग uncountable nouns के साथ अधिकतर
(i) negative sentences में,
(ii) questions में, तथा
(iii) subject noun के पूर्व या उसके स्थान पर किया जाता है।

जैसे-
(i) There is not much milk in the glass.
गिलास में ज्यादा दूध नहीं है।

(ii) I could not eat much of it.
मैं ज्यादा नहीं खा सकता था।

(iii) Does he spend much of his money on books?
क्या वह अपना ज्यादा धन पुस्तकों पर व्यय करता

(iv) Did you have much difficulty in finding the place?
क्या तुम्हें वह स्थान ढूँढ़ने में बहुत कठिनाई हुई?

(v) How much money would they need?
उन्हें कितने धन की आवश्यकता होगी?

(vi) Let them take as much as they like.
उन्हें जितने चाहिए उतना लेने दें।

(vii) This is too much, I won’t be able to eat all of it.
यह बहुत अधिक है, मैं यह सब नहीं खा सकता।

Note-More तथा most दोनों many व much की क्रमशः comparative व superlative degree हैं।

Each/Every (प्रत्येक)
In every the attention is focussed on the collection of units with emphasis on the units (every= all). Every में हमारा ध्यान units के संग्रह पर होता है। Every का प्रयोग दो से अधिक के लिए किया जाता है।

In each attention is focussed on units considered one by one individually and separately.
Each में हमारा ध्यान units पर एक-एक करके एकाग्र किया जाता है। Each का प्रयोग दो या दो से अधिक दोनों के लिए किया जाता है। जैसे

  1. Each boy participated in the game.
  2. Each satellite has its own orbit.
  3. Every girl won the prize.
  4. I go to him after every two days.
  5. The teacher gave marks to each boy.

Few (थोडे)
इसका प्रयोग Countable Nouns के पूर्व कम अर्थात् पर्याप्त नहीं के अर्थ में किया जाता है। जैसे

(i) There are few oranges on the table.
मेज पर थोड़े सन्तरे हैं।

(ii) The benefits of this scheme are few.
इस योजना के बहुत कम लाभ हैं।

(iii) Few of us will take part in it.
हममें से कुछ इसमें हिस्सा लेंगे।

(iv) The gardener plucked few leaves.
माली ने कुछ पत्तियाँ तोड़ीं।

MP Board Solutions

A Few (बहुत थोड़े, कुछ)
(i) A few persons attended the meeting.
बहुत थोड़े से लोग सभा में उपस्थित हुए।

(ii) He gave me a few pencils.
उसने मुझे बहुत थोड़ी पेंसिलें दीं।

(iii) She knew a few things about me.
वह मेरे बारे में कुछ चीजें जानती थी।

(iv) A few of my friends are non-vegetarian.
मेरे कुछ मित्र माँसाहारी हैं।

The Few थोड़े (बचे हुए)

(i) The few oranges left were rotten.
बाकी बचे हुए सन्तरे सड़े हुए थे।

(ii) He was helped by the few persons standing there.
वहाँ खड़े हुए बाकी बचे लोगों ने उसकी मदद की।

(iii) The few girls standing there were of class X.
वहाँ खड़ी लड़कियाँ कक्षा दस की थीं।

Little (थोड़ा)
किसीuncountable noun की मात्रा थोड़ी अर्थात् अपर्याप्त के अर्थ में होने पर little का प्रयोग किया जाता है।

जैसे
(i) There is little water in the glass.
ग्लास में थोड़ा पानी है।

(ii) Give me little oil.
मुझे थोड़ा तेल दो।

(iii) He earned little money.
उसने थोड़ा धन कमाया।

(iv) There is little hope of her recovery.
उसके. अच्छा होने की थोड़ी उम्मीद है।

A Little (थोड़ा मात्रात्मक)

(i) A little knowledge is dangerous.
थोड़ा ज्ञान खतरनाक है।

(ii) Will you take a little coffee?
क्या तुम थोड़ी कॉफी लोगे?

(iii) He knows a little English,
वह थोड़ी अंग्रेजी भाषा जानता है।

(iv) I have a little time for studying.
मेरे पास पढ़ने का बहुत कम समय है।

The Little (थोड़ा)
(i) Ram cares for the little ones.
राम छोटे बच्चों की देखभाल करता है।

(ii) The cat drank the little milk.
बचा हुआ थोड़ा दूध बिल्ली पी गई।

(iii) He tried to spend the little money he had.
उसने अपने पास बचे हुये थोड़े से धन को खर्च करने की कोशिश की।

(iv) The little experience he had, helped him much.
उसके पास जो थोड़ा अनुभव था उसने उसकी काफी मदद की।

Whole (सम्पूर्ण)
इसके पूर्व प्रायः ‘the’ का या किसी possessive का प्रयोग होता है।

जैसे-
(i) The whole world thinks so.
सारा संसार ऐसा सोचता है।

(ii) He paid his whole attention to his studies.
उसने अपना सारा ध्यान अपने अध्ययन पर लगा दिया।

(iii) The merchant sold the whole lot of his goods.
व्यापारी ने अपना सारा माल बेच दिया।

(iv) Please take the whole loaf of bread.
ब्रेड का पूरा हिस्सा ले लीजिए।

None (कोई नहीं) No one (None)
(i) Father did not give money to any one.
= Father gave fruit to none.

