Bhagya

Punjab State Board PSEB 10th Class Maths Book Solutions Chapter Statistics Ex 14.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3

Question 1.
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Solution:

Here, \(\Sigma f_{i}\) = 68 then \(\frac{n}{2}=\frac{68}{2}\) = 34
Which lies in interval 125 – 145
Median class = 125 – 145
So, l = 125; n = 68; f = 20; çf = 22 and h = 20

Using formula, Median = l + \(\left[\frac{\frac{n}{2}-c f}{f}\right]\) × h

= 125 + \(\left\{\frac{\frac{68}{2}-22}{20}\right\}\) × 20

=125+ \(\frac{34-22}{20}\) × 20

= 125 + 12 = 137

For mean:

From above data, assumed mean (a) = 135
Width of class (h) = 20
∴ \(\bar{u}=\frac{\Sigma f_{i} u_{i}}{\Sigma f_{i}}=\frac{7}{68}\) = 0.102
Using formula, Mean \((\overline{\mathrm{X}})=a+h \bar{u}\)
\(\overline{\mathrm{X}}\) = 135 + 20 (0.102)
= 135 + 2.04 = 137.04.

For Mode:
In the given data,
Maximum frequency is 20 and it correspond to 125 – 145.
∴ Modal class = 125 – 145
So l = 125; f₁ = 20; f₀ = 13; f₂ = 14and h = 20
Using formula, Mode = l + \(\left(\frac{f_{1}-f_{0}}{2 f_{1}-f_{0}-f_{2}}\right)\) × h

Mode = 125 + \(\left(\frac{20-13}{2(20)-13-14}\right)\) × 20

= 125 + \(\frac{7}{40-27}\) × 20

= 125 + \(\frac{140}{13}\)
= 125 + 10.76923
= 125 + 10.77 = 135.77.
Hence. median, mean and mode of given data is 137 units: 137.04 units and 135.77 units.

Question 2.
If the median of the distribution given below is 28.5, find the values of x and y.

Solution:

In thegiven data, \(\Sigma f_{i}\) = n = 60
∴ \(\frac{n}{2}=\frac{60}{2}\) = 30
Also, median of the distribution = 28.5 ………….(Given)
which lies in the class interval 20 – 30
Median class = 20 – 30
So, l = 20; f = 20; cf = 5 + x; h = 10
From table, it is clear that 45 + x + y = 60
x + y = 60 – 45 = 15
or x + y = 15 ……………….(1)
Now, using formula, Median = l + {\(\left\{\frac{\frac{n}{2}-c f}{f}\right\}\)

28.5 = 2o + \(\left\{\frac{30-(5+x)}{20}\right\}\)

or 28.5 = 20 + \(\frac{30-5-x}{2}\)

or 28.5 = \(\)

or 2(28.5) = 65 – x
or 57.0 = 65 – x
or x = 65 – 57 = 8
∴ x = 8
Substitute this value of x in (1), we get
8 + y = 15
Hence, values of x and y is 8 and 7.

Question 3.
A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onwards but less than 60 years.

Solution:

Here, \(\Sigma f_{i}\) = n = 100
then, \(\frac{n}{2}=\frac{100}{2}\) = 50, which lies in the interval 35 – 40
∴ Median class = 35 – 40
So, l = 35; n = 100; f = 33; cf = 45 and h = 5
Using formula, Median = l + \(\left\{\frac{\frac{n}{2}-c f}{f}\right\}\) × h

= 35 + \(\left\{\frac{\frac{100}{2}-45}{33}\right\}\) × 5

= 35 + \(\frac{50-45}{33}\) × 5

= 35 + \(\frac{25}{33}\)
= 35 + 0.7575 = 35 + 0.76 (approx.) = 35.76
Hence, median age of given data is 35.76 years.

Question 4.
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table:

Find the median length of the leaves.
Solution:
Since the frequency distribution is not continuous, so firstly we shall make it continuous.

Here, \(\Sigma f_{i}\) = n = 40
then, \(\frac{n}{2}=\frac{40}{2}\) = 20, which lies in the interval 144.5 – 153.5
∴ Median class = 144.5 – 153.5
So, l = 144.5; f = 12; cf = 17; h = 9
Using formula, Median = l + \(\left\{\frac{\frac{n}{2}-c f}{f}\right\}\) × h

Median = 144.5 + \(\left\{\frac{20-17}{12}\right\}\) × 9

= 144.5 + \(\frac{3 \times 9}{12}\)
= 144.5 + 225 = 146.75
Hence, median length of the leaves is 146.75 mm.

Question 5.
The following table gives the distribution of the life time of 400 neon lamps:

Find the median life time of a lamp.

Solution:

Here, \(\Sigma f_{i}\) = n = 400
∴ \(\frac{n}{2}=\frac{400}{2}\) = 200; which lies in the interval 3000 – 3500.
∴ Median class = 3000 – 3500
So, l = 3000; n = 400; f = 86; cf = 130 and h = 500
Using formula, Median = l + \(\left\{\frac{\frac{n}{2}-c f}{f}\right\}\) × h

Median = 3000 + \(\left\{\frac{\frac{400}{2}-130}{86}\right\}\) × 500

= 3000 + \(\left(\frac{200-130}{86}\right)\) × 500

= 3000 + \(\frac{70 \times 500}{86}\) + 406.9767441

= 3000 + 406.98 (approx.) = 3406.98
Hence, median life time of a lamp is 3406.98 hours.

Question 6.
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames ? Also, find the modal size of the surnames.
Solution.
For Median:

Here, Here, \(\Sigma f_{i}\) = n = 100
∴ \(\frac{n}{2}=\frac{100}{2}\) = 50, which lies in interval 7 – 10.
∴ Median class = 7 – 10
So, l = 7; n = 100; f = 40; cf = 36 and h = 3
Using formula, Median = l + \(\left\{\frac{\frac{n}{2}-c f}{f}\right\}\) × h

Median = 7 + \(\left\{\frac{\frac{100}{2}-36}{40}\right\}\) × 3

= 7 + \(\left\{\frac{50-36}{40}\right\}\) × 3

= 7 + \(\frac{14 \times 3}{40}\)

= 7 + \(\frac{21}{20}\) = 7 + 1.05 = 8.05
Hence, the median of letters in the surnames is 8.05.

For Mean:

From above data, Assumed Mean (a) = 8.5
Width of class (h) = 3
∴ \(\bar{u}=\frac{\Sigma f_{i} u_{i}}{\Sigma f_{i}}=\bar{u}=\frac{-6}{100}\) = – 0.06

Using formula, Mean \((\overline{\mathrm{X}})=a+h \bar{u}\)
\(\bar{X}\) = 8.5 + 3 (- 0.06) = 8.5 – 0.18 = 8.32
Hence, mean number of letters in the surnames is 8.32.

For Modal:
In the given data Maximum frequency is 44 and it corresponds to interval 7 — 10
∴ Modal class = 7 – 10
So l = 7; f₁ = 40; f₀ = 30; f₂ = 16 and h = 3
Using formula, Mode = l + \(\left(\frac{f_{1}-f_{0}}{2 f_{1}-f_{0}-f_{2}}\right)\) × h

Mode = 7 + \(\left(\frac{40-30}{2(40)-30-16}\right)\) × 3

= 7 + \(\frac{10}{80-46}\) × 3

= 7 + \(\frac{30}{34}\) = 7 + 0.882352941

= 7 + 0.88 (approx.) = 7.88.
Hence. modal size of the surnames is 7.88 letters.

Question 7.
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Solution:

Here, \(\Sigma f_{i}\) = n = 30
∴ \(\frac{n}{2}=\frac{30}{2}\) = 15; which lies in the interval 55 – 60.
∴ Median class = 55 – 60
So, l = 55; n = 30; f = 6; cf = 13 and h = 5
Using formula, Median = l + \(\left\{\frac{\frac{n}{2}-c f}{f}\right\}\) × h

Median = 55 + \(\left\{\frac{\frac{30}{2}-13}{6}\right\}\) × 5

= 55 + \(\left\{\frac{15-13}{6}\right\}\) × 5

= 55 + \(\frac{2 \times 5}{6}\)

= 55 + \(\frac{5}{3}\) = 55 + 1.66666
= 55 + 1.67 (approx.) = 56.67
Hence, median weight of the students are 56.67 kg.

