Approximately What Percentage of These Hours Is Spent on Art and Math Combine

NCERT Exemplar Solutions Class 8 Maths Chapter two – Free PDF Download

NCERT Exemplar for Grade viii Maths Chapter 2 Data Treatment, is provided here for students to set up for exams. These exemplars problems and solutions are designed by experts in accordance with CBSE syllabus(2021-2022) for eighth standard, which covers all the topics of Maths Affiliate 2. Solving the questions from the exemplars will assist the students to learn the concepts of data handling in a better and easy way. In this chapter, the students will acquire almost different types of data and how to represent them. Solving the Exemplar questions for Course 8 will assistance the students to clear the cardinal concepts present in each chapter. Below is the listing of topics covered in Chapter 2 of Class 8 Maths subject.

• Stand for the data in Pictorial form, using bar graphs and double bar graph
• Learn, organizing and group of information
• Representation of data via histogram and pie chart
• Probability basic concepts

Solve these Exemplars problems and score good marks in the master exams. Likewise, it is recommended to solve sample papers and previous twelvemonth question papers which gives an idea of question types asked in the lath exam from Affiliate ii Information treatment. BYJU'Southward also provide notes, exemplar books, Maths NCERT Solutions for eighth standard and question papers to aid students practice well for their exams.

NCERT Exemplar Solutions for Course viii Maths Affiliate ii Data Handling:-Download PDF Hither

Access Answers to NCERT Exemplar SOluti Class 8 Maths Chapter 2

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In questions i to 35 there are iv options given, out of which one is correct. Cull the correct answer.

1. The height of a rectangle in a histogram shows the

(a) Width of the class (b) Upper limit of the form

(c) Lower limit of the form (d) Frequency of the class

Solution:-

(d) Frequency of the class

2. A geometric representation showing the relationship between a whole and its parts is a

(a) Pie chart (b) Histogram (c) Bar graph (d) Pictograph

Solution:-

(a) Pie chart

A geometric representation showing the relationship between a whole and its parts is pie nautical chart.

3. In a pie nautical chart, the total bending at the centre of the circle is

(a) 180^o (b) 360^o (c) 270^o (d) ninety^o

Solution:-

(b) 360^o

four. The range of the data 30, 61, 55, 56, 60, xx, 26, 46, 28, 56 is

(a) 26 (b) 30 (c) 41 (d) 61

Solution:-

(c) 41

The divergence between the lowest and the highest ascertainment in a given data is chosen its Range.

Then, Range = Highest observation – Lowest observation

= 61 – 20

= 41

five. Which of the following is not a random experiment?

(a) Tossing a coin (b) Rolling a dice

(c) Choosing a carte from a deck of 52 cards

(d) Throwing a stone from a roof of a building

Solution:-

(d) Throwing a stone from a roof of a edifice.

There is merely one output that is the rock volition fall down therefore information technology is non a random experiment.

6. What is the probability of choosing a vowel from the alphabets?

(a) 21/26 (b) 5/26 (c) ane/26 (d) iii/26

Solution:-

(b) five/26

Probability = Number of Vowels/ Total number of alphabets

= five/26

7. In a school simply, iii out of 5 students can participate in a contest. What is the probability of the students who do not arrive to the contest?

(a) 0.65 (b) 0.iv (c) 0.45 (d) 0.6

Solution:-

(b) 0.4

Probability = Number of students who do not make information technology to the competition / Total number

of students.

= 2/5

= 0.4

Students of a grade voted for their favorite colour and a pie chart was prepared based on the data nerveless.

Observe the pie chart given below and answer questions 8 –10 based on it.

8. Which color received one/5 of the votes?

(a) Red (b) Bluish (c) Green (d) Yellow

Solution:-

(c) Dark-green

= 1/5 × 100

= 0.2 × 100

= 20%

9. If 400 students voted in all, then how many did vote 'Others' color as their favorite?

(a) 6 (b) xx (c) 24 (d) xl

Solution:-

(c) 24

From the pie chart, 6% out of 400 students voted for others,

So,

= (half-dozen%/100%) × 400

= 0.06 × 400

= 24

ten. Which of the following is a reasonable determination for the given data?

(a) (1/twenty)^th student voted for blue colour

(b) Green is the least popular color

(c) The number of students who voted for cherry-red colour is two times the number of students who voted for yellow color

(d) Number of students liking together yellow and dark-green colour is approximately the same equally those for red colour.

Solution:-

(d) Number of students liking together yellow and green colour is approximately the same equally those for ruby color.

xi. Listed beneath are the temperature in ^oC for ten days.

–six, –eight, 0, three, 2, 0, 1, 5, 4, 4

What is the range of the data?

Solution:-

(a) 8 (b) thirteen^oC (c) x^oC (d) 12^oC

Solution:-

(b) 13^oC

The difference between the everyman and the highest observation in a given data is called its Range.

So, Range = Highest observation – Lowest observation

= 5 – (-8)

= v + 8

= 13^oC

12. Ram put some buttons on the table. There were 4 bluish, vii crimson, iii black and half dozen white buttons in all. All of a sudden, a cat jumped on the table and knocked out 1 push button on the floor. What is the probability that the button on the flooring is blue?

(a) 7/20 (b) 3/5 (c) 1/5 (d) ¼

Solution:-

(c) 1/v

Probability = Number of blue buttons on the table / Total number of buttons on the

table

= four/twenty … [carve up both numerator and denominator by 4]

= 1/five

13. Rahul, Varun and Yash are playing a game of spinning a coloured wheel. Rahul wins if spinner lands on cherry. Varun wins if spinner lands on bluish and Yash wins if it lands on green. Which of the following spinner should exist used to make the game fair?

(a) (i) (b) (two) (c) three (d) (4)

Solution:-

(d) (four) this figure contains equal share for three colours.

xiv. In a frequency distribution with classes 0 –x, 10 –20 etc., the size of the class intervals is ten. The lower limit of fourth class is

(a) forty (b) l (c) 20 (d) 30

Solution:-

(d) 30

The lower value of the class interval is called its Lower Course Limit.

