Category: ICSE

Understanding ICSE Mathematics Class 6 ML Aggarwal Solved Solutions

Get Latest Edition of ML Aggarwal Class 6 Solutions PDF Download on LearnInsta.com. It provides step by step solutions for ML Aggarwal Maths for Class 6 ICSE Solutions Pdf Download. You can download the Understanding ICSE Mathematics Class 6 ML Aggarwal Solved Solutions with Free PDF download option, which contains chapter wise solutions. APC Maths Class 6 Solutions ICSE all questions are solved and explained by expert Mathematic teachers as per ICSE board guidelines.

APC Understanding ICSE Mathematics Class 6 ML Aggarwal Solutions 2019 Edition for 2020 Examinations

ML Aggarwal Class 6 Maths Chapter 1 Knowing Our Numbers

• Chapter 1 Knowing Our Numbers Ex 1.1
• Chapter 1 Knowing Our Numbers Ex 1.2
• Chapter 1 Knowing Our Numbers Ex 1.3
• Chapter 1 Knowing Our Numbers Ex 1.4
• Chapter 1 Knowing Our Numbers Objective Type Questions
• Chapter 1 Knowing Our Numbers Check Your Progress

ML Aggarwal Class 6 Maths Chapter 2 Whole Numbers

• Chapter 2 Whole Numbers Ex 2.1
• Chapter 2 Whole Numbers Ex 2.2
• Chapter 2 Whole Numbers Ex 2.3
• Chapter 2 Whole Numbers Objective Type Questions
• Chapter 2 Whole Numbers Check Your Progress

ML Aggarwal Class 6 Maths Chapter 3 Integers

• Chapter 3 Integers Ex 3.1
• Chapter 3 Integers Ex 3.2
• Chapter 3 Integers Ex 3.3
• Chapter 3 Integers Ex 3.4
• Chapter 3 Integers Objective Type Questions
• Chapter 3 Integers Check Your Progress

ML Aggarwal Class 6 Maths Chapter 4 Playing with Numbers

• Chapter 4 Playing with Numbers Ex 4.1
• Chapter 4 Playing with Numbers Ex 4.2
• Chapter 4 Playing with Numbers Ex 4.3
• Chapter 4 Playing with Numbers Ex 4.4
• Chapter 4 Playing with Numbers Ex 4.5
• Chapter 4 Playing with Numbers Objective Type Questions
• Chapter 4 Playing with Numbers Check Your Progress

ML Aggarwal Class 6 Maths Chapter 5 Sets

• Chapter 5 Sets Ex 5.1
• Chapter 5 Sets Ex 5.2
• Chapter 5 Sets Objective Type Questions
• Chapter 5 Sets Check Your Progress

ML Aggarwal Class 6 Maths Chapter 6 Fractions

• Chapter 6 Fractions Ex 6.1
• Chapter 6 Fractions Ex 6.2
• Chapter 6 Fractions Ex 6.3
• Chapter 6 Fractions Ex 6.4
• Chapter 6 Fractions Ex 6.5
• Chapter 6 Fractions Ex 6.6
• Chapter 6 Fractions Ex 6.7
• Chapter 6 Fractions Objective Type Questions
• Chapter 6 Fractions Check Your Progress

ML Aggarwal Class 6 Maths Chapter 7 Decimals

• Chapter 7 Decimals Ex 7.1
• Chapter 7 Decimals Ex 7.2
• Chapter 7 Decimals Ex 7.3
• Chapter 7 Decimals Ex 7.4
• Chapter 7 Decimals Ex 7.5
• Chapter 7 Decimals Objective Type Questions
• Chapter 7 Decimals Check Your Progress

ML Aggarwal Class 6 Maths Chapter 8 Ratio and Proportion

• Chapter 8 Ratio and Proportion Ex 8.1
• Chapter 8 Ratio and Proportion Ex 8.2
• Chapter 8 Ratio and Proportion Ex 8.3
• Chapter 8 Ratio and Proportion Ex 8.4
• Chapter 8 Ratio and Proportion Ex 8.5
• Chapter 8 Ratio and Proportion Objective Type Questions
• Chapter 8 Ratio and Proportion Check Your Progress