Punjab State Board PSEB 6th Class English Book Solutions English Reading Comprehension Conversation / Dialogue Based Exercise Questions and Answers, Notes.

PSEB 6th Class English Reading Comprehension Conversation / Dialogue Based

Read the following conversation carefully and answer the questions that follow:

1. Anil : Hello Nimmy, how are you?
Nimmy : Hey Anil, I’m good and how are you doing ?
Anil : Well, I’m quiet bored this vacation. Let us join some dance classes.
Nimmy : That sounds great. I’ll ask my parents and let you know tommorow.
Anil : Sure then we’ll go and fix the timings at Bollywood Dance Centre.
Nimmy : Alright and what about holidays homework ?
Anil : I have finished my work and what about you ?
Nimmy : I will finish it in a day or two.
Anil : Great, see you tomorrow. Bye !
Nimmy : Bye.

1. How Is Anil feeling during the vacation ?
(a) happy
(b) bored
(c) energetic
(d) sad.
Answer:
(b) bored.

2. Whom does Nipimy want to ask about dance classes ?
(a) her brother
(b) her sister
(c) her parents
(d) her friend
Answer:
(c) her parents.

3. Which dance centre do Anil and Nimmy wish to join ?
(a) New Centre
(b) Bollywood Dance Centre
(c) Modem Dance Centre
(d) High Heels Centre.
Answer:
(b) Bollywood Dance Centre

4. Has Anil finished his holidays homework?
(a) no
(b) yes
(c) partially
(d) not at all.
Answer:
(b) yes.

5. Nimmy is planning to finish her work:
(a) tomorrow
(b) in a day or two
(c) in a week
(d) in ten days.
Answer:
(b) in a day or two.

2. All friends of Neha come to the party at 6 o’clock in the evening in their best party clothes. Then the teacher enters the room.)

Children : Good evening, madam.
Teacher : Good evening, children. (To Neha) God bless you,
Neha! Here is a birthday gift for you. Have a nice time.
Neha : Thank you, madam.
Mother : Children come here. Now Neha is going to cut the cake.
Chidren : Happy birthday to Neha.
Uncle : Sony, I am late. Happy birthday Neha. Here is a gift for you, a packet of books!
Neha : Thank you, uncle. Thank you very much. That is the nicest gift I have ever received.
Father : Children now have a piece of cake and sweets. Here are small presents for all of you.
(Neha’s mother gives the presents to the children.)
Children : Thank you, uncle, Thank you, aunt for nice gifts.
Neha : Thank you, everyone. Thanks for my birthday presents.

1. Whose birthday party is it ?
(a) Teacher’s
(b) Neha’s
(c) Uncle’s
(d) Father’s
Answer:
(b) Neha’s.

2. Who comes late to the party ?
(a) Neha’s father
(b) Neha’s teacher
(c) Neha’s friends
(d) Neha’s uncle.
Answer:
(d) Neha’s uncle.

3. Uncle brings ……….. as a birthday gift.
(a) cake
(b) some sweets
(c) a packet of books
(d) a beautiful dress.
Answer:
(c) a packet of books

4. Neha’s mother gives children at the end of the party.
(a) small presents
(b) some books
(c) a piece of cake
(d) nothing.
Answer:
(a) small presents.

5. Children are asked to have a piece of cake and ……………
(a) fruit
(b) biscuits
(c) coffee
(d) sweets.
Answer:
(d) sweets.

3. Teacher : Good morning children ! I have some good news for you. We are going to a fair at Ropar tomorrow.
Raj : How are we going ?
Teacher : We shall take a bus to Ropar.
Gurudev : When shall we leave ?
Teacher : We shall leave at 9 o’clock in the morning.
Harpreet : Who will go with us ?
Teacher : Mr. Shanna and Mrs. Singh will go with us.
Mini : Will there be something to eat ?
Teacher : Oh yes, there will be lots of things to eat and many different games to play.
Raj : I will go on the merry-go-round.
Rani : I will go on the giant-wheel.
Ali : Will there be some rides too ?
Teacher : Oh yes ! There will be elephant, camel and hore rides. Some of you may enjoy these rides. You will have a lot of fun.
Nina : What other things shall we see at the fair ?

1. A fair is going to be held at
(a) Amritsar
(b) Patiala
(c) Ropar
(d) Chandigarh.
Answer:
(c) Ropar.

2. Mr. Sharma and ……………. will go with the students.
(a) Mrs. Singh
(b) Mrs. Sharma
(c) Mr. Singh
(d) All the three.
Answer:
(a) Mrs. Singh.

3. Raj wishes to enjoy ……………..
(a) the merry-go-round
(b) the giant-wheel
(c) slides
(d) swings.
Answer:
(a) the merry-go-round.

4. At the fair, the students can enjoy …………..
(a) elephant rides
(b) camel rides
(c) horse rides
(d) all these.
Answer:
(d) all these.

5. The party will leave at……………. in the morning.
(a) 7 o’clock
(b) 9 o’clock
(c) 8 o’clock
(d) 10 o’clock
Answer:
(b) 9 o’clock.

Or
The party will go to Ropar
(a) by train
(b) on bicycles
(c) by bus
(d) on foot.
Answer:
(c) by bus.

4. The sun is out. It is early morning. Amrit and Harpreet are still sleeping.

Mother : Wake up children ! It is six o’clock. You will be late for school.
Amrit is still sleeping but Harpreet is quickly getting up. He is going to the bathroom to brash his teeth and wash his face,
Harpreet : Wake up Amrit, we will be late for school! Look I am washing my face and brushing my teeth.
Amrit : What’s the time ?
Harpreet : It is half past six.
Amrit : Please let me sleep a little longer. Wake me up at half past seven.
Mother : Now get up Amrit. It is seven o’clock. Look Harpreet is finishing his breakfast and dressing for school.
Harpreet : I am leaving for school, it is eight o’ clock. You are late Amrit. You know the school starts at half past eight.

1. It is morning but the children are still ……………….
(a) reading
(b) playing
(c) talking
(d) sleeping.
Answer:
(d) sleeping.

2. Mother wakes up the children at ………………
(a) six o’clock
(b) seven o’clock
(c) eight o’clock
(d) nine o’clock
Answer:
(a) six o’clock.

3. Mother wakes up Amrit and Harpreet because they can be late for
(a) breakfast
(b) school
(c) office
(d) library.
Answer:
(b) school.

4. Harpreet leaves for school at………….
(a) 7 o’clock
(b) half past seven
(c) 8 o’clock
(d) half past eight.
Answer:
(c) 8 o’clock.

5. The school starts at…………………….
(a) eight o’clock
(b) half past eight
(c) seven o’clock
(d) half past seven.
Answer:
(b) half past eight.

5. Neera : Hello Amar ! Where did you go this weekend ?
Amar : I had gone to Amritsar with my mother.
Neera : How lovely ! What did you see there ?
Amar : We visited Sri Darbar Sahib. It is also called the Golden Temple.
Neera : Isn’t it beautiful ?
Amar : Oh yes ! It is very beautiful. The temple is covered in gold. It shines brightly as the sunlight falls on it. We bathed in the holy tank.
Neera : Are there some other places to see ?
Amar: Yes, we also visited the Durgiana Mandir and the Jallianwala Bagh.
Neera : Were there many shops ?
Amar : Yes, there were ! Some shops were big and some small. We bought many things from the market.-
Neera : I will also go there next week with my grandfather.

1. Amar had gone to Amritsar with ……………..
(a) his friends
(b) Neera
(c) his mother
(d) parents.
Answer:
(c) his mother.

2. In Amritsar Amar visited ……………..
(a) Sri Darbar Sahib
(b) Durgiana Mandir
(c) Jalianwala Bagh
(d) All the above.
Answer:
(d) All the above.