First grade = 0 -10

Second class = 10 – 20

Third class = 20 – xxx

4th class = xxx – 40

5th class = 40 – fifty

and Tenth class = ninety – 100

15. A coin is tossed 200 times and head appeared 120 times. The probability of getting a head in this experiment is

(a) ii/5 (b) three/five (c) 1/v (d) 4/five

Solution:-

(b) 3/5

Probability = Number of times head appeared / Total number of times coin is tossed

= 120/200

= 12/20 … [divide both numerator and denominator past 4]

= 3/5

16. Data collected in a survey shows that 40% of the buyers are interested in buying a particular brand of toothpaste. The central bending of the sector of the pie chart representing this information is

(a) 120^o (b) 150^o (c) 144^o (d) xl°

Solution:-

(c) 144^o

= (forty/100) × 360^o

= 0.four × 360^o

= 144^o

17. Monthly salary of a person is Rs. 15000. The central angle of the sector representing his expenses on food and house hire on a pie chart is 60°. The amount he spends on food and business firm rent is

(a) Rs. 5000 (b) Rs. 2500 (c) Rs. 6000 (d) Rs. 9000

Solution:-

(b) Rs. 2500

From the question,

The office of monthly salary spent on food and house rent = 60^o/360^o

The amount he spends on nutrient and house rent is = (60^o/360^o) × 15000

= Rs. 2500

eighteen. The following pie chart gives the distribution of constituents

in the human body. The central angle of the sector showing the

distribution of protein and other constituents is

(a) 108^o (b) 54^o (c) thirty^o (d) 216^o

Solution:-

(a) 108^o

The following pie chart gives the distribution of constituents

in the human body = xvi% + fourteen% = xxx%

= (thirty/100) × 360^o

= 108^o

19. Rohan and Shalu are playing with 5 cards as shown

in the figure. What is the probability of Rohan picking

a menu without seeing, that has the number two on it?

(a) two/5 (b) 1/5 (c) three/five (d) 4/5

Solution:-

(a) 2/v

Probability = Number of cards having 2/ Total number of cards

= ii/v

20. The following pie nautical chart represents the distribution of

proteins in parts of a human body. What is the ratio of

distribution of proteins in the muscles to that of proteins

in the bones?

(a) 3 : i (b) 1 : two (c) 1 : 3 (d) ii : i

Solution:-

(d) 2 : 1

From the chart,

Distribution of poly peptide in the muscles = i/iii

Distribution of protein in the bones = 1/vi

So,

Ratio of distribution of proteins in the muscles to that of proteins in the bones,

= 1/3 : one/6

= (ane/3) × (6/1)

= (1/1) × (ii/1)

= two/one

= two : 1

21. What is the central angle of the sector (in the above pie chart) representing peel and bones together?

(a) 36^o (b) 60^o (c) xc^o (d) 96^o

Solution:-

(d) 96^o

Distribution of protein in the pare = 1/10

Distribution of protein in the bones = i/6

Central bending of the sector representing skin and basic,

= 1/ten + one/six

= (iii + v)/30

= eight/xxx × 360^o

= 96^o

22. What is the cardinal angle of the sector (in the to a higher place pie chart) representing hormones enzymes and other proteins.

(a) 120^o (b) 144^o (c) 156^o (d) 176^o

Solution:-

(b) 144^o

Distribution of protein in the skin = one/x

Distribution of protein in the bones = ane/6

Distribution of protein in the Muscles = 1/3

Central bending of the sector representing skin, muscles and bones,

= i/x + ane/6 + 1/3

= (three + 5 + x)/30

= 18/30 × 360^o

= 216^o

So,

Central bending of the sector representing hormones enzymes and other proteins,

= 360^o – 216^o

= 144^o

23. A money is tossed 12 times and the outcomes are observed as shown below:

The chance of occurrence of Head is

(a) ½ (b) 5/12 (c) 7/12 (d) 5/7

Solution:-

(b) five/12 … [from the effigy]

24. Total number of outcomes, when a ball is fatigued from a bag which contains 3 blood-red, 5 black and 4 blue balls is

(a) 8 (b) 7 (c) 9 (d) 12

Solution:-

(d) 12

25. A graph showing two sets of data simultaneously is known equally

(a) Pictograph (b) Histogram (c) Pie chart (d) Double bar graph

Solution:-

(d) Double bar graph

26. Size of the class 150 –175 is

(a) 150 (b) 175 (c) 25 (d) –25

Solution:-

(c) 25

The difference betwixt the upper class limit and lower class limit of a form is called the Size of the class.

= Upper limit – lower limit

= 175 – 150

= 25

27. In a throw of a dice, the probability of getting the number vii is

(a) ½ (b) ane/6 (c) 1 (d) 0

Solution:-

(d) 0

Only one, 2, three, 4, 5 and half dozen are in the dice. Then, no chance of getting number seven.

28. Data represented using circles is known equally

(a)Bar graph (b) Histogram (c) Pictograph (d) Pie chart

Solution:-

(d) Pie chart.

29. Tally marks are used to find

(a) Class intervals (b) Range (c) Frequency (d) Upper limit

Solution:-

(c) Frequency

30. Upper limit of class interval 75 –85 is

(a) x (b) –10 (c) 75 (d) 85

Solution:-

(d) 85

31. Numbers ane to five are written on split slips, i.e. one number on one sideslip and put in a box. Wahida pick a skid from the box without looking at it. What is the probability that the slip bears an odd number?

(a) i/five (b) ii/5 (c) 3/5 (d) four/5

Solution:-

(c) 3/5

Number i to 5 = one, 2, 3, iv, 5

Odd number one to 5 = ane, 3, 5

Probability = total number of odd number slips/ Total number of slips

= 3/5

32. A drinking glass jar contains vi red, 5 green, four bluish and 5 yellow marbles

of same size. Hari takes out a marble from the jar at random.