ML Aggarwal Class 6 Maths Chapter 9 Algebra

• Chapter 9 Algebra Ex 9.1
• Chapter 9 Algebra Ex 9.2
• Chapter 9 Algebra Ex 9.3
• Chapter 9 Algebra Ex 9.4
• Chapter 9 Algebra Ex 9.5
• Chapter 9 Algebra Objective Type Questions
• Chapter 9 Algebra Check Your Progress

ML Aggarwal Class 6 Maths Chapter 10 Basic Geometrical Concept

• Chapter 10 Basic Geometrical Concept Ex 10.1
• Chapter 10 Basic Geometrical Concept Ex 10.2
• Chapter 10 Basic Geometrical Concept Ex 10.3
• Chapter 10 Basic Geometrical Concept Ex 10.4
• Chapter 10 Basic Geometrical Concept Objective Type Questions
• Chapter 10 Basic Geometrical Concept Check Your Progress

ML Aggarwal Class 6 Maths Chapter 11 Understanding Symmetrical Shapes

• Chapter 11 Understanding Symmetrical Shapes Ex 11.1
• Chapter 11 Understanding Symmetrical Shapes Ex 11.2
• Chapter 11 Understanding Symmetrical Shapes Ex 11.3
• Chapter 11 Understanding Symmetrical Shapes Ex 11.4
• Chapter 11 Understanding Symmetrical Shapes Ex 11.5
• Chapter 11 Understanding Symmetrical Shapes Ex 11.6
• Chapter 11 Understanding Symmetrical Shapes Objective Type Questions
• Chapter 11 Understanding Symmetrical Shapes Check Your Progress

ML Aggarwal Class 6 Maths Chapter 12 Symmetry

• Chapter 12 Symmetry Ex 12.1
• Chapter 12 Symmetry Ex 12.2
• Chapter 12 Symmetry Objective Type Questions
• Chapter 12 Symmetry Check Your Progress

ML Aggarwal Class 6 Maths Chapter 13 Practical Geometry

• Chapter 13 Practical Geometry Ex 13.1
• Chapter 13 Practical Geometry Ex 13.2
• Chapter 13 Practical Geometry Ex 13.3
• Chapter 13 Practical Geometry Objective Type Questions
• Chapter 13 Practical Geometry Check Your Progress

ML Aggarwal Class 6 Maths Chapter 14 Mensuration

• Chapter 14 Mensuration Ex 14.1
• Chapter 14 Mensuration Ex 14.2
• Chapter 14 Mensuration Objective Type Questions
• Chapter 14 Mensuration Check Your Progress

ML Aggarwal Class 6 Maths Chapter 15 Data Handling

• Chapter 15 Data Handling Ex 15.1
• Chapter 15 Data Handling Ex 15.2
• Chapter 15 Data Handling Ex 15.3
• Chapter 15 Data Handling Ex 15.4
• Chapter 15 Data Handling Ex 15.5
• Chapter 15 Data Handling Objective Type Questions
• Chapter 15 Data Handling Check Your Progress

ML Aggarwal Class 6 Maths Model Question Papers

• Model Question Paper 1
• Model Question Paper 2
• Model Question Paper 3
• Model Question Paper 4
• Model Question Paper 5
• Model Question Paper 6

FAQs on ML Aggarwal Class 6 Solutions

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ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 6

Questions 1 to 8 is of 1 mark each.
Question 1.
If x + y = 11 and xy = 24, then x² + y² =
(a) 121
(b) 73
(c) 48
(d) none of these
Solution:

Question 2.
Factors of a³ – 64a are
(a) a(a – 8)²
(b) (a + 8) (a – 8)
(c) a(a + 8) (a – 8)
(d) a(a + 8)²
Solution:

Question 3.
If 3(y – 3) = 5(2y + 1) then y is equal to
(a) 3
(b) -3
(c) 2
(d) -2
Solution:

Question 4.
If one angle of a parallelogram is 30° less than other angles, then the larger angle is
(a) 150°
(b) 75°
(c) 105°
(d) 210°
Solution:

Question 5.
A polyhedron has 7 faces, 10 vertices and 15 edges. Name of the polyhedron is
(a) hexagonal prism
(b) pentagonal prism
(c) hexagonal pyramid
(d) none of these
Solution:

Question 6.
The base of a triangle is twice its height. If the area of the triangle is 25 cm², then the base is
(a) 10 cm
(b) 20 cm
(c) 5 cm
(d) 25 cm
Solution:

Question 7.
From a well-shuffled deck of 52 playing cards, one card is drawn at random then the probability that card drawn is a blackjack

Solution:

Question 8.
Amongst the following digits, the one having exactly one line of symmetry is
(a) 0
(b) 3
(c) 6
(d) 8
Solution:

Section-B
Questions 9 to 14 are of 2 marks each.
Question 9.
Using a suitable identity, evaluate (9.7)².
Solution:

Question 10.
Factorize x²y²(a⁴ + b⁴) + a²b²(x⁴ + y⁴).
Solution:

Question 11.
Sum of three consecutive odd numbers is 153. Find the numbers.
Solution:

Question 12.
If each interior angle of a regular polygon is 108°, then find the number of sides of the polygon.
Solution:

Question 13.
Verify Euler’s formula for a decagonal pyramid.
Solution:

Question 14.
A cuboid is of dimensions 24 cm × 30 cm × 36 cm. How many small cubes with side 6 cm can be placed in the cuboid?
Solution:

Section-C
Questions 15 to 24 are of 4 marks each.
Question 15.
Simplify the following expressions and evaluate it when x = 1, y = -1
(5xy – 3x² + 2y²) × (5y² – 8xy + 3x²) + 9x³y – 8y⁴ + 12x⁴
Solution:

Question 16.
Factorize: 15(2x – 3y)² – 4(4x – 6y) – 16
Solution:

Question 17.
Two years ago Ramesh was three times as old as his son. Two years later, twice of his age will be equal to the five times that of his son’s age. Find their present ages.
Solution:

Question 18.
In the given figure ABCD is a parallelogram in which ∠DAP = 40°, ∠BAP = 25° and ∠CPD = 105°, find
(i) ∠ABP
(ii) ∠PDC
(iii) ∠ACB
(iv) ∠CBD
Solution:

Question 19.
Construct a rhombus TRUE whose one side TR = 4 cm and diagonal TU = 6.5 cm.
Solution:

Question 20.
Construct a parallelogram GOLD in which diagonal GL = 3.8 cm, diagonal OD = 4.6 cm and angle between diagonals is 60°.
Solution:

Question 21.
In the given figure, O is the centre of the circle. If PT is tangent to the circle at point T, find the size of each lettered angle.

Solution:

Question 22.
A rectangular sheet of tin foil of size 30 cm × 18 cm can be rolled to form a cylinder two ways along length and breadth. Find the ratio of volumes of the two cylinders thus formed.
Solution:

Question 23.
Construct a histogram for the following data:

Solution:

Question 24.
Height of a room is half of its length and its breadth is \(\frac{3}{2}\) of the height. If the cost of painting its four walls at the rate of ₹1.75 per m² is ₹ 196, then find the cost of tiling the floor of the room at the rate of ₹8.50 per m².
Solution:

Section-D
Questions 25 to 29 are of 6 marks each.
Question 25.
If \(x+\frac{1}{x}=5\), them find

Solution:

Question 26.
In the given figure, ABCD is a rhombus and DCFE is a square, If ∠ABC = 56°, find
(i) ∠DAG
(ii) ∠FEG
(iii) ∠AGC

Solution:

Question 27.
The figure given below shows a field with the measurement given in metres. Find the area of the field.