3. Sri Darbar Sahib is also called ……………
(a) the Golden Temple
(b) the Durgiana Mandir
(c) the Jalianwala Temple
(d) None of these.
Answer:
(a) the Golden Temple

4. Neera will go to Amritsar with her
(a) parents
(b) brother and sister
(c) grandfather
(d) grandmother.
Answer:
(c) grandfather.

5. At Amritsar, Amar and his mother bathed in
(a) a lake
(b) a canal
(c) the holy tank
(d) a river.
Answer:
(c) the holy tank.

6. Lion (showing a lot of interest): Do you store food in your stomach ?

Camel : No, I don’t. I store it in my hump. I eat a lot of food at one time. Then I don’t need to eat for a fortnight.
Lion : That’s interesting. But what do you eat ?
Camel : I eat leaves, but there are no trees in a desert.
Lion : What do you eat there ?
Camel : There are thorny bushes in the desert. I eat the thorns. The thorns don’t prick my thick tongue.
Lion : How funny!
Camel : Mr. King of die Forest, please come with me to the desert.
Lion : No, I’d better not. I can’t walk on burning sand. I can’t store food and water and I can’t eat thorns. Good-bye and good luck, Mr Ship of the Desert.

1. The camel can live without eating (food) for …………….
(a) a week
(b) A fortnight
(c) a mo nth
(d) three days.
Answer:
(b) a fortnight.

2. The camel stores food in its ………….
(a) stomach
(b) belley
(c) hump
(d) month.
Answer:
(c) hump.

3. In deserts the camel eats ……………
(a) thorns
(b) green grass
(c) small plants
(d) fallen fruit
Answer:
(a) thorns.

4. Who is Mr King of the Forest in the passage?
(a) elephant
(b) camel
(c) lion
(d) none of these.
Answer:
(c) Lion.

5. Mr. Ship of the desert is……………….
(a) camel
(b) lion
(c) burning sand
(d) camel’s hump.
Answer:
(a) camel.

Punjab State Board PSEB 6th Class English Book Solutions English Reading Comprehension Picture / Poster Based Exercise Questions and Answers, Notes.

PSEB 6th Class English Reading Comprehension Picture / Poster Based

Look at the picture carefully and answer the questions that follow

1.

(i) The weather is …………….
(a) sunny
(b) snowy
(c) clear
(d) rainy.
Answer:
(d) rainy.

(ii) There are …………. puddles in the picture.
(a) three
(b) four
(c) two
(d) one.
Answer:
(c) two.

(iii) There are……………… children in the picture.
(a) two
(b) five
(c) three
(d) four.
Answer:
(d) four.

(iv) A ……………. is hiding under a leaf.
(a) snail
(b) frog
(c) bird
(d) fish.
Answer:
(b) frog.

(v) We use umbrellas to save ourselves from …………..
(a) clouds
(b) puddles
(c) trees
(d) rain.
Answer:
(d) rain.

2.

(i) There are …………….. plants under the tree.
(a) thorny
(b) flower
(c) fruit
(d) dry.
Answer:
(b) flower.

(ii) There are…………… huts in the picture.
(a) two
(b) three
(c) many
(d) few
Answer:
(a) two.

(iii) A river flows under the …………
(a) trees
(b) plants
(c) bridge
(d) hills.
Answer:
(c) bridge.

(iv) The weather is ……………….
(a) sunny
(b) snowy
(c) clear
(d) rainy.
Answer:
(c) clear.

(v) It is a …………………. area.
(a) sandy
(b) sea-side
(c) forest
(d) hilly.
Answer:
(d) hilly.

3.

Two children are ………… in their kitchen garden.
(a) walking
(b) working
(c) playing
(d) running.
Answer:
(b) working.

(ii) They are ………… plants.
(a) watering
(b) growing
(c) cleaning
(d) manuring.
Answer:
(a) watering.

(iii) The day is …………..
(a) snowy
(b) cloudy
(c) sunny
(d) rainy.
Answer:
(c) sunny

(iv) A ……………. is flying under a tall tree.
(a) bird
(b) butterfly
(c) fly
(d) kite.
Answer:
(b) butterfly.

(v ) The flowers in the picture look very …………….
(a) faded
(b) beautiful
(c) ugly
(d) muddy.
Answer:
(b) beautiful.

4.

(i) This is a big
(a) school office
(b) consumer store
(c) booking office
(d) library.
Answer:
(d) library.

(ii) Books are lying on the
(a) shelves
(b) roof
(c) tables
(d) floor.
Answer:
(a) shelves.

(iii) In a library, there are books on different ………….
(a) religions
(b) jobs
(c) subjects
(d) problems
Answer:
(c) subjects.

(iv) The reading of books gives us ……………
(a) health
(b) wealth
(c) property
(d) knowledge
Answer:
(d) knowledge.

(v) This library can be given the name of ……………
(a) Entertaining Hut
(b) Knowledge Garden
(c) Knowledge Show
(d) None of these.
Answer:
(b) Knowledge Garden.

5.

(i) The atmosphere in the picture is ………….
(a) dirty
(b) pretty
(c) lovely
(d) charming.
Answer:
(a) dirty.

(ii) We can see a large …………… of garbage.
(a) basket
(b) dustbin
(c) heap
(d) sack.
Answer:
(c) heap

(iii) Many young ………….. are collecting the garbage.
(a) girls
(b) men and women
(c) persons
(d) women
Answer:
(c) persons

(iv) They will …………… it outside the city.
(a) dump
(b) throw
(c) sell
(d) display.
Answer:
(a) dump

(v) At a little distance we can see …………….
(a) a car
(b) a bus
(c) a jeep
(d) an e-rickshaw.
Answer:
(b) a bus.

6.

(i) The weather is …………..
(a) hot
(b) warm
(c) rainy
(d) snowy.
Answer:
(d) snowy.

(ii) There are …………….. children in die picture.
(a) two
(b) three
(c) four
(d) five
Answer:
(a) four

(iii) A dog is running ………….. a boy lying on the snow.
(a) after
(b) towards
(c) near
(d) under
Answer:
(b) towards

(iv) The tree in the picture is a…………….. tree.
(a) Christmas
(b) Diwali
(c) Mango
(d) Neem
Answer:
(a) Christmas.

(v) A girl is putting a cap on ……………….
(a) the dog
(b) the tree
(c) a snow man
(d) his friend
Answer:
(c) a snow man.

Punjab State Board PSEB 6th Class English Book Solutions English Grammar Verbs Exercise Questions and Answers, Notes.

PSEB 6th Class English Grammar Verbs

A Verb is an action word. It tells us something about a person or thing.
Verb एक क्रिया शब्द है। यह हमें किसी व्यक्ति या वस्तु के बारे में कुछ बताता है।

A Verb tells us-
1. What a person or thing is; as-

• The rose is red.
• The mouse was dead.
• Camels are useful animals.

2. What a person or thing has; as-

• A week has seven days.
• Monkeys have long tails.
• They had a good day yesterday.

3. What a person or thing does; as-

• She made a doll.
• He is writing a poem.
• The sun rises in the east.

Parts of a Verb क्रिया के भाग

A Verb in English can have two parts:
1. The Main (Primary) (मुख्य) Verb.
2. The Auxiliary (Helping) (सहायक) Verb.

1. The Main Verb tells us ‘what happened or ‘what the situation is’. The main verb can have four different forms:
(i) V₁ (go) or the root form.
(ii) V₂ (went) or the past form.
(iii) V₃ (gone) or the past participle form.
(iv) V₁-ing (going) or the present participle form.

2. The Auxiliary Verb helps the Main Verb to complete its meaning. It helps the Main Verb to form a Tense, or to form Negatives and Questions.
सहायक क्रिया Main verb (मख्य क्रिया) के अर्थ को पूरा करने में सहायता करती है। यह काल (Tense), नकारात्मक कथनों अथवा प्रश्नों के निर्माण में मुख्य क्रिया की सहायता करती है।

The following verbs are often used as Auxiliary Verbs:

• is, am, are, was, were.
• has, have, had.
• do, does, did.
• will, would, shall, should.
• can, could, may, might, must, etc.