What is the probability that the called marble is of red colour?

(a) 7/10 (b) iii/x (c) four/5 (d) 2/5

Solution:-

(b) 3/10

Probability = total number of scarlet marbles/ Full number of marbles

= 6/20 … [divide numerator and denominator by 2]

= 3/10

33. A coin is tossed two times. The number of possible outcomes is

(a) one (b) 2 (c) 3 (d) iv

Solution:-

(d) 4

Head Head, Tail Tail, Tail Head, Head Tail.

34. A coin is tossed iii times. The number of possible outcomes is

(a) iii (b) 4 (c) 6 (d) 8

Solution:-

(d) 8

HHH, TTT, THH, HTH, HHT, HTT, THT, TTH

35. A dice is tossed two times. The number of possible outcomes is

(a) 12 (b) 24 (c) 36 (d) xxx

Solution:-

(c) 36

(1, 1), (1, 2), (1, 3), (ane, 4), (i, 5), (i, six) = 6

(2, 1), (2, 2), (2, 3), (ii, 4), (2, 5), (2, 6) = six

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (iii, 6) = 6

(4, 1), (4, ii), (4, 3), (4, four), (four, v), (4, 6) = 6

(5, 1), (5, ii), (5, 3), (5, four), (5, 5), (5, half dozen) = 6

(6, 1), (6, ii), (half-dozen, 3), (6, iv), (6, v), (6, 6) = vi

= 36

In questions 36 to 58, make full in the blanks to brand the statements truthful.

36. Information available in an unorganised course is chosen data.

Solution:-

Data available in an unorganised form is called raw data.

37. In the class interval xx – 30, the lower class limit is .

Solution:-

In the class interval 20 – 30, the lower class limit is twenty.

38. In the class interval 26 – 33, 33 is known every bit .

Solution:-

In the course interval 26 – 33, 33 is known equally upper class limit.

39. The range of the information vi, viii, xvi, 22, 8, 20, seven, 25 is .

Solution:-

The divergence between the lowest and the highest observation in a given data is called its Range.

Then, Range = Highest observation – Lowest observation

= 25 – six

= nineteen

The range of the information 6, 8, 16, 22, 8, 20, 7, 25 is nineteen.

twoscore. A pie chart is used to compare to a whole.

Solution:-

A pie chart is used to compare parts to a whole.

41. In the experiment of tossing a coin one time, the event is either or

.

Solution:-

In the experiment of tossing a coin one fourth dimension, the outcome is either Head or Tail.

42. When a dice is rolled, the half dozen possible outcomes are .

Solution:-

When a dice is rolled, the six possible outcomes are one, 2, 3, 4, 5 and 6.

43. Each outcome or a collection of outcomes in an experiment makes an .

Solution:-

Each outcome or a collection of outcomes in an experiment makes an Event.

44. An experiment whose outcomes cannot exist predicted exactly in advance is chosen a

experiment.

Solution:-

An experiment whose outcomes cannot be predicted exactly in advance is called a random experiment.

45. The difference between the upper and lower limit of a class interval is called the

of the class interval.

Solution:-

The divergence between the upper and lower limit of a form interval is called the

Size/width of the class interval.

46. The 6th class interval for a grouped data whose first two class intervals are x – 15 and 15 – 20 is .

Solution:-

The sixth class interval for a grouped data whose offset 2 grade intervals are 10 – xv and 15 – twenty is 35 – twoscore.

Histogram given on the right shows the number of

people owning the different number of books.

Answer 47 to fifty based on it

47. The total number of people surveyed is .

Solution:-

Form the Histogram,

The total number of people surveyed is 35.

48. The number of people owning books more than

60 is .

Solution:-

The number of people owning books more than

60 is eight.

49. The number of people owning books less than

40 is .

Solution:-

The number of people owning books less than forty is 22.

50. The number of people having books more than 20 and less than 40 is .

Solution:-

The number of people having books more than than 20 and less than 40 is fourteen.

51. The number of times a particular observation occurs in a given data is called its

.

Solution:-

The number of times a particular observation occurs in a given data is called its Frequency.

52. When the number of observations is large, the observations are usually organised in groups of equal width called .

Solution:-

When the number of observations is large, the observations are usually organised in groups of equal width chosen class intervals.

53. The total number of outcomes when a money is tossed is .

Solution:-

The total number of outcomes when a money is tossed is 2.

54. The class size of the interval lxxx – 85 is .

Solution:-

= 85 – 80

= 5

The class size of the interval 80 – 85 is 5.

55. In a histogram __________ are drawn with width equal to a grade interval without leaving whatever gap in betwixt.

Solution:-

In a histogram bars are drawn with width equal to a class interval without leaving any gap in between.

56. When a dice is thrown, outcomes i, 2, 3, 4, 5, 6 are equally .

Solution:-

When a dice is thrown, outcomes 1, 2, 3, 4, v, half dozen are equally likely.

57. In a histogram, course intervals and frequencies are taken forth __________ centrality and __________ axis.

Solution:-

In a histogram, class intervals and frequencies are taken along 10 axis and Y axis.

58. In the course intervals x –20, 20 –30, etc., respectively, 20 lies in the grade .

Solution:-

In the course intervals ten –20, 20 –30, etc., respectively, twenty lies in the course 20 – xxx.

In questions 59 to 81, state whether the statements are truthful (T) or false (F).

59. In a pie chart a whole circle is divided into sectors.

Solution:-

True.

Pie chart shows the relationship between a whole and its parts.

threescore. The central angle of a sector in a pie chart cannot be more than 180^o.

Solution:-

Imitation.

The key bending of a sector in a pie nautical chart is more than than 180^o. Just, cannot be more than than 360^o.

61. Sum of all the central angles in a pie nautical chart is 360°.

Solution:-

True.

62. In a pie chart ii cardinal angles can be of 180^o.

Solution:-

True.