Solution:

Question 28.
A bag contains 5 red, 6 black and 4 white balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is
(i) white
(ii) not black
(iii) red or black
Solution:

Question 29.
A school decided to award prizes to their students for three values, honesty, punctuality and obedience. The value of prize for punctuality is \(\frac{5}{6}\) of the value of prize for honesty and value of prize for obedience is \(\frac{4}{5}\) of the value of prize for punctuality. If the total value of the three prizes is ₹1500, find the value of each prize. Which quality you prefer to be rewarded most and why? What values are being promoted?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 5

Choose the correct answer from the given four options (1-2):
Question 1.
In a pentagonal pyramid number of faces, vertices and edges are
(a) F = 6, V = 6, E = 10
(b) F = 7, V = 7, E = 12
(c) F = 6, V = 8, E = 12
(d) none of these.
Solution:

Question 2.
If the lateral surface area of a cube is 144 cm, then its volume is
(a) 36cm³
(b) 216 cm³
(c) 288 cm³
(d) none of these
Solution:

Question 3.
Draw the top, front and side views of the given solid.

Solution:

Question 4.
The area of a trapezium is 96 cm². If the lengths of its two parallel sides are 14 cm and 10 cm, then find the perpendicular distance between parallel sides.
Solution:

Question 5.
In the given figure, C is the centre of the circle. The tangent to the circle of radius 6 cm from a point P outside the circle is of length 8 cm. Find the distance of the point P from the farthest point of the circumference.

Solution:

Question 6.
Construct a quadrilateral PQRS in which PQ = 5.5 cm, RS = 6.5 cm, PS = 4.4 cm, PR = 6.5 cm and QS = 7.1 cm.
Solution:

Question 7.
The length, breadth and height of cuboidal water tank is 7 m, 6 m and 2 m respectively. If 4200 litre of water is pumped out from the tank. Find the fall in water level in the tank.
Solution:

Question 8.
Construct a rhombus PQRS such that PQ = 5.4 cm and ∠P = 60°. Also, draw its lines of symmetry.
Solution:

Question 9.
A road roller has a diameter 84 cm and its width is 1.2 m. If it takes 500 complete revolutions to level a playground. Find the area of the playground. Also, find the cost of levelling the playground at a rate of 50 paise per m².
Solution:

Question 10.
Construct a rectangle ABCD, such that AB = 6.4 cm and BD = 7.6 cm.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 3

Questions 1 to 8 is of 1 mark each.
Question 1.
Product of rational number \(\frac{-4}{7}\) and itsadditive inverse is
(a) \(\frac{16}{49}\)
(b) \(\frac{-16}{49}\)
(c) 1
(d) 0
Solution:

Question 2.
What should be subtracted from \(\frac{-3}{5}\) to get \(\frac{-2}{3}\)?

Solution:

Question 3.
The value of \(\left(\frac{2}{3}\right)^{0}+\left(\frac{2}{3}\right)^{-1}\) is

Solution:

Question 4.
Standard form of 0.00000000234 is
(a) 2.34 × 10^-8
(b) 23.4 × 10^-10
(c) 2.34 × 10^-9
(d) 234 × 10^-1
Solution:

Question 5.
The volume of a cube is 216 m³. Length of its side is
(a) 3 m
(b) 6 m
(c) 9 m
(d) 12 m
Solution:

Question 6.
When the difference of a 2-digit number ab (a > b) and the number obtained by reversing the digits is divided by 9, then quotient is
(a) a + b
(b) b – a
(c) a – b
(d) none of these
Solution:

Question 7.
Amar buys a toy for ₹ 120 and sells it for ₹ 144, his profit % is
(a) 5%
(b) 10%
(c) 20%
(d) 24%
Solution:

Question 8.
If 567×8 is divisible by 9, then value of x is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Section-B
Questions 9 to 14 are of 2 marks each.
Question 9.
Ramesh bought a fan for ₹ 1320 including 10% VAT. Find the price of the fan before VAT was added.
Solution:

Question 10.
Find A in the addition

Solution:

Question 11.
Find the value of x for which \(\left(-\frac{4}{5}\right)^{2} \times\) \(\left(-\frac{5}{4}\right)^{2 x}=\frac{625}{256}\).
Solution:

Question 12.
Using appropriate properties of operations of rational numbers, evaluate:

Solution:

Question 13.
What number should be subtracted from the sum of \(\frac{-5}{12}\) and \(\frac{2}{3}\) to get \(\frac{5}{4}\) ?
Solution:

Question 14.
If n(ξ) = 40, n(A) = 23, n(B’) = 28 and n(A ∪ B’) = 9, find n(A ∩ B).
Solution:

Section-C
Questions 15 to 24 are of 4 marks each.
Question 15.
In an auditorium, the number of rows is equal to the number of chairs in each row. If there are 5184 chairs in the auditorium, find the number of rows.
Solution:

Question 16.
Insert 5 rational numbers between \(\frac{1}{3}\) and \(\frac{1}{2}\).
Solution:

Question 17.
Find the smallest number by which 10584 should be multiplied so that product is a perfect cube. Also find the cube root of the product.
Solution:

Question 18.
In a 3-digit number unit’s digit is 2 less than hundred’s digit and hundred’s digit is 3 less than the ten’s digit. If the sum of the original number and number obtained by reversing the digits is 968, find the number.
Solution:

Question 19.
Rohit purchased some oranges at 3 for ₹5 and sold them at 5 for ₹12. Thus he gained ₹143 in all. How many oranges did he purchase?
Solution:

Question 20.
How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 20% he still earns a profit of 20%?
Solution:

Question 21.
Find the difference between S.I. and C.I. on ₹2000 for \(1 \frac{1}{2}\) years at 6% p.a., compound interest being reckoned half-yearly.
Solution:

Question 22.
If 5 men or 7 women can earn ₹903 in a day, how much will 10 men and 5 women earn in a day?
Solution:

Question 23.
A hostel had rations for 150 students for 60 days. After 12 days, 30 more students join the hostel. How long will the remaining rations last?
Solution:

Question 24.
Simplify the following expression and write in the exponential form:
3^-5 × 3² ÷ 3⁶ × (2² × 3)² + \(\left(\frac{2}{3}\right)^{-1}\) + 2^-1 + \(\left(\frac{1}{19}\right)^{-1}\).
Solution:

Section-D
Questions 25 to 29 are of 6 marks each.
Question 25.
Ramesh scored 30% marks in an exam and failed by 20 marks, while Suresh scored 40% marks and got 40 marks more than the minimum marks required to pass the exam. Find the maximum marks and pass percentage.
Solution:

Question 26.
If ξ = {x | x ϵ W, x < 20}, A = {factors of 18} and B = {multiples of 3}, find
(i) A ∪ B
(ii) A ∩ B
(iii) (A ∪ B)’.
Also verify that n(A ∪ B) = n(A) + n(B) – n(A ∩ B).
Solution:

Question 27.
A and B together can do a piece of work in 15 days; B and C together can do it in 12 days; C and A can do it in 20 days. How long will they take to finish the work, working together? Also find the number of days taken by each to do the same work, working alone.
Solution:

Question 28.
Is 31104 a perfect square number? If not then find the smallest number by which 31104 should be divided so that quotient is a perfect square. Also, find the square root of the quotient.
Solution:

Question 29.
Three numbers are in the ratio 1:3:5 and sum of their cubes is 52479. Find the numbers.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2

Choose the correct answer from the given four options (1-2):
Question 1.
If 295×703 is divisible by 11, then value of x is
(a) 5
(b) 6
(c) 7
(d) 8
Solution:

Question 2.
If C.P. of an article is ₹500 and S.P. is ₹600, then, his profit % is
(a) 10%
(b) 15%
(c) 20%
(d) 25%
Solution:

Question 3.
Find the values of the letters in the following and give reasons for the steps involved:

Solution:

Question 4.
Ramu bought a fan for ₹1080 including 8% VAT. Find the price of fan before VAT was added.
Solution:

Question 5.
Find the amount and compound interest on ₹2000 for 2 years at 5% per annum, interest payable yearly.
Solution:

Question 6.
If P = {letters of the word HYDERABAD} and Q= {letters ofthewordALLAHABAD}, find
(i) P ∪ Q
(ii) P ∩ Q
Also verify that
n(P ∪ Q) = n(P) + n(Q) – n(P ∩ Q).
Solution:

Question 7.
A blanket was marked for ₹500. A shopkeeper allows a discount of 10%. But due to partial damage in the blanket he has to give an extra discount of 20%. Find the S.P. of the blanket.
Solution:

Question 8.
In a 3 digit number unit’s digit, ten’s digit and hundred’s digit are in the ratio 3 : 5 : 7. If the difference of original number and number obtained by reversing the digits is 396, find the number.
Solution:

Question 9.
In an exam atleast 40% marks are required to pass the exam. Rohit uses unfair means to pass the exam but fails by 20 marks. If he scored 220 marks, then find the maximum marks.
Is using unfair means in exam is good? Why should we not use unfair means?
Solution:

Question 10.
Find the sum invested for \(1 \frac{1}{2}\) years compounded half-yearly at the rate of 8% p.a. that will amount to ₹ 17576.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1

Choose the correct answer from the given four options (1-2):
Question 1.
Sum of rational number \(\frac { 5 }{ 7 }\) and its additiveinverse is
(a) 1
(b) 0
(c) -1
(d) none of these
Solution:

Question 2.
Product of two rational numbers is 1. If one of them is \(\frac { 4 }{ 5 }\), then other is

Solution:

Question 3.
Find the value of x for which \(\left(\frac{4}{9}\right)^{x} \times\left(\frac{3}{2}\right)^{-1}\) = \(\frac{8}{27}\).
Solution:

Question 4.
Express the following numbers in standard form:
(i) 0.0000000000578
(ii) 345700000000000
Solution:

Question 5.
Insert ten rational numbers between \(\frac{-4}{5}\) and \(\frac{2}{3}\).
Solution:

Question 6.
Find the cube root of 50653.
Solution:

Question 7.
Find the smallest number by which 3645 should be divided so that quotient is a perfect cube.
Solution:

Question 8.
If p = \(\frac{-3}{5}\), q = \(\frac{1}{2}\), r= \(\frac{-7}{9}\),then verify p × (q + r) = p × q + p × r.
Solution:

Question 9.
Find the square root of 7056 by prime factorisation method.
Solution:

Question 10.
Find the least number which must be added to 59000 to make it a perfect square.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress

Question 1.
Each student from the group of 40 students was asked to roll a dice independently. The results are given below:
2, 3, 3, 4, 1, 5, 2, 6, 1, 4, 2, 3, 4, 4, 6, 1, 5, 5, 2, 4, 5, 5, 3, 1, 6, 5, 4, 2, 3, 6, 1, 1, 4, 4, 5, 3, 2, 2, 6,6
Make a frequency distribution table for the same.
Solution:

Question 2.
The marks obtained by 30 students of a class in a test of maximum marks 20 are as follows:
15, 11, 12, 10, 9, 8, 19, 13, 16, 3, 2, 17, 18, 19, 14, 6, 20, 15, 16, 12, 10, 4, 9, 8, 12, 17, 18, 20, 19, 12.
Prepare a frequency distribution table for the above data using class intervals 0-4, 4-8 and so on.
Solution:

Question 3.
Construct a frequency distribution table for the following weights (in grams) of 35 oranges, using class intervals 40—45, 45-50 and so on.
30, 40, 45, 32, 43, 50, 55, 63, 72, 73, 62, 61, 54, 53, 50, 43, 76, 38, 54, 55, 66, 70, 74, 75, 45, 47, 59, 58, 60, 63, 74, 33, 35, 70, 68.
(i) How many classes are there in the frequency distribution table?
(ii) Which weight group has the lowest frequency?
(iii) Which weight group has the highest frequency?
Solution:

Question 4.
Draw a histogram of the following data:
Marks obtained by students in a Mathematics Paper of maximum marks 100.

Solution:

Question 5.
The following data represents the number of students using a different mode of transportation to come to school.

Draw a pie chart to represent this data Pie chart is given below:
Solution:

Question 6.
Answer the following questions based on the pie chart given below:
(i) Which type of programmes are viewed the most?
(ii) Which type of programmes are viewed the least?
(iii) Which two types of programmes have number of viewers equal to those watching sports channels?