Exercises (Solved)

I. Underline the Verbs in the following sentences:

1. I live in Delhi.
2. The lion roars.
3. It is raining outside.
4. I have two brothers.
5. Rina gave me a flower.
6. A cobbler mends shoes.
7. I will give you my book.
8. The driver was cleaning the car.
Hints:
1. live
2. roars
3. is raining
4. have
5. gave
6. mends
7. will give
8. was cleaning

II. Fill in the blanks with appropriate Auxiliaries:

1. …………… I come in, sir ?
2. I ………….. finished my work.
3. You …………… pay your debts.
4. We …………… help our friends.
5. I ………….. solve this question.
6. You ……………. sit on this bench.
7. Anyone ……………. make mistakes.
8. He ………….. not telling the truth.
Hints:
1. May
2. have
3. must
4. shall
5. can
6. can
7. can
8. is

Three Forms (Conjuction) of the verb

Exercises (Solved)

I. Conjugate the following Verbs:

build, fall, rise, speak, teach, weep, ruin, look, sleep, learn, study, throw, weave, forget, destroy
Answer:

Present	Past	Past Participle
build	built	built
fall	fell	fallen
rise	rose	risen
speak	spoke	spoken
teach	taught	taught
weep	wept	wept
ruin	ruined	ruined
look	looked	looked
sleep	slept	slept
learn	learnt	learnt
study	studied	studied
throw	threw	thrown
weave	wove	woven
forget	forgot	forgotten
destroy	destroyed	destroyed

II. Give the present participle form of the following Verbs:

1. sit
2. die
3. sink
4. fight
5. catch
6. tie
7. run
8. bite
9. shine
10. apply
11. hit
12. live
13. swim
14. writer
15. begin
Hints:
1. sitting
2. dying
3. sinking
4. fighting
5. catching
6. tying
7. running
8. biting
9. shining
10. applying
11. hitting
12. living
13. swimming
14. writing
15. beginning.

Note : 1. Verb की Present participle form verb के साथ ‘ing’ जोड़ने से बनती है।
2. कुछ verbs में ‘ing’ जोड़ते समय उनके अंतिम अक्षर अक्षरों में कुछ फेरबदल भी करना पड़ता है।

Punjab State Board PSEB 6th Class English Book Solutions English Grammar Preposition Exercise Questions and Answers, Notes.

PSEB 6th Class English Grammar Preposition

A Preposition is a word used before a Noun or Pronoun to indicate place, direction, source; as-
on, in, at, under, upon, into, from.
In the following pictures, study the different positions of the cat.

The italicized words show the position of the cat. We call them prepositions. Some other Propositions of common use are-
of, near, to, after, with, during, off, down, by, above, before, between, at, from, for, among, below, without

Use of Some Prepositions

1. On, Upon.
On indicates position of rest on something.
Upon indicates motion.

• The books are on the table.
• The cat jumped upon the wall.

2. In, Into.
In expresses position of rest inside something.
Into indicates motion towards the inside of something.

• Meera was sitting in her room.
• Neha went Into the room.

3. At, In, On
At is used for a point of time.
On is used with days and dates.
In is used with months and years.

• My brother came here at eight.
• I met my friend at 5 o’clock.
• India got freedom in 1947.
• I shall go to Mumbai on Monday.
• His birthday falls on 15 Nov.
• He went to Ludhiana in May.

Note some other uses of ‘at’ and ‘in’.

• At dawn / noon / night
• In the morning
• In the evening
• In the afternoon

4. At, In
At is used with names of small villages and towns.
In is used with names of big cities and states.

• I was bom at Rampur.
• My uncle lives in Delhi.

5. Between, Among.
‘Between’ is used for two persons, places or things.
‘Among’ is used for more than two persons, places or things.

• The two brothers divided their property between themselves.
• The three brothers quarrelled among themselves.

Exercises (Solved)

I. Underline the prepositions in the following sentences:

1. She sat beside me.
2. Rani is afraid of her teacher.
3. The bird flew over the trees.
4. The dog ran after the mouse.
5. The sky and clouds are above us.
6. The river flows under the bridge.
7. December comes after November.
8. There is a big well behind his house.
9. She brought a beautiful dress for me.
10. I went with my friend to see a movie.
Hints:
2. of
3. over
4. after
5. above
6. under
7. after
8. behind
9. for
10. with, to.

II. Fill in the blanks with a suitable preposition from the box:

of, on, for, near, into, at, by, after, from, with
1. I am fond …………… music.
2. Look …………… the blackboard.
3. I am waiting …………… the bus.
4. The policeman ran …………… the thief.
5. Keep the books …………… the shelf.
6. What is Ludhiana famous …………… ?
7. We are proud …………… our country.
8. My ball has fallen …………… the well.
9. Are you coming …………… road or rail ?
10. I went …………… my Mends for a picnic.
11. There is a temple …………… the hospital.
12. Tony cleaned the floor …………… a broom.
13. The girls are waiting …………… the station.
14. My Mend’s house is far …………… our house.
15. She lives …………… her parents.

Hints:
1. of
2. at
3. for
4. after
5. on
6. for
7. of
8. into
9. by
10. with
11. near
12. with
13. at
14. from
15. with.

III. Write what you see in this picture. Use a suitable preposition in each one of your sentences; as-

Mrs. Raj and Mrs. Rani are sitting on a bench.
Tony is trying to get at the apple.
Some birds are flying in the sky.
A crow is sitting on the branch of a tree.
A dog is running after a ball.
Neha is reading a book under a tree.
Sonu and Anu are waiting for the fancy ball to come down.

Punjab State Board PSEB 6th Class English Book Solutions English Grammar Articles Exercise Questions and Answers, Notes.

PSEB 6th Class English Grammar Articles

‘A’, “an’, ‘the’ are called Articles.
An Article is a word that determines or limits the noun that follows it.
An Article is always used with a Noun. So it can also be called an Adjective.
Article वह शब्द है जो अपने बाद प्रयोग किए गए Noun को निरिचत अथवा सीमित करता है।
Article का प्रयोग हमेशा Noun के साथ ही किया जाता है। इसलिए इसे Adjective भी कहा जा सकता है।

Use of ‘a’, ‘an’

You have already learnt that ‘an’ is used before words beginning with a vowel sound and ‘a’ before words beginning with a consonant sound.

Look at these pictures and name the objects using appropriate articles. Two have been done for you:

Exercise (Solved)

Put ‘a’ or ‘an’ for each:

1. …………. ox
2. ………… kite
3. ………… unit
4. ………… cart
5. ………… M.A.
6. ……….. hour
7. …………. table
8. ………. inkpot
9. ……….. monkey
10. ……….. elephant
11. ……….. honest man
12. ………. useful thing
13. ……….. European lady
14. ……….. one-eyed man.
Hints:
1. an
2. a
3. a
4. a
5. an
6. an
7. a
8. an
9. a
10. an
11. an
12. a
13. a
14. a.

Use of ‘the’

We use “the’ to talk of some specific (विशिष्ट) person, animal, place or thing. We use the’ in the following cases also:

1. Before the names of rivers and seas–
the Ganges, the Sutlej, the Jamuna; the Indian Ocean, the Arabian sea.

2. Before the names of magazines, newspapers and holy books–
the India Today, the Observer, the Tribune, the Times of India; the Bible, the Quran, the Gita.