(ii) She took none with her.
(iii) No one played with him.
(iv) She spoke to none.
(v) No one is so happy as you.
None is so happy as you.

MP Board Solutions

All (सब)

प्रयोग-

  1. Countable plural व uncountable nouns के साथ
  2. Nouns के पूर्व determiners के उपयोग के साथ
  3. Personal pronouns determiners + nouns के साथ
  4. Pronouns के समान “किया जा सकता है।

जैसे-
(i) All animals have to eat in order to live.
सभी पशुओं को जीने के लिए खाना होता है।

(ii) All timber must be chemically treated.
सब इमारती लकड़ी पर रासायनिक क्रिया आवश्यक

(iii) All that glitters is not gold. .
वह सब जो चमकता है सोना नहीं होता।

(iv) All of his money was stolen.
उसका सारा धन चोरी हो गया।

(v) He has two brothers and two sisters. All are teachers.
उसके दो भाई व दो बहनें हैं। सभी शिक्षक हैं।

(vi) (a) He was here all day.
(=The whole of the day).
वह यहाँ पूरे दिन रहा।

(b) He was here every day.
(= don’t miss a single day).
वह यहाँ प्रत्येक दिन रहा।

Exercise-
1. Fill in the correct determiners :

1. …….. pages of this book are torn.
2. He hasn’t got ……… money now.
3. ……… milk left in the pot has spilt.
4. She worked the ………. night.
5. Have you seen ………. cow on your way?
6. I want …….. flowers. :
7. You have ……… right to say so.
8. Not ……… has been done in this field.
9. There are ……. flowers in this garden.
10. There aren’t ……. good books on the subject.
Answer:
1. Some,
2. any,
3. The little,
4. whole,
5. any,
6. some,
7. no,
8. much,
9. many,
10. any.

MP Board Solutions

Exercise-2

Fill in the blanks with the suitable determiner:
1. There is hardly ……… rice left.
2. He gave me ………. money.
3. You have ………. right to say so.
4. There is ……….. water in the river.
5. His ………. life was spoilt.
6. ……… the boys are present.
7. ……… boy got a prize.
8. ………. of us liked him.
9. How ………. ink is left in the bottle?
10. Last night ………. thieves entered the house.
Answer:
1. any,
2. some,
3. no,
4. a little,
5. whole,
6. All,
7. Each,
8. None, All,
9. much,
10. some.

Exercise-3

Rearrange the following to make meaningful sentences.
1. I/a little brought/apple juice/market/from the.
2. little/there is/success/hope/of his.
3. he/hardly/any/money/has.
4. in/this/book/are there/pages/how/many?
5. social work/for/time/spare/some/you/can’t?
Answer:
1. I brought a little apple juice from the market.
2. There is little hope of his success.
3. He hardly has any money.
4. How many pages are there in this book?
5. Can’t you spare some time for social work?

MP Board Class 9th English Solutions

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.5

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.5

Assume π = \(\frac{22}{7}\), unless stated otherwise.

Question 1.
A matchbox measures 4 cm x 2.5 cm. x 1.5 cm. What will be the volume of a packet containing 12 such boxes?
Solution:
Measures of matchbox (cuboid) is 4 cm x 2.5 cm x 1.5 cm
l = 4 cm,
b = 2.5 cm and
h = 1.5 cm
∴ Volume of matchbox = (l x b) x h
= [4 cm x 2.5 cm] x 1.5 cm3
= 4 x \(\frac{25}{10}\) x \(\frac{25}{10}\) cm3 = 15 cm3
Volume of 12 boxes =12 x 15 cm3 = 180 cm3

MP Board Solutions

Question 2.
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m3 = 1000 l)
Solution:
Here, Length (l) = 6 m
Breadth (b) = 5 m
Depth (h) = 4.5 m
Capacity = l x b x h = 6 x 5 x 4.5 m3
= 6 x 5 x \(\frac{45}{10}\) m3 = 3 x 45
= 135 m3
∴ 1 m3 can hold 1000 l.
∴ 135 m3 can hold (135 x 1000 l = 135000 l) of water.
∴ The required amount of water in the tank = 135000 l.