We know that sum of all the central angles in a pie chart is 360^o. So, if 2 angles have 180^o each and then the sum of two angles is 360^o.

63. In a pie nautical chart ii or more than cardinal angles can be equal.

Solution:-

True.

Yes, in a pie chart two or more key angles can exist equal.

64. Getting a prime number number on throwing a die is an event.

Solution:-

Truthful.

Each result or a collection of outcomes in an experiment makes an Event.

Using the following frequency table, answer question 65-68

Marks (obtained out of ten)	4	5	7	eight	9	10
Frequency	5	10	8	6	12	9

65. nine students got total marks.

Solution:-

True.

From the table, given that 9 students got 10 out of ten marks.

66. The frequency of less than viii marks is 29.

Solution:-

False.

The frequency of less than 8 marks is 8 + 10 + v = 23 students.

67. The frequency of more than 8 marks is 21.

Solution:-

True.

The frequency of more than than eight marks is 12 + 9 = 21 students.

68. x marks the highest frequency.

Solution:-

Imitation.

ix marks has highest frequency, i.e. 12. But, 10 has 9 frequency.

69. If the 5th class interval is 60 – 65, 4th class interval is 55 – lx, then the start class interval is 45 –fifty.

Solution:-

False.

The first class interval is 40 – 45, 2nd grade interval is 45 – 50, 3rd course interval is

l – 55, fourth class interval 55 – sixty, fifth class interval is 60 – 65.

lxx. From the histogram given on the right, we

can say that 1500 males to a higher place the age of 20 are

literate.

Solution:-

False.

From the histogram given on the correct, we

tin say that 1900 (600 + 800 + 500) males above the age of 20 are

literate.

71. The class size of the course interval sixty – 68 is 8.

Solution:-

Truthful.

The difference between the upper and lower limit of a class interval is called the

Size of the class interval. i.e. 68 – sixty = eight

72. If a pair of coins is tossed, so the number of outcomes are 2.

Solution:-

False.

If a pair of coins is tossed, then the number of outcomes are four, i.e. HH, TT, TH and HT.

73. On throwing a dice once, the probability of occurence of an even number is ½.

Solution:-

True.

The even numbers in a die are two, 4 and 6.

Probability = full number of even numbers/ Total numbers

= 3/half-dozen … [divide numerator and denominator by three]

= ½

74. On throwing a dice once, the probability of occurence of a composite number is ½.

Solution:-

Faux.

The composite numbers in a dice are 4 and 6.

Probability = total number of blended numbers/ Total numbers

= 2/6 … [carve up numerator and denominator by 2]

= i/3

75. From the given pie chart, nosotros tin infer that production of Manganese is least in state B.

Solution:-

Simulated.

It is not possible to declare, from the given pie chart that the production of Manganese is to the lowest degree in country B. Because, we do non know the primal angle of the sectors.

76. I or more outcomes of an experiment make an outcome.

Solution:-

True.

Each outcome or a collection of outcomes in an experiment makes an Event.

77. The probability of getting number six in a throw of a dice is 1/6. Similarly the probability of getting a number 5 is ane/5.

Solution:-

Fake.

The probability of getting a number 5 is 1/6.

78. The probability of getting a prime number number is the same as that of a blended number in a throw of a dice.

Solution:-

False.

The composite numbers in a dice are 4 and vi.

Probability = full number of composite numbers/ Full numbers

= 2/6 … [divide numerator and denominator past 2]

= 1/3

The prime number numbers in a dice are 2, 3 and 5.

Probability = full number of prime numbers/ Total numbers

= three/6 … [carve up numerator and denominator by iii]

= ½

79. In a throw of a die, the probability of getting an even number is the same as that of getting an odd number.

Solution:-

True.

The even numbers in a dice are 2, 4 and 6.

Probability = full number of even numbers/ Total numbers

= 3/6 … [divide numerator and denominator by 3]

= ½

The odd numbers in a die are 1, iii and 5.

Probability = full number of odd numbers/ Full numbers

= 3/6 … [divide numerator and denominator by 3]

= ½

eighty. To verify Pythagoras theorem is a random experiment.

Solution:-

False.

Nosotros know the result i.east. just 1 result before going to verify the Pythagoras theorem. So, it is not a random experiment.

81. The following pictorial representation of data is a histogram.

Solution:-

True.

Histogram is a blazon of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars (rectangles) evidence the frequency of the course interval, but in that location is no gap betwixt the confined as at that place is no gap between the class intervals.

82. Given beneath is a frequency distribution table. Read information technology and answer the question that follow.

Course Interval	Frequency
10 – 20	5
20 – 30	10
30 – twoscore	4
40 – 50	15
50 – threescore	12

(a) What is the lower limit of the 2d form interval?

Solution:-

The lower limit of the second grade interval 20 – xxx is 20.

(b) What is the upper limit of the last course interval?

Solution:-

The upper limit of the last class interval 50 – lx is 60.

(c) What is the frequency of the third form?

Solution:-

The frequency of the third grade 30 – 40 is 4.

(d) Which interval has a frequency of 10?

Solution:-

Second class interval 20 – 30 has a frequency of 10.

(e) Which interval has the everyman frequency?

Solution:-

Third interval 30 – forty has the lowest frequency i.east. 4.

(f) What is the form size?

Solution:-

The departure between the upper and lower limit of a class interval is called the Size of the class interval.

Size = Upper limit – Lower limit

= 20 – 10

= 10

83. The elevation speeds of thirty different land animals have been organised into a frequency table. Draw a histogram for the given data.

Maximum Speed (Km/h)	Frequency
10 – 20	v
20 – 30	five
xxx – 40	10
forty – fifty	8
50 – 60	0
sixty – seventy	2

Solution:-

Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars (rectangles) testify the frequency of the form interval, but there is no gap between the confined every bit there is no gap betwixt the form intervals.