3. Before the names of races or people–
the Hindus, the Punjabis, the English.

4. Before superlatives–
the hardest, the best, the eldest

5. Before the names of natural objects–
the sun, the moon, the earth.

6. Before the names of mountain ranges–
the Himalayas, the Vindhyas, the Alps

7. Before the names of historical places–
the Jallianwalla Bagh; the Red Fort, the Taj Mahal

8. Before a noun that is modified-
She is the girl who stands first in the class.

Exercises (Solved)

I. Fill in the blanks with the articles ‘a’, ‘an’ or ‘the’:

1. I waited for ……………. hour.
2. ………….. ant is …………… insect.
3. …………. Red Fort is in Delhi.
4. Jack and Jill went up …………… hill.
Speak truth. Don’t tell …………. lie.
6. She rode on …………… elephant at the zoo.
7. ………….. earth is covered with land and water.
8. Bible is ……………. sacred book of Christians.
9. In ………….. sky at night we can see …………… stars and ……………. moon.
10. He took …………… banana, …………… orange and ………….. apple for breakfast.
11. ………….. Sun shines in the east.
12. He is …………….. engineer.
Hints:
1. an
2. An, an
3. The
4. the
5. the, a
6. an
7. The
8. The, a, the
9. the, the, the
10. a, an, an.
11. The
12. an

II. Fill in the blanks with suitable articles (a/an/the):

1. Rohit wrote …………. essay.
2. I saw …………… one eyed man.
3. ………….. sun rises in the east.
4. watch tells us …………. time.
5. accident is ……………. ugly sight.
6. She went home in …………….. morning.
7. …………….. boy standing there is my friend.
8. Mohit saw ……………… old man crossing the road.
9. In the north of our country are ……………. Himalayas.
10. ………….. Ganges, ……………… Yamuna and Saraswati meet at Sangam.
Hints:
1. an
2. a
3. The
4. The, the
5. An, an
6. the
7. The
8. an
9. the
10. The, the, the

III. Rewrite each sentence correctly:

1. He is an European.
2. I heard loud noise.
3. Look at blackboard.
4. Rajan is honest man.
5. I go for the walk in evening.
6. Gardener is watering plants.
7. I gave him an one-rupee coin.
8. An umbrella is an useful thing.
9. He was a best judge of horses.
10. She is a tallest girl in our class.
Answer:
1. He is a European.
2. I heard a loud noise.
3. Look at the blackboard.
4. Rajan is an honest man.
5. I go for a walk in the evening.
6. The gardener is watering the plants.
7. I gave him a one-rupee coin.
8. An umbrella is a useful thing.
9. He was the best judge of horses.
10. She is the tallest girl in our class.

Punjab State Board PSEB 6th Class English Book Solutions English Grammar Adjectives Exercise Questions and Answers, Notes.

PSEB 6th Class English Grammar Adjectives

An Adjective is a defining word. It is used with a Noun to tell us something more about that noun; as-
Adjective एक व्याख्यात्मक शब्द है। इसका प्रयोग किसी संज्ञा (Noun) के साथ उसके बारे में कुछ और बताने के लिए किया जाता है।

1. He is a tall boy.
2. She is a rich lady.
3. I have many books.

We can use Adjectives to compare (तुलना करना) the qualities of Nouns; as-

1. Chintu is a fat boy.
2. Mintu is fatter than Chintu.
3. Pintu is the fattest of the three.

The words fat, fatter and fattest show the degrees of a quality. We call them Degrees of Comparison.

Degrees Of Comparison

There can be three Degrees of Comparison:

1. Positive Degree.
2. Comparative Degree.
3. Superlative Degree.

1. Positive Degree : The ordinary form (साधारण रूप) of the adjective is called Positive Degree; as-

• Meena is a tall girl.
• June is a hot month.
• Dhawan is a good player.

2. Comparative Degree : When two things of the same class are compared, we use the Comparative Degree; as-

• Anita is taller than Payal.
• May is hotter than April.
• Virat is a better player than Murli.

3. Superlative Degree : When one thing is compared with all others of the same class, we use the Superlative Degree; as-

• Anita is the tallest of the three.
• June is the hottest month of the year.
• Virat is the best player in our cricket team.

Note that we usually use-
“the’ before a Superlative Degree.
“than’ after a Comparative Degree.

Forming Degrees Of Comparison

1. By adding -er and -est:

Positive	Comparative	Superlative
tall	taller	tallest
fast	faster	fastest
long	longer	longest
kind	kinder	kindest
slow	slower	slowest
poor	poorer	poorest
short	shorter	shortest
small	smaller	smallest
old	older	oldest
young	younger	youngest

2. By adding -r and -st:

Positive	Comparative	Superlative
late	later	latest
fine	finer	finest
nice	nicer	nicest
wise	wiser	wisest
large	larger	largest
brave	braver	bravest
gentle	gentler	gentlest

3. By adding -ier and -iest in place of the final ‘-y’:

Positive	Comparative	Superlative
dirty	dirtier	dirtiest
noisy	noisier	noisiest
funny	funnier	funniest
heavy	heavier	heaviest
happy	happier	happiest
pretty	prettier	prettiest
greedy	greedier	greediest

4. By doubling the final consonant before adding -er and -est:

Positive	Comparative	Superlative
fat	fatter	fattest
big	bigger	biggest
hot	hotter	hottest
sad	sadder	saddest
thin	thinner	thinnest
wet	wetter	wettest

5. By adding more and most:

Positive	Comparative	Superlative
honest	more honest	most honest
popular	more popular	most popular
beautiful	more beautiful	most beautiful
wonderful	more wonderful	most wonderful
interesting	more interesting	most interesting

6. By using a different word:

Positive	Comparative	Superlative
good	better	best
little	less	least
old	elder	eldest
bad	worse	worst
much / many	more	most

Exercises (Solved)

I. Fill in the blanks with ‘than’ or ‘the’:

1. June is hotter ————– April.
2. This is ———— best book I have.
3. Riding is ———- best kind of exercise.
4. She is more intelligent ———– her sister.
5. A wise enemy is better ———— a foolish friend.
6. Shakespeare was ———— greatest dramatist of England.
Hints:
1. than
2. the
3. the
4. than
5. than
6. the.

II. Complete the following table for Degrees of Comparison:

Positive	Comparative	Superlative
dim	dimmer	dimmest
lazy	lazier	laziest
cool	cooler	coolest
dull	duller	dullest
hard	harder	hardest
wide	wider	widest
good	better	best.
quick	quicker	quickest
clever	cleverer	cleverest
happy	happier	happiest
narrow	narrower	narrowest
greedy	greedier	greediest
naughty	naughtier	naughtiest
important	more important	most important

III. Fill in each blank with the correct form of the given Adjective:

1. Soni is ———– than Neha. (pretty)
2. My bag is ———— than his. (heavy)
3. Today is ———— than yeserday. (cold)
4. Raj has ———– friends than I have. (much)
5. A hare runs ———— than a tortoise. (fast)
6. Rosy is the ———– girl in our town. (beautiful)
7. I am not ———– happy than you are. (little)
8. She is the ————– student in our class. (good)
9. This is the ———— thing I have ever seen. (bad)
Hints:
1. prettier
2. heavier
3. colder
4. more
5. faster
6. most beautiful
7. less
8. best
9. worst.

IV. Point out the Adjective and its Degree of Comparison in each sentence:

1. This is an easy question.
2. Ashoka was a great king.
3. She is wiser than her brother.
4. Mumbai is hotter than Shimla.
5. Neeru was wearing a red frock.
6. Manu got more marks than Rajan.
7. Which is the longest river of India ?
8. Who is the best player of your team?
Hints:
1. easy – positive
2. great – positive
3. wiser – comparative
4. hotter – comparative
5. red – positive
6. more – comparative
7. longest – superlative
8. best – superlative.

V. Supply the proper form of the given Adjectives:

1. Hot : May is ———– than April.
2. Tall : Megha is ————- than her sister.
3. Old : My uncle is ———- than my father.
4. Rich : He is the ————- man in our town.
5. Large : Name the ———— city in the world.
6. Dry : Rajasthan is the part ———- of India.
7. Good : This pen is ————- than any other pen.
8. Sharp : Your knife is sharp, but mine is ———-

Hints:
1. hotter
2. taller
3. older
4. richest
5. largest
6. driest
7. better
8. sharper.

Punjab State Board PSEB 6th Class English Book Solutions English Reading Comprehension Unseen Passages Exercise Questions and Answers, Notes.

PSEB 6th Class English Reading Comprehension Unseen Passages

Read the given passages and answer the questions the follow each:

1. It is said that health is wealth. Healthy mind stays in a he%y body. Human body is like a machine. Over-eating and eating junk food harms our body. Ivular exercise keeps us fit and healthy. We must eat at regular intervals. It is our duty to ke, Gur body in good condition. Walking for a few kilometres daily is also a good exercise. If ycr body is in perfect health, you enjoy life. So we all must do regular exercise and stay fit.