Question 3.
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?
Solution:
Volume of the vessel = l x b x h
380 = 10 x 8 x h
380 = 80 x h
h = \(\frac{380}{80}\) = 4.75m.

Question 4.
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of ₹ 30 per m3.
Solution:
Volume of cuboidal pit = 8 x 6 x 3 = 144 m3
Cost of digging = 144 x 30 = ₹ 4320.

Question 5.
The capacity of a cuboidal tank is 50000 liters of water. Find the breadth of the tank, it its length and depth are respectively 2.5 m and 10 m.
Solution:
Capacity of cuboidal tank = \(\frac{50000}{1000}\) m3 = 50 m3
Volume of cuboidal tank = l x b x h
50 = 2.5 x 6 x 10
50 = 25b
Breadth of tank, b = \(\frac{50}{25}\) = 2 m.

MP Board Solutions

Question 6.
A village, having a population of4000, requires 150 liters of water per head per day. It has a tank measures 20 m x 15 m x 6m. For how many days will the water of this tank last?
Solution:
Volume of water required for the village per day = \(\frac{4000×150}{1000}\)
Volume of tank = 20 x 15 x 6 = 1800 m3
No. of days = \(\frac{1800}{600}\) = 3.

Question 7.
A godown measures 60 m x 25 m x 10 m. Find the maxium number of wooden crates each measuring 1.5 m x 1.25 m x 0.5 m that can be stored in the godown.
Solution:
Volume of godown = (60 x 25 x 10) m3 = 15000 m3
Volume of one wooden crate = (1.5 x 1.25 x 0.5) m3 = 0.9375 m3
No. of wooden crates which can be stored in the godown
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.5 img-1
= 16000.

Question 8.
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cubk? Also, find the ratio between their surface area.
Solution:
Volume of cube of side 12 cm = (12 x 12 x 12) cm3
Let V be volume of new cube.
Volume of cube of side 12 cm = 8 x volume of new cube
12 x 12 x 12 = 8 x V
V = \(\frac{12x12x12}{8}\) = \(\frac{12x12x12}{2x2x2}\) = 216 cm3
Let a be the side of new cube
a3 = 216 = 63
a = 6 cm
TSA of cube of side 12 = 6 x (12)2
TSA of new cube = 6 x (6)2
MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.5 img-2

MP Board Solutions

Question 9.
Anver 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Solution:
b = 40 m,
h = 3 m
V = 2 km/hr
= \(\frac{2×1000}{60}\) = \(\frac{100}{3}\) m/min
Volume of water coming out of the river per min = b x h x V
= \(\frac{100}{3}\) x 3 x 40 = 4000 m3.

MP Board Class 9th Maths Solutions

MP Board Class 9th General English Grammar Modals

MP Board Class 9th General English Grammar Modals

Modals विशेष प्रकार की Helping verbs हैं जो मुख्य (Finite) verb के Mood (भाव) को प्रकट करने में सहायता करती हैं।

Modals के बाद not लगाकर वाक्य Negative बन जाता है।

Will, shall, should, would, can, could, may, might, ought, need, dare, has to, have to, had to, ought to Modals हैं। आपके पाठ्यक्रम में सिर्फ has to, have to, had to, must, ought to, need, should और इनके negative forms हैं।

MP Board Solutions

Modals की निम्न विशेषताएँ हैं
(1) यह कभी अकेला प्रयुक्त नहीं होता वरन् सदैव किसी मुख्य क्रिया (main verb) के साथ ही आता है।

जैसे-
(i) You should wait for half an hour.
(ii) I had to go there.

(2) Has to व have to को छोड़कर अन्य Modals पर Subject के Number तथा Gender का कोई प्रभाव नहीं पड़ता।

Uses of Some Modals
1. Have to/Had to/Has to (and their negatives)
इनका प्रयोग बाध्यता व्यक्त करने के लिए किया जाता है।

I. (i) I had to bring his clothes.
मुझे उसके कपड़े लाने पड़े।

(ii) You have to bow before him.
तुम्हें उनके सामने झुकना पड़ता है।

(iii) Ramesh had not to eat it.
रमेश को यह नहीं खाना पड़ा।

(iv) She has to go there.
उसे वहाँ जाना पड़ा।

(v) Sheela has not to fetch water in the morning.
शीला को सुबह पानी नहीं लाना पड़ता है।

(vi) I have not to clean my room these days.
‘मुझे अपना कमरा इन दिनों साफ नहीं करना पड़ता है।

अत: ‘Have to’ व उसके negative का प्रयोग first person, second person तथ third person, plural pronouns के साथ present tense में किया जाता है।

‘Has to’ व उसके negative का प्रयोग 3rd person singular number (he, she, it, name, of a person आदि) के साथ Present Tense में किया जाता है

‘Had to’ व उसके negative का प्रयोग Past Tense में सभी persons तथ numbers के साथ किया जाता है

Exercise-1

Fill in the blanks with has to/have to/had to
1. I ……… wear the shirt without ironing.
2. The teachers don’t ……… wear any uniform.
3. We ……… work till midnight.
4. The driver ……… drive the car fast.
5. His mother ……… go away.
6. You don’t ……… worry about it.
Answer:
1. had to,
2. have to,
3. have to,
4. has to,
5. had to,
6. have to.