84. Given below is a pie chart showing the time spend by a group of 350 children in dissimilar games. Detect it and answer the questions that follow.

(a) How many children spend at to the lowest degree i hour in playing games?

Solution:-

From the given pie chart,

Percent of children who at least spend one hour in playing = 16 + thirty + 34 + 10 + four

= 94 %

Number of children out of 350 who at least spend one 60 minutes in playing = (94/100) × 350

= 0.94 × 350

= 329 children

(b) How many children spend more than ii hours in playing games?

Solution:-

From the given pie nautical chart,

Percentage of children who spend two hours in playing = 34 + 10 + 4

= 48 %

Number of children out of 350 who at least spend one hr in playing = (48/100) × 350

= 0.48 × 350

= 168 children

(c) How many children spend 3 or bottom hours in playing games?

Solution:-

From the given pie chart,

Percentage of children who at least spend one hour in playing = half-dozen + 16 + 30 + 34

= 86 %

Number of children out of 350 who at least spend i hour in playing = (86/100) × 350

= 0.86 × 350

= 301 children

(d) Which is greater — number of children who spend 2 hours or more per day or number of children who play for less than one hour?

Solution:-

Number of children who spend 2 hours or more per 24-hour interval = 30 + 34 + 10 + iv = 78%

= (78/100) × 350

= 0.78 × 350

= 273 children

Number of children who play for less than i 60 minutes = 6%

= (6/100) × 350

= 0.06 × 350

= 21 children

So, by comparison both it is articulate that number of children who spend two hours or more per day is greater

85. The pie chart on the right shows the result of a survey

Carried out to find the modes of travel used by the children to go

to school. Study the pie chart and reply the questions that

follow.

(a) What is the most common mode of transport?

Solution:-

Past observing the given pie chart the most mutual mode of transport is Omnibus i.e. its central angle is 120^o.

(b) What fraction of children travel by car?

Solution:-

By observing the given pie chart, cardinal angle of the children travel past car is 90^o.

Then,

The fraction of children travel by motorcar,

= (90^o/360^o)

= 9/36 … [divide both numerator and denominator by ix]

= ¼

(c) If eighteen children travel past automobile, how many children took function in the survey?

Solution:-

Let us presume total number of children took office in the survey be y

Number of children travel by machine = (¼) of total number of children

18 = ¼ × y

Y = 18 × 4

Y = 72

So, 72 children took role in the survey.

(d) How many children use taxi to travel to schoolhouse?

Solution:-

Key angle of children use taxi to travel to school = (360^o – (120^o + lx^o + 90^o + 60^o)

= (360^o – 330^o)

= 30^o

Then,

Out of 72 children number of children use taxi to travel to schoolhouse = (xxx^o/360^o) × 72

= 6

(e) By which two modes of send are equal number of children travelling?

Solution:-

By observing the given pie chart, bicycle and walk are the two modes of ship are equal number of children travelling. Considering, fundamental angle of the two modes are same i.e. threescore^o.

86. A dice is rolled once. What is the probability that the number on pinnacle will exist

(a) Odd

(b) Greater than 5

(c) A multiple of three

(d) Less than 1

(due east) A gene of 36

(f) A factor of 6

Solution:-

A die is rolled once, the possible outcomes are i, 2, three, 4, 5 and six.

And then,

The probability that the number on acme will be

(a) Odd

Odd numbers in the die are i, 3, 5

And then,

Probability = total number of odd numbers/ Full number of outcomes

= iii/half dozen … [carve up numerator and denominator by 3]

= ½

(b) Greater than 5

Greater than 5 is 6

And so,

Probability = total number Greater than 5/ Full number of outcomes

= i/6

(c) A multiple of 3

Multiple of 3 = 3 and half-dozen

And so,

Probability = total number of multiple of 3/ Total number of outcomes

= two/6 … [divide numerator and denominator past 2]

= one/iii

(d) Less than 1

There is no number is less than ane.

So, probability of less than 1 = 0

(eastward) A factor of 36

Factors of 36 are i, 2, 3, 4 and 6

Probability = total number of gene of 36/ Total number of outcomes

= five/6

(f) A factor of 6

Factors of half-dozen are 1, 2, 3 and 6

Probability = total number of factor of half-dozen/ Total number of outcomes

= iv/six … [divide numerator and denominator by ii]

= 2/three

87. Allocate the following statements under appropriate headings.

(a) Getting the sum of angles of a triangle equally 180°.

(b) Republic of india winning a cricket match against Pakistan.

(c) Sun setting in the evening.

(d) Getting 7 when a dice is thrown.

(eastward) Sun rising from the due west.

(f) Winning a racing competition by you.

Certain to happen	Impossible to happen	May or may not happen

Solution:-

(a) It is sure to happen. Because, the sum of angles of a triangle equally 180^o.

(b) It may or may not happen. Because, the event of match is unpredictable.

(c) Information technology is sure to happen. Because, the dominicus e'er sets in the evening.

(d) It is impossible to happen. Because, 7 is not an outcome when a dice is thrown.

(e) It is impossible to happen. Because, Sun ever rises from the east.

(f) It may or may not happen. Because, the result is unpredictable.

89. Ritwik draws a brawl from a pocketbook that contains white and yellow balls. The probability of choosing a white ball is two/nine. If the total number of balls in the bag is 36, find the number of xanthous balls.

Solution:-

From the question is given that,

Probability of choosing a white brawl is = 2/9

The total number of balls in the bag is = 36

Number of white ball called = (2/9) × 36

= eight white balls

Then, the number of yellow balls = Total balls in bag – number of white assurance

= 36 – 8

= 28 xanthous balls

90. Look at the histogram below and answer the questions that follow.

(a) How many students accept top more than or equal to 135 cm but less than 150 cm?

Solution:-

Past observing the given histogram,

Students have meridian more than or equal to 135 cm but less than 150 = 14 + 18 + 10

= 42

(b) Which class interval has the least number of students?