Choose the correct option:

(i) Health is ……………
(a) money
(b) wealth
(c) gold
(d) nothing
Answer:
(b) wealth.

(ii) Human body is like a …………….
(a) scooter
(b) machine
(c) engine
(d) furniture.
Answer:
(b) machine.

(iii) When should we eat ?
(a) every time
(b) at regular in;rvals
(c) after long hours
(d) not eat in thtmorning.
Answer:
(b) at regular intervals.

(iv) What is our duty ?
(a) to eat junk food
(b) to eat all the tine
(c) to keep our body fit
(d) to get up late in the morning.
Answer:
(c) To keep our body fit.

(v) If your body is in perfect health
(a) you enjoy life
(b) you do not enjoy mything
(c) everything sounds dull
(d) you feel tired all tie time.
Answer:
(a) you enjoy life.

2. Golu did not like to read that much. One day, Golu’s mother bought him a nev book and Golu loved it. His favourite character in the book was a dog named Sheru. Golu read the whole book in one day. He read three pages before school, five pages after school and two pages before he went to bed. Golu loves reading now.

Choose the correct option:

(i) Golu did not like to:
(a) playgames
(b) watch t.v.
(c) read much
(d) talk to his mother.
Answer:
(c) read much.

(ii) Who bought a new book for Golu ?
(a) his father
(b) his mother
(c) his sister
(d) Sheru.
Answer:
(b) his mother.

(iii) Sheru was the name of:
(a) a dog
(b) Golu’s friend
(c) Golu’s neighbour
(d) none of these.
Answer:
(a) a dog.

(iv) Golu read three page’s of the book:
(a) after he went to bed
(b) before he went to bed
(c) before school
(d) after school.
Answer:
(c) before school

(v) Golu liked:
(a) the book
(b) the dog
(c) neither of these two
(d) both the book and the dog.
Answer:
(d) both the book and the dog.

3. Deenu was so involved r a his dream that he forgot he was carrying a tin on his head. He started running and slipped. The t: in fell down and the oil spilled on the ground. He felt very upset. He came back to the grocer w ith a sad heart and narrated the incident. The grocer scolded him and said. ‘ ‘You have caused m e a loss of rupees five hundred.”

Choose the correct option:

(i) Deenu was invo lved in:
(a) his story
(b) his dream
(c) a grocer
(d) shopping.
Answer:
(b) his dream.

(ii) In the tin, there was:
(a) milk
(b) ghee
(c) sugar
(d) oil.
Answer:
(d) oil

(iii) Why did the grocer scold Deenu ?
(a) because he stole his money.
(b) because of hi$ loss
(c) because he told a lie
(d) none of the above.
Answer:
(b) because of his loss.

(iv) Deem went to the grocer:
(a) happily
(b) cheerfully
(c) With a sad heart
(d) dreaming.
Answer:
(c) with a sad heart.

(v) Deenu felt very upset because:
(a) he fell down
(b) the oil spilled on the ground
(c) the oil made his clothes dirty
(d) he got hurt.
Answer:
(b) the oil spilled on the ground.

4. Shravan is the month of rains. After a long spell of summer, the weather becomes cool and pleasant. There is greenery all around. New plants start growing. All men, women and children begin to feel happy and cheerful. The festival of Teej in this month expresses their feelings of joy. People put on new and colourful clothes on this day. Girls sing folk songs and enjoy swinging.

Choose the correct option:

(i) Shravan is the month of:
(a) fairs
(b) festival after festival
(c) hot summer days
(d) rains
Ans.
(d) rains.

(ii) The weather becomes cool and pleasant in the month of:
(a) Barisakh
(b) Ashad
(c) Shravan
(d) Kartik.
Answer:
(c) Shravan.

(iii) What brings greenery all around ?
(a) rains
(b) summer heat
(c) cold winter
(d) all these.
Answer:
(a) rains.

(iv) The girls sing:
(a) fake songs
(b) folk songs
(c) new songs
(d) film songs
Answer:
(b) folk songs.

(v) When do girls enjoy swinging ?
(a) on Diwali
(b) on Lohri
(c) on Holi
(d) on Teej.
Answer:
(d) On Teej.

5. It was the 15th August last Monday. This day is celebrated as a national festival in India. It was on this day in the year 1947 that we won our Independence from the British rule after a long struggle. This year we celebrated this festival in our school with a great zeal. We had been working hard for a week to beautify our school. We prepared colourful banners and placards with patriotic slogans written on them.

Choose the correct option:

(i) We won our freedom from the British rule in:
(a) 1950
(b) 1952
(c) 1947
(d) 1974.
Answer:
(c) 1947.

(ii) We celebrate 15th August as a:
(a) social festival
(b) religious festival
(c) national festival
(d) none of these.
Answer:
(c) national festival

(iii) How did we win our freedom ?
(a) after a short period of struggle.
(b) after a long period of struggle
(c) without any struggle
(d) after a bloody struggle.
Answer:
(b) after a long period of struggle.

(iv) This year we celebrated the Independence Day
(a) with a great zeal
(b) without any preparation
(c) in a simple manner
(d) with the help of students
Answer:
(a) with a great zeal.

(v) Patriotic slogans were written on ………………….
(a) die walls
(b) walls and banners
(c) playcards
(d) both banners and placards
Answer:
(d) both banners and placards.

6. After the Headmaster’s speech, a cultural programme was organised. The children sang patriotic songs. Some recited poems related to the freedom movement. Some students spoke about the great patriots of India such as Jhansi ki Rani. Tantya Tope, Sardar Bhagat Singh, Neta Ji Subhash Chander Bose, Mahatma Gandhi and the other great sons and daughters of our motherland.

Choose the correct option:

(i) There was a cultural programme:
(a) before the Headmaster’s speech
(b) after the Headmaster’s speech.
(c) after the poems were recited
(d) after the speech of the students.
Answer:
(b) after the Headmaster’s speech.

(ii) What did the cultural programme include ?
(a) patriotic songs
(b) poems related to freedom movement
(c) speeches about the great patriots of India
(d) all the above.
Answer:
(d) all the above.

(iii) Mahatma Gandhi was:
(a) a common man
(b) an ordinary person
(c) a great scholar
(d) a great patriot.
Answer:
(d) a great patriot.

(iv) A great daughter of India mentioned in the passage is:
(a) Jhansi ki Rani
(b) Rani of motherland
(c) Tantya Tope
(d) None of the above.
Answer:
(a) Jhansi ki Rani.

(v) What was the first item of the day?
(a) recitation of poems
(b) patriotic songs
(c) the Headmaster’s speech
(d) a cultural programme.
Answer:
(c) The Headmaster’s speech.

7. Vineet, a student of class VIII was also in the same bus. He swung into action. The exit door near the engine was all on fire. He broke open the emergency door and started pushing the children out through this door. The driver and the conductor saw Vineet, struggling alone. They rushed to help him. By the time the last student was rescued the entire bus had turned into a ball of fire. It was Vineet’s timely action that averted a big tragedy. He saved twenty seven lives. However, he himself suffered some bums during this heroic deed.

Choose the correct option:

(i) Vineet was the student of:
(a) Class VI
(b) Class VII
(c) Class Vin
(d) none of these.
Answer:
(c) Class VIII.

(ii) Which door was on fire ?
(a) entrance door
(b) front door
(c) exit door
(d) emergency dpor.
Answer:
(c) exit door.

(iii) The children were taken out through the ……………….
(a) main door
(b) exit door
(c) frontdoor
(d) emergency door.
Answer:
(d) emergency door.

(iv) Who helped Vineet ?
(a) The driver and the teacher
(b) The conductor and the children
(c) Both the driver and the conductor
(d) The teachers and the children.
Answer:
(c) Both the driver and the conductor.

(v) What happened to Vineet during the heroic deed ?
(a) He suffered some bums.
(b) His face was badly wounded.
(c) All his clothes were burnt.
(d) He came out safe and sound.
Answer:
(a) He suffered some bums.

8. One day the librarian said to him. “Do you really read the books or just return them without reading ?” Narendra said, “Of course, Sir, I thoroughly read all the books borrowed from the library. You can ask me any question from these books.” The librarian took out a book and asked him the questions. Narendra answered all the questions correctly. The librarian was amazed at his sharp memory.