MP Board Solutions

Exercise-2

Rewrite these sentences into negative

1. He has to pass.
2. They have to write to his father…
3. He has to agree with me.
4. Your sister has to come here.
5. We had to throw it.
Ans.
1. He has not to pass.
2. The have not to write to his father.
3. He has not to agree with me.’
4. Your sister has not to come here.
5. We had not to throw it.

(2) Must

Must is used –
(1) To express compulsion (बाध्यता) जैसे-
(i) You must deposit the money by tomorrow.
तुम्हें रुपये कल तक जमा कर देने चाहिए।
(ii) They must obey the rules.
उन्हें नियमों का पालन करना चाहिए।

(2) To express prohibition (निषेध) जैसे-
(i) You must not come home late.
तुम्हें घर देर से नहीं आना चाहिए।
(ii) Students must’not talk in the classroom.
विद्यार्थियों को कक्षा में बात नहीं करनी चाहिए।

(3) To advice in the form of order.
जैसे-
Mother said to me, “You must lock the doors properly.”
माँ ने मुझसे कहा, “तुम्हें दरवाजे ठीक तरह से बन्द करने चाहिए।”

Exercise-3

Fill in the blanks with must/must not
1. You ……… try your luck.
2. We ……… go there.
3. I………. work hard now.
4. You ……… roam about like this.
Answer:
1. must,
2. must,
3. must,
4. must not.

(3) Should

Should का प्रयोग advice, prohibition, duty, probability or expectation, condition, intention, suggestion इत्यादि को बताने के लिए किया जाता है।

You should consult the doctor immediately.
तुम्हें शीघ्र ही डॉक्टर से परामर्श करना चाहिए।

Boys should be present daily.
लड़कों को प्रतिदिन उपस्थित रहना चाहिए।

MP Board Solutions

Exercise-4

Fill in the blanks using should/should not
1. The peon ……… ring the bell.
2. You ……… tell lies.
3. All of you ……… come in time.
4. I ……… let her down.
5. People ……… spit on the walls.
Answer:
1. should,
2. should not,
3. should,
4. should not,
5. should not.

(4) Ought to/Ought not to

‘Ought to’ का प्रयोग नैतिक कर्तव्य (moral obligation) या सामाजिक बन्धक (binding) बताने के लिए किया जाता है। इसके बाद सदैव verb की Ist form आती है।

जैसे-
You ought to obey your parents.
तुम्हें अपने माता-पिता का कहा मानना चाहिए।

Exercise-5
Fill in the blanks using ought to/ought not to.
1. You ……… obey the traffic rules.
2. Children ……… back answer their elders.
3. You ……… abuse others.
4. People ……… take their own decisions.
5. We ……. be kind to animals.
Answer:
1. ought to,
2. ought not to,
3. ought not to,
4. ought to,
5. ought to

(5) Need/Needn’t

सहायक क्रिया के रूप में need का प्रयोग नकारात्मक और प्रश्नवाचक वख्यों में होता है Need बन्धन या अनिवार्यता को प्रकट नहीं करना

मुख्य Verb के रूप में need का अर्थ होता है to stand. in need of.
1. You need not go there. (Negative)
2. Need he go there? (Interrogative)
3. I need your help. (main verb 264 )

MP Board Solutions

Defective verb के रूप में इसका अर्थ necessity होता है।

जैसे-
(i) You need not pay the fee.
(ii) He need not insist for it.

Exercise-6

Fill in the blanks using need (s) needn’t
1. You ……… go to the hospital now.
2. Uncle Sam ……… your help.
3. It is the ……… of the time to speak the truth.
4. ……. she stay there?
Answer:
1. need not,
2. needs,
3. need,
4. Need.

Exercise-7

Rearrange the following words to make meaningful sentences.

1. Tomorrow/school/to/go/I/must.
2. Early/ought to/you/rise.,
3. Work/night/I/have to/till.
4. Bicycle/man/sell/had to/poor/the/his.
Ans.
1. I must go to school tomorrow.
2. You ought to rise early.
3. I have to work till night.
4. The poor man had to sell his bicycle.

MP Board Class 9th English Solutions