Solution:-

150 – 155 has the to the lowest degree number of students i.e. four.

(c) What is the course size?

Solution:-

The divergence between the upper and lower limit of a class interval is called the

Size of the grade interval.

Size = Upper limit – Lower limit

= 130 – 125

= 5

(d) How many students have height less than 140 cm?

Solution:-

By observing the given histogram,

Students accept height less than 140 cm = 6 + 8 + 14

= 28

91. Following are the number of members in 25 families of a hamlet:

vi, 8, vii, 7, six, five, 3, 2, 5, 6, 8, seven, seven, 4, 3, half-dozen, 6, 6, 7, 5, four, 3, three, 2, 5. Set up a frequency distribution tabular array for the data using form intervals 0 –two, two –4, etc.

Solution:-

First, we accept to adjust the number of members in 25 families of a hamlet ascending society.

= two, 2, 3, three, 3, 3, 4, four, five, v, 5, 5, 6, 6, half-dozen, 6, 6, 6, 7, vii, 7, 7, vii, 8, viii.

Now, nosotros volition draw the frequency table of the given data.

92. Draw a histogram to represent the frequency distribution in question 91.

Solution:-

Calibration:

On X – axis, 1 big division = 2 member

On Y – centrality, ane big division = 2 family unit

93. The marks obtained (out of 20) by 30 students of a form in a test are as follows:

14, sixteen, 15, 11, 15, 14, 13, 16, viii, 10, 7, eleven, 18, 15, xiv, 19, 20, 7, x, xiii, 12, 14, 15, 13, xvi, 17, 14, 11, ten, xx.

Prepare a frequency distribution tabular array for the above data using class intervals of equal width in which one class interval is 4 –8 (excluding 8 and including 4).

Solution:-

First, we have to arrange marks obtained (out of 20) by 30 students in an ascending order.

= 7, 7, eight, x, 10, 10, 11, eleven, 11, 12, 13, 13, thirteen, 14, 14, 14, 14, xiv, 15, 15, xv, xv, sixteen, xvi, 16, 17, 18, 19, 20, 20.

Now, nosotros will depict the frequency table of the given data.

94. Prepare a histogram from the frequency distribution tabular array obtained in question 93.

Solution:-

Scale:

On X – centrality, 1 big partition = 4 marks

On Y – axis, 1 big partition = two students

95. The weights (in kg) of 30 students of a form are:

39, 38, 36, 38, xl, 42, 43, 44, 33, 33, 31, 45, 46, 38, 37, 31, 30, 39, 41, 41, 46, 36, 35, 34, 39, 43, 32, 37, 29, 26.

Prepare a frequency distribution tabular array using one class interval as (xxx – 35), 35 not included.

(i) Which grade has the least frequency?

(ii) Which class has the maximum frequency?

Solution:-

First, we have to conform the weights (in kg) of 30 students of a class in an ascending lodge.

= 26, 29, 30, 31, 31, 32, 33, 33, 34, 35, 36, 36, 37, 37, 38, 38, 38, 39, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 46, 46

Now, we will depict the frequency table of the given data.

(i) Class first has the least frequency.

(two) Grade third has the maximum frequency.

96. Shoes of the post-obit brands are sold in Nov. 2007 at a shoe shop. Construct a pie chart for the data.

Make	Number of pair of shoes sold
A	130
B	120
C	xc
D	xl
E	20

Solution:-

From the tabular array,

Total number of pairs of shoes sold = 130 + 120 + xc + forty +xx

= 400

Central bending of pie chart for each brands,

A = (130/400) × 360^o

= 117^o

B = (120/400) × 360^o

= 108^o

C = (90/400) × 360^o

= 81^o

D = (40/400) × 360^o

= 36^o

E = (20/400) × 360^o

= 18^o

97. The following pie chart depicts the expenditure of a land regime under different heads.

(i) If the total spending is 10 crores, how much money was spent on roads?

Solution:-

Given, full corporeality spent by state regime under dissimilar heads = ten crores

From the given pie nautical chart,

Percentage of money spent on Roads = ten %

Total money spent on Roads = (ten/100) × 100000000

= 1,00,00,000

(ii) How many times is the amount of money spent on education compared to the amount spent on roads?

Solution:-

Given, total amount spent by land government under unlike heads = 10 crores

From the given pie chart,

Percentage of money spent on Roads = 10 %

Full money spent on Roads = (10/100) × 100000000

= ₹ ane,00,00,000

Percentage of money spent on Education = 25 %

Total money spent on Pedagogy = (25/100) × 100000000

= ₹ 2,50,00,000

So,

= Total money spent on Education/ Full money spent on Roads

= ₹ two,50,00,000/₹ 1,00,00,000

= ₹ 25/10

∴Money spent on education is 2.5 times of money spent on roads.

(iii) What fraction of the full expenditure is spent on both roads and public welfare together?

Solution:-

Given, total amount spent by country government under different heads = ten crores

From the given pie chart,

Percentage of money spent on Roads = 10 %

Per centum of coin spent on Public Welfare = 20 %

So,

Fraction of the total expenditure is spent on both roads and public welfare together,

= 10% + xx%

= (10/100) + (20/100)

= (1/10) + (ii/x)

= (3/10)

98. The following information represents the different number of animals in a zoo. Prepare a pie chart for the given data.

Animals	Number of animals
Deer	42
Elephant	15
Giraffe	26
Reptiles	24
Tiger	13

Solution:-

From the tabular array,

Full number of animals in a zoo = 42 + xv + 26 + 24 +thirteen

= 120

Central angle of pie chart for each animals,

Deer= (42/120) × 360^o

= 126^o

Elephant = (15/120) × 360^o

= 45^o

Giraffe = (26/120) × 360^o

= 78^o

Reptiles = (24/120) × 360^o

= 72^o

Tiger = (thirteen/120) × 360^o

= 39^o

99. Playing cards

(a) From a pack of cards the following cards are kept face down:

[Queen, Rex and Jack cards are called face cards.]