Choose the correct option:

(i) Narendra answered correctly:
(a) two questions
(b) three questions
(c) all the questions
(d) no question.
Answer:
(c) all the questions.

(ii) Who borrowed books from the library ?
(a) librarian
(b) Narendra
(c) Surendra
(d) Narendra’s friends.
Answer:
(b) Narendra.

(iii) The librarian thought that Narendra:
(a) returned the books after reading them.
(b) returned the books after spoiling them.
(c) returned the books without reading them.
(d) all these.
Answer:
(c) returned the books without reading them.

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 5 Data Handling Ex 5.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 5 Data Handling Ex 5.2

1. A survey was made to find the type of music that a certain group of young people liked in a city. Given pie chart shows the findings of this survey.

From this pie chart answer the following:

Question (i).
If 20 people liked classical music, how many young people were surveyed ?
Solution:
Let the required number of total young people surveyed = x
∴ 10% of x = 20
∴ \(\frac {10}{100}\) × x = 20
∴ x = \(\frac{20 \times 100}{10}\)
∴ x = 200
200 young people were surveyed.

Question (ii).
Which type of music is liked by the maximum number of people ?
Solution:
Maximum number of people like the light music.

Question (iii).
If a cassette company were to make 1000 CD’s, how many of each type would they make ?
Solution:
Total number of CD’s = 1000
(a) Number of CD’s for semi classical music = 20 % of 1000
= \(\frac {20}{100}\) × 1000 = 200
(b) Number of CD’s for classical music = 10 % of 1000
= \(\frac {10}{100}\) × 1000 = 100
(c) Number of CD’s for folk music = 30 % of 1000
= \(\frac {30}{100}\) × 1000 = 300
(d) Number of CD’s for light music = 40 % of 1000
= \(\frac {40}{100}\) × 1000 = 400

2. A group of 360 people were asked to vote for their favourite season from the ? three seasons rainy, winter and summer:

Question (i).
Which season got the most votes ?
Solution:
Winter season got the most votes (150).

Question (ii).
Find the central angle of each sector.
Solution:
Total Votes = 90 + 120 + 150 = 360
∴ Central angle of the sector corresponding to :
Summer season = \(\frac {90}{360}\) × 360° = 90°
Rainy season = \(\frac {120}{360}\) × 360° = 120°
Winter season = \(\frac {150}{360}\) × 360° = 150°

Question (iii).
Draw a pie chart to show this information.
Solution:
Draw three radi in such a way that it makes angles of 90°, 120° and 150° at the centre.

3. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.

Colours	Number of people
Blue	18
Green	9
Red	6
Yellow	3
Total	36

Solution:
Central angle of the sector corresponding to :
(i) The blue colour = \(\frac {18}{36}\) × 360°
= 18 × 10° = 180°
(ii) The green colour = \(\frac {9}{36}\) × 360° = 90°
(iii) The red colour = \(\frac {6}{36}\) × 360° = 60°
(iv) The yellow colour = \(\frac {3}{36}\) × 360° = 30°
Thus, the required pie chart is given below.

4. The given pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.

Question (i).
In which subject did the student score 105 marks ?
[Hint: For 540 marks, the central angle = 360°. So for 105 marks, what is the central angle ?]
Solution:
Toted marks = 540
∴ Central angle corresponding to 540 marks = 360°
∴ Central angle corresponding to 105 marks = \(\frac {360}{540}\) × 105° = 70°
The sector having central angle 70° is corresponding to Hindi.
Thus, the student scored 105 marks in Hindi.

Question (ii).
How many more marks were obtained by the student in Mathematics than in Hindi?
Solution:
The central angle corresponding to the sector of Mathematics = 90°
∴ Marks scored in Mathematics = \(\frac{90^{\circ}}{360^{\circ}}\) × 540 = 135
30 (135 – 105) more marks were obtained by the student in Mathematics than in Hindi.

Question (iii).
Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
[Hint:Just study the central angles.]
Solution:
The sum of the central angles for Social Science and Mathematics = 65° + 90° = 155°
The sum of the central angles for Science and Hindi = 80° + 70° = 150°
∴ Marks obtained in Social Science and Mathematics is more than the marks scored in Science and Hindi.

5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart:

Solution:
Central angle of the sector representing:
(i) Gujarati language = \(\frac {40}{72}\) × 360°
= 40 × 5° = 200°
(ii) English language = \(\frac {12}{72}\) × 360°
= 12 × 5°= 80°
(iii) Urdu language = \(\frac {9}{72}\) × 360°
= 9 × 5° = 45°
(iv) Hindi language = \(\frac {7}{72}\) × 360°
= 7 × 5° = 35°
(v) Sindhi language = \(\frac {4}{72}\) × 360°
= 4 × 5° = 20°
The required pie chart is as follows.

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 5 Data Handling InText Questions and Answers.

PSEB 8th Class Maths Solutions Chapter 5 Data Handling InText Questions

Textual (Textbook Page No. 69 – 70)

1. A Pictograph : Pictorial representation of data using symbols.

Question (i).
How many cars were produced in the month of July ?
Solution:
250 cars were produced in the month of July.

Question (ii).
In which month were maximum number of cars produced?
Solution:
Maximum number of cars were produced in the month of September.

2. A Bar Graph : A display of information using bars of uniform width, their heights being proportional to the respective values.

Question (i).
What is the information given by the bar graph ?
Solution:
Here, the bar graph gives information about number of students of class VIII in different academic years.

Question (ii).
In which year is the increase in the number of students maximum ?
Solution:
In year 2004-05, the increase in the number of students is maximum.

Question (iii).
In which year is the number of students maximum ?
Solution:
In year 2007 – 08, the number of students is maximum.

Question (iv).
State whether true or false:
‘The number of students during 2005 – 06 is twice that of 2003 – 04.’
Solution :
False, the number of students during 2005 – 06 is not twice that of 2003 – 04 but more than twice.

3. Double Bar Graph : A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data.

Question (i).
What is the information given by the double bar graph?
Solution :
Here, the double bar graph provides information about marks obtained by a student in different subjects and comparison of his marks in year 2005 – 06 and 2006 – 07.

Question (ii).
In which subject has the performance improved the most?
Solution :
In the subject Maths, the performance has improved the most.

Question (iii).
In which subject has the performance deteriorated?
Solution :
In the subject English, the performance has deteriorated.

Question (iv).
In which subject is the performance at par?
Solution:
In the subject Hindi, the performance is at par.

Think, Discuss and Write (Textbook Page No. 71)

Question 1.
If we change the position of any of the bars of a bar graph, would it change the information being conveyed? Why?
Solution:
If the height of a bar remains unchanged, then changing of its position does not change the information being conveyed.

Try These (Textbook Page No. 71)

Question 1.
Draw an appropriate graph to represent the given information:

Solution:
To represent the given data by a bar graph, draw two axes perpendicular to each other. Let us represent ‘Months’ on \(\overrightarrow{\mathrm{OX}}\) and ‘Number of watches sold’ \(\overrightarrow{\mathrm{OY}}\) on OY. Let us make rectangles of same width. The heights of the rectangles are proportional to the number of watches, using a suitable scale :
Here, scale is 1 cm = 500 watches
Since, 500 watches = 1 cm
1000 watches = 2 cm
1500 watches = 3 cm
2000 watches = 4 cm
2500 watches = 5 cm

Question 2.

Children who prefer	School A	School B	School C
Walking	40	55	15
Cycling	45	25	35

Solution:
Since, a comparison of two activities is to be represented, therefore a double graph is drawn by taking the ‘Schools’ along X-axis and ‘Number of children’ along Y-axis, using a scale of 1 cm = 5 children.

Question 3.
Percentage wins in ODI by 8 top cricket teams.

Teams	From Champions Trophy to World Cup ’06	Last 10 ODI in ’07
South Africa	75%	78%
Australia	61 %	40%
Sri Lanka	54%	38%
New Zealand	47%	50%
England	46%	50%
Pakistan	45%	44%
West Indies	44%	30%
India	43%	56%

Solution:
To compare the percentage win in ODI achieved by various teams, we represent the data by a double bar graph. We represent the ‘Team’s Names’ along the X-axis and their ‘percentage win’ along Y-axis, using the scale 1 cm – 5%.

Try These (Textbook Page No. 72)

1. A group of students were asked to say which animal they would like most to have as a pet. The results are given below:
dog, cat, cat, fish, cat, rabbit, dog, cat, rabbit, dog, cat, dog, dog, dog, cat, cow, fish, rabbit, dog, cat, dog, cat, cat, dog, rabbit, cat, fish, dog.
Make a frequency distribution table for the same.
Solution:
Using tally-marks, we have

Try These (Textbook Page No. 73-74)

1. Study the following frequency distribution table and answer the questions given below.
Frequency Distribution of Daily Income of 550 Workers of a factory:

Class Interval (Daily Income in ₹)	Frequency (Number of workers)
100 – 125	45
125 – 150	25
150 – 175	55
175 – 200	125
200 – 225	140
225 – 250	55
250 – 275	35
275 – 300	50
300 – 325	20
Total	550

Question (i).
What is the size of the class intervals ?
Solution:
Class size = [Upper class limit] – [Lower class limit]
= 125 – 100
= 25

Question (ii).
Which class has the highest frequency ?
Solution:
The class 200 – 225 is having the highest frequency (140).

Question (iii).
Which class has the lowest frequency ?
Solution :
The class 300 – 325 has the lowest frequency (20).

Question (iv).
What is the upper limit of the class interval 250 – 275?
Solution:
The upper limit of the class interval 250 – 275 is 275.

Question (v).
Which two classes have the same frequency ?
Solution :
The classes 150 – 175 and 225 – 250 are having the same frequency (55).

2. Construct a frequency distribution table for the data on weights (in kg) of 20 students of a class using intervals 30 – 35, 35 – 40 and so on.
40, 38, 33, 48, 60, 53, 31, 46, 34, 36, 49, 41, 55, 49, 65, 42, 44, 47, 38, 39
Solution:
Lowest observation = 31
Highest observation = 65
Class intervals :
30-35, 35-40, 40-45, ……..
The frequency distribution table for above data can be prepared as follows :

Try These (Textbook Page No. 75 – 76)

1. Observe the histogram and answer questions given below:

Question (i).
What information is being given by the histogram ?
Solution:
This histogram represents the heights (in cms) of girls of class VII.

Question (ii).
Which group contains maximum girls ?
Solution:
The group 140- 145 contains maximum number of girls (7).

Question (iii).
How many girls have a height of 145 cms and more?
Solution:
7 girls have a height of 145 cm and more (4 + 2 + 1 = 7).

Question (iv).
If we divide the girls into the following three categories, how many would there be in each?
150 cm and more-Group A
140 cm to less
than 150 cm – Group B
Less than 140 cm – Group C
Solution:
Number of girls in
Group A : 150 cm and more = 2 + 1 = 3
Group B : 140 cm and less than 150 cm = 7 + 4 = 11
Group C : Less them 140 cm = 3 + 2 + 1 = 6

Try These (Textbook Page No. 78)

1. Each of the following pie charts gives you a different piece of information !; about your class. Find the fraction of the circle representing each of these information:

Solution:
(i) Fraction of the circle representing the ‘girls’ 50 % = \(\frac {50}{100}\) = \(\frac {1}{2}\)
Fraction of the circle representing the ‘boys’ 50% = \(\frac {50}{100}\) = \(\frac {1}{2}\)

(ii) Fraction of the circle representing ‘walk’ 40 % = \(\frac {40}{100}\) = \(\frac {2}{5}\)
Fraction of the circle representing ‘bus or car’ 40 % = \(\frac {40}{100}\) = \(\frac {2}{5}\)
Fraction of the circle representing ‘cycle’ 20 % = \(\frac {20}{100}\) = \(\frac {1}{5}\)

(iii) Fraction of the circle representing those who love mathematics = (100 – 15)%
= 85 %
= \(\frac {85}{100}\) = \(\frac {17}{20}\)
Fraction of the circle representing those who hate mathematics = 15%
= \(\frac {15}{100}\) = \(\frac {3}{20}\)

2. Answer the following questions based on the pie chart given:

(i) Which type of programmes are viewed the most?
(ii) Which two types of programmes have number of viewers equal to those watching sports channels ?
Solution:
From the given pie chart,

Type of viewers	Percentage
Sports viewers	25 %
News viewers	15 %
Information viewers	10 %
Entertainment viewers	50%

(i) The entertainment programmes are viewed the most (50 %).
(ii) The news and informative programmes have the number of viewers equal to those watching sports channels (15 % + 10 % = 25 %).

Try These (Textbook Page No. 81)

1. Draw a pie chart of the data given below : The time spent by a child during a day.
Sleep – 8 hours
School – 6 hours
Homework – 4 hours
Play – 4 hours
Others – 2 hours
Solution:
First we find the central angle corresponding to each of the given activities.

Activity	Duration of the activity in a day out of 24 hours	Central angle corresponding to the activity
Sleep	8 hours	\(\frac {8}{24}\) × 360° = 120°
School	6 hours	\(\frac {6}{24}\) × 360° = 90°
Home­ work	4 hours	\(\frac {4}{24}\) × 360° = 60°
Play	4 hours	\(\frac {4}{24}\) × 360° = 60°
Others	2 hours	\(\frac {2}{24}\) × 360° = 30°

The required pie chart is given below.
[Note: Dividing a circle into sectors with corresponding angle (with protractor) you get the required pie chart.]

Think, Discuss and Write (Textbook Page No. 81)

Which form of graph would be appropriate to display the following data.

Question 1.
Production of food grains of a state.

Solution :
A bar graph will be an appropriate representation to display given data.

Question 2.

Favourite food	Number of people
North Indian	30
South Indian	40
Gujarati	25
Others	25
Total	120

Solution :
A pie chart (circle graph) will be an appropriate representation to display given data.

Question 3.
The daily income of a group of a factory workers:

Daily income (in Rupees)	Number of workers (in a factory)
75 – 100	45
100 – 125	35
125 – 150	55
150 – 175	30

Solution :
A histogram will be an appropriate representation to display given data.

Try These (Textbook Page No. 83 – 84)

Question 1.
If you try to start a scooter, what are the possible outcomes ?
Solution:
It may start.
It may not start.

Question 2.
When a die is thrown, what are the six possible outcomes?
Solution:
When a die is thrown, the possible outcomes are: 1, 2, 3, 4, 5 or 6 on the upper face of the die.

Question 3.
When you spin the wheel shown, what are the possible outcomes ? (Fig 5.9)
List them.
(Outcome here means the sector at which the pointer stops.)

Solution:
When we spin the wheel shown, the possible outcomes are A, B or C.
[Note: The sector at which the pointer stops is outcome.]

Question 4.
You have a pot with five identical balls of different colours and you are to pull out (draw) a ball without looking at it; list the outcomes you would get (Fig 5.10).

Solution:
When we draw a ball from a bag with five identical balls of different colours, the possible outcomes are : W, R, B, G or Y.

Think, Discuss and Write (Textbook Page No. 84)

In throwing a die:

1. Does the first player have a greater chance of getting a six?
Solution:
No.

2. Would the player who played after him have a lesser chance of getting a six?
Solution:
No.

3. Suppose the second player got a six. Does it mean that the third player would not have a chance of getting a six ?
Solution:
No.

Try These (Textbook Page No. 86)

Suppose you spin the wheel:

1. ( i ) List the number of outcomes of getting a green sector and not getting a green sector on this wheel.
Solution:
Number of outcomes of getting a green sector = 5
Number of outcomes of not getting a green sector = 3

(ii) Find the probability of getting a green sector.
Solution :
∴ The total number of outcomes = 8
Number of outcomes of getting a green sector = 5
∴ Probability of getting a green sector = \(\frac {5}{8}\)

(iii) Find the probability of not getting a green sector.
Solution:
∴ The total number of outcomes = 8
Number of outcomes of not getting a green sector = 3
∴ Probability of not getting a green sector = \(\frac {3}{8}\)