Suhail wins if he picks up a face carte du jour. Discover the probability of Suhail winning?

Solution:-

From the above figure,

Number of confront cards = 1

Total number of cards = 7

Number of outcomes = 7

Probability = Number of face cards / Full number cards

= 1/7

(b) Now the following cards are added to the higher up cards:

What is the probability of Suhail winning now? Reshma wins if she picks upward a 4. What is the probability of Reshma winning?

[Queen, Rex and Jack cards are called face cards.]

Solution:-

Number of face cards = four

Total number of cards = 15

Number of outcomes = 15

Probability = Number of face cards / Total number cards

= 4/fifteen

100. Construct a frequency distribution table for the post-obit weights (in grams) of 35 mangoes, using the equal class intervals, 1 of them is forty – 45 (45 non included).

30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74, 45, 46, 58, 59, threescore, 62, 74, 34, 35, 70, 68.

(a) How many classes are at that place in the frequency distribution table?

(b) Which weight grouping has the highest frequency?

Solution:-

First, we have to arrange weights (in grams) of 35 mangoes in an ascending social club.

= 30, 32, 34, 35, 35, 37, 40, 42, 43, 45, 45, 46, 50, 50, 52, 53, 53, 55, 55, 58, 59, 60, 61, 62, 62, 62, 65, 68, 70, seventy, lxx, seventy, 73, 74, 74.

Now, we will draw the frequency table of the given data.

(a) In that location are 9 classes in the frequency distribution table.

(b) seventy – 75 weight has the highest frequency.

101. Complete the following table:

Discover the total number of persons whose weights are given in the to a higher place tabular array.

Solution:-

102. Draw a histogram for the following information.

Course interval	x – 15	15 – 20	20 – 25	25 – 30	thirty – 35	35 – 40
Frequency	thirty	98	fourscore	58	29	50

Solution:-

Scale:

On X – axis, 1 big partition = 5 marks

On Y – axis, 1 big division = 10 students

103. In a hypothetical sample of twenty people, the corporeality of money (in thousands of rupees) with each was found to be equally follows:

114, 108, 100, 98, 101, 109, 117, 119, 126, 131, 136, 143, 156, 169, 182, 195, 207, 219, 235, 118.

Describe a histogram of the frequency distribution, taking one of the course intervals every bit

fifty –100.

Solution:-

From the information given in the question, first we have to ready frequency distribution table,

Scale:

On X – axis, 1 big division = 50 ₹ marks

On Y – axis, 1 big segmentation = 2 persons

104. The below histogram shows the number of literate females in the age group of 10 to 40 years in a town.

(a) Write the classes bold all the classes are of equal width.

(b) What is the classes width?

(c) In which age group are literate females the least?

(d) In which age group is the number of literate females the highest?

Solution:-

(a) The classes are, 10-15, 15-xx, 20-25, 25-30, 30-35, and 35-40

b) The class width is 15 – 10 = 5

c) In the grade first group i.e. 10-15 have the least female literate.

d) In the class 2d group i.e. 15-20 have the highest female literate.

105. The following histogram shows the frequency distribution of teaching experiences of thirty teachers in various schools:

(a) What is the course width?

Solution:-

The width of the class is 5.

(b) How many teachers are having the maximum teaching experience and how many take the least instruction experience?

Solution:-

Teachers having maximum teaching feel is 2 and Teachers having least educational activity experience is v.

(c) How many teachers have teaching experience of 10 to 20 years?

Solution:-

Teachers have educational activity experience of 10 to 20 years is 7 + two = 9.

106. In a district, the number of branches of different banks is given below:

Bank	Land Banking company of India	Bank of Baroda	Punjab National Depository financial institution	Canara Bank
Number of Branches	30	17	fifteen	10

Draw a pie chart for this information.

Solution:-

From the table,

Full number of branches of different banking concern in a district = 30 + 17 + fifteen + ten

= 72

Central angle of pie chart for each depository financial institution,

State Bank of India = (30/72) × 360^o

= 150^o

Bank of Baroda = (17/72) × 360^o

= 85^o

Punjab National bank = (15/72) × 360^o

= 75^o

Canara Bank = (10/72) × 360^o

= l^o

107. For the development of basic infrastructure in a commune, a projection of Rs 108 crore approved past Development Bank is as follows:

Item Head	Road	Electricity	Drinking water	Sewerage
Amount in crore (Rs)	43.2	16.2	27.00	21.vi

Draw a pie nautical chart for this information.

Solution:-

From the question,

Total number approved = 108 crore

Primal angle of pie chart for each infrastructure,

Road = (43.two/108) × 360^o

= 144^o

Electricity = (xvi.2/108) × 360^o

= 54^o

Drinking h2o = (27/108) × 360^o

= 90^o

Sewerage = (21.half dozen/108) × 360^o

= 72^o

108. In the time table of a schoolhouse, periods allotted per calendar week to different teaching subjects are given beneath:

Subject	Hindi	English	Maths	Scientific discipline	Social Science	Reckoner	Sanskrit
Periods Allotted	7	eight	8	viii	seven	4	three

Draw a pie chart for this data.

Solution:-

From the question,

Full number periods allotted = 7 + eight + 8 + 8 + vii + 4 + 3 = 45 periods

Central angle of pie chart for each subject area,

Hindi = (seven/45) × 360^o

= 56^o

English = (8/45) × 360^o

= 64^o

Maths = (viii/45) × 360^o

= 64^o

Scientific discipline = (8/45) × 360^o

= 64^o

Social Scientific discipline = (vii/45) × 360^o

= 56^o

Computer = (4/45) × 360^o

= 32^o

Sanskrit = (3/45) × 360^o

= 24^o

109. A survey was carried out to notice the favorite beverage preferred past a certain group of immature people. The following pie chart shows the findings of this survey. From this pie nautical chart answer the following:

(i) Which type of beverage is liked past the maximum number of people.

Solution:-

Cold drink is liked by the maximum number of people.

(2) If 45 people similar tea, how many people were surveyed?

Solution:-

From the question information technology is given that,

45 people like tea

So,

Permit u.s.a. assume total number of people surveyed exist 10,

= 45 = (15/100) × (x)

= 45 = 0.15x

= x = 45/0.xv

= 10 = 300

Then, the total number of people surveyed is 300.

110. The following information represents the approximate percentage of water in various oceans. Gear up a pie chart for the given data.

Pacific 40%

Atlantic 30%

Indian 20%

Others 10%

Solution:-

The primal angle of the given approximate percentage of water in various oceans,

Pacific = (40/100) × 360^o

= 144^o

Atlantic = (thirty/100) × 360^o

= 108^o

Indian = (20/100) × 360^o

= 72^o

Others = (10/100) × 360^o

= 36^o

111. At a Altogether Party, the children spin a wheel to get a souvenir. Discover the probability of

(a) getting a ball

Solution:-

Number of assurance in wheel = 2

Full number of gifts = 8

Probability of getting a ball = Number of balls in wheel/ total number of gifts

= ii/eight … [split up both by 2]

= one/4

(b) getting a toy car

Solution:-

Number of cars in wheel = three

Total number of gifts = 8

Probability of getting a ball = Number of balls in bike/ total number of gifts

= iii/8

(c) whatever toy except a chocolate

Solution:-

Number of toys except a chocolate = 7

Full number of gifts = eight

Probability of getting a ball = Number of balls in wheel/ total number of gifts

= 7/8

112. Sonia picks upward a card from the given cards.

Calculate the probability of getting

(a) an odd number

Solution:-

Total number of odd numbers in given cards = five

Total number of cards = 10

Probability of getting an odd number = Total number of odd numbers/ full number of

cards

= 5/10

= ½

(b) a Y carte du jour

Solution:-

Total number of y cards = 3

Full number of cards = 10

Probability of getting a Y card = Total number of Y cards/ total number of cards

= 3/10

(c) a Grand menu

Total number of Grand cards = 2

Full number of cards = 10

Probability of getting a Y card = Total number of Y cards/ full number of cards

= 2/10

= ane/5

(d) B card begetting number > seven

Total number B card bearing number > 7= 0

Total number of cards = 10

Probability of getting a Y card = Total number B bill of fare bearing number > seven/ full number

of cards

= 0/10

= 0

113. Identify which symbol should appear in each sector in 113, 114.

Solution:-

From the given effigy,

Full number of symbol = 800 + 700 + 550 + 450 = 2500

And so,

(i) = (32/100) × 2500

114.

Solution:-

From the given figure,

Total number of ice-creams = 192 + 228 + 180 = 600

Then,

(i) = (38/100) × 600

= 228

∴
yellow colour icecream should appear in sector having 38%.

(ii) = (32/100) × 600

= 192

∴
red colour icecream should announced in sector having 32%.

(iii) = (thirty/100) × 600

= 180

∴
pink colour icecream should announced in sector having xxx%.

115. A financial counselor gave a client this pie chart describing how to budget his income. If the client brings home Rs. l,000 each month, how much should he spend in each category?

Solution:-

From the question information technology is given that,

Full money spent on 7 categories = Rs. 50,000

Then,

(i) Money spent on Housing = (30/100) × 50,000

= Rs. xv,000

(2) Money spent on Nutrient (including eating out) = (20/100) × fifty,000

= Rs. 10,000

(3) Coin spent on Automobile Loan and Maintenance = (25/100) × 50,000

= Rs. 12,500

(4) Money spent on Utilities = (10/100) × 50,000

= Rs. 5,000

(5) Coin spent on Telephone = (v/100) × 50,000

= Rs. 2,500

(6) Money spent on Habiliment = (5/100) × 50,000

= Rs. 2,500

(7) Coin spent on Amusement = (5/100) × 50,000

= Rs. 2,500

116. Post-obit is a pie nautical chart showing the amount spent in rupees (in thousands) by a visitor on various modes of advertisement for a product.

Now reply the post-obit questions.

ane. Which blazon of media advertising is the greatest corporeality of the full?

Solution:-

From the given figure,

The blazon of media advert is the greatest amount of the full is Newspaper.

2. Which blazon of media ad is the least amount of the total?

Solution:-

From the given figure,

The type of media advertisement is the least amount of the total is Radio.

three. What per cent of the total advert corporeality is spent on direct postal service campaigns?

Solution:-

From the given figure,

Full amount spent by a company on various modes of advertising for a product,

= 40 + 42 + 23 + 7 + eleven + 39 + 14 + 15 + 9

= Rs. 200

Then,

Per cent of the total advertising amount is spent on direct mail service campaigns

= (39/200) × 100

= 19.5%

four. What per cent of the ad corporeality is spent on paper and mag advertisements?

Solution:-

From the given figure,

Total amount spent by a visitor on diverse modes of advertising for a product,

= 40 + 42 + 23 + seven + 11 + 39 + 14 + 15 + 9

= Rs. 200

Then,

Per cent of the full advertising amount is spent on newspaper and mag

= ((42 + 23)/200) × 100

= (65/200) × 100

= 32.v%

v. What media types do y'all recollect are included in miscellaneous?

Why aren't those media types given their own category?

Solution:-

Internet and webmedia are included in miscellaneous.

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Frequently Asked Questions on NCERT Exemplar Solutions for Grade 8 Maths Chapter 2

Listing out the topics present in NCERT Exemplar Solutions for Class viii Maths Chapter 2?

The topics present in NCERT Exemplar Solutions for Class eight Maths Affiliate 2 are
1. Correspond the data in Pictorial form, using bar graphs and double bar graph
2. Learn, organizing and grouping of data
3. Representation of data via histogram and pie chart
iv. Probability basic concepts
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Why should I opt NCERT Exemplar Solutions for Class 8 Maths Chapter two?

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