Solution:

Question 7.
Suppose you spin the wheel shown in adjoining figure.
(i) List the outcomes of getting a green sector and not getting a green sector on this wheel.
(ii) Find the probability of getting a green sector.
(iii) Find the probability of not getting a green sector.

Solution:

Question 8.
A bag has 4 red and 2 yellow balls. A ball is drawn from the bag without looking into the bag. What is the probability of getting
(i) a red ball?
(ii) not a red ball?
Solution:

Question 9.
Three coins are tossed together, find the probability of getting
(i) atmost 2 heads
(ii) 3 heads.
Solution:

Question 10.
A letter is chosen from the word ‘RECTANGLE’. What is the probability that it is
(i) a consonant
(ii) not a consonant.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) Bar graphs are ……….. representation of ungrouped data.
(ii) In a grouped frequency distribution, the difference between lower limit and upper limit of a class is called ………..
(iii) The mid point of the class interval is called ………..
(iv) Bar graphs of grouped data are called ………..
(v) The circle graphs are commonly called ………..
(vi) An experiment which has more than one possible outcomes and it is not possible to predict the outcome in advance is called ………..
(vii) The outcomes which ensures the occurrence of an event are called ………..
(viii) An event which never happens is called ………..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The data arranged in ascending or descending order of size is called data array.
(ii) The lower limit of class 10-20 is 20.
(iii) The class size of class 20-30 is 10.
(iv) The class mark of 25-35 is 30.
(v) There is no difference between bar graphs and histograms.
(vi) In histograms the breadth of a rectangle is meaningless.
(vii) In histograms, there is no gap between two adjacent rectangle.
(viii) In a pie chart, size of each sector is proportional to the value of item represented by it.
(ix) In a pie chaiangle of sector
= \(\frac{\text { value of item }}{\text { sum of values of all items }} \times 180^{\circ}\)
(x) In tossing a coin getting head or tail are equally likely events.
(xi) Probability of an event E satisfies 0 ≤ P(E) ≤ 1.
(xii) P(occurrence of an event) = P(non occurence of an event).
(xiii) Total number of outcomes when two dice are rolled togehter = 6 + 6.
Solution:

Multiple Choice Questions
Study the following frequency distribution table:
The table shows the pocket money (in ?) per month of 50 students. Choose the correct answer from the given four options for questions 3 to 7;

Question 3.
Size of the class-intervals is
(a) 50
(b) 20
(c) 10
(d) 30
Solution:

Question 4.
The class having the maximum frequency is
(a) 10-20
(b) 20-30
(c) 30-40
(d) 40-50
Solution:

Question 5.
The upper limit of the class having minimum frequency is
(a) 30
(b) 40
(c) 50
(d) 60
Solution:

Question 6.
Which two are classes having the same frequency?
(a) 10-20 and 20-30
(b) 20-30 and 30-40
(c) 30-40 and 50-60
(d) 40-50 and 50-60
Solution:

Question 7.
The frequency of class whose class mark is 25 is
(a) 14
(b) 11
(c) 10
(d) 4
Solution:

The pie graph shown in the adjoining figure representing the different subjects liked by the students of class VIII. Study the pie graph carefully and choose the correct answer from the given four options for questions 8 to 11.

Question 8.
Which subject is liked by the maximum number of students
(a) Maths
(b) Science
(c) S. Science
(d) English
Solution:

Question 9.
Which subject is liked by the minimum number of students
(a) Maths
(b) Science
(c) S. Science
(d) English
Solution:

Question 10.
If there are 200 students in class VIII then the number of students who like S. Science
(a) 10
(b) 20
(c) 40
(d) 80
Solution:

Question 11.
Number of students who like Science
(a) 20
(b) 40
(c) 60
(d) 80
Solution:

Choose the correct answer from the given four options (12 to 17):
Question 12.
Probability of getting the sum as 4 when a pair of dice is rolled

Solution:

Question 13.
Probability of getting exactly 2 heads when three coins are tossed together

Solution:

Question 14.
Probability of selecting a consonant from the letters of the word ‘FATHER’

Solution:

Question 15.
Probability of getting more than 2 heads when a pair of coins is tossed.
(a) 1
(b) \(\frac{1}{2}\)
(c) \(\frac{1}{3}\)
(d) 0
Solution:

Question 16.
Probability of getting a red ball from a bag containing 20 red balls
(a) 0
(b) 1
(c) \(\frac{1}{20}\)
(d) \(\frac{1}{2}\)
Solution:

Question 17.
Probability of getting a non-red ball from a bag containing 4 red, 5 blue and 3 black balls is

Solution:

Value Based Questions
Question 1.
Draw a pie chart of the data given below:
The time spent by a Class VIII student during a day.

Should a student of class VIII study for just 2 hours daily? Which time is considered the best time for self-study?
Solution:

Question 2.
From a bag containing 2 saffron, 3 white and 4 green balls a ball is drawn at random. Find the probability that ball drawn is
(i) Saffron
(ii) White
(iii) Green
Which are three colours in our National Flag? What values did they indicate? What values are being promoted?
Solution:

Question 3.
Four defective oranges are accidentally mixed with 16 good ones. One orange is drawn at random. Find the probability that the orange drawn is good one.
What will happen if 4 bad persons are mixed with 16 good ones?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
A bag contains 12 balls out of which x are black.
(i) If a ball drawn at random, what is the probability that it will be a black ball?
(ii) If 6 more black balls are put in the bag, the probability of drawing a black ball will be double than that of (i). Find the value of x.
Solution:

Question 2.
Ankita and Nagma are friends. They were both born in 1998. What is the probability that they have
(i) same birthday?
(ii) different birthday?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3

Question 1.
List the outcomes you can see in these experiments.

Solution:

Question 2.
A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3
Solution:

Question 3.
Two coins are tossed together. Find the probability of getting
(i) two tails
(ii) atleast one tail
(iii) no tail
Solution:

Question 4.
Three coins are tossed together. Find the probability of getting
(i) atleast two heads
(ii) atleast one tail
(iii) atmost one tail.
Solution:

Question 5.
Two dice are rolled simultaneously. Find the probability of getting
(i) the sum as 7
(ii) the sum as 3 or 4
(iii) prime numbers on both the dice.
Solution:

Question 6.
A fcox contains 600 screws, one tenth are rusted. One screw is taken out at random from the box. Find the probability that it is
(i) a rusted screw
(ii) not a rusted screw
Solution:

Question 7.
A letter is chosen from the word ‘TRIANGLE’. What is the probability that it is a vowel?
Solution:

Question 8.
A bag contains 5 red, 6 black and 4 white balls. A ball is drawn at random from the bag, find the probability the ball is drawn is
(i) white
(ii) not black
(iii) red or black
(iv) neither red nor black
Solution:

Question 9.
A box contains 17 cards numbered 1, 2, 3, ……….,17 and are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is
(i) odd
(ii) even
(iii) prime
(iv) divisible by 3
(v) divisible by 2 and 3 both
Solution:

Question 10.
A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is:
(i) an ace
(ii) a red card
(iii) neither a king nor a queen
(iv) a red face card or an ace
(v) a card of spade
(vi) non-face card of red colour.
Solution:

Question 11.
In a lottery, there are 5 prized tickets and 995 blank tickets. A person buys a lottery ticket. Find the probability of his winning a prize.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2

Question 1.
The following data represents the different number of animals in a zoo. Prepare a pie chart for the given data.

Solution:

Question 2.
The following data represents the monthly expenditure of a family (in T) on various items. Draw a pie chart to represent this data.

Solution:

Question 3.
The following data represents the percentage distribution of the expenditure incurred in publishing a book.

Draw a pie chart to represent this data.
Solution:

Question 4.
The following data represents the number of students got admission in different streams of a college:

Draw a pie chart to represent this data.
Solution:

Question 5.
The adjoining pie chart shows the expenditure of a country on various sports during year 2012. Study the pie chart carefully and answer the following questions:

(i) What percent of total expenditure is spent on cricket?
(ii) How much percent more is spent on hockey than that on tennis?
(iii) If the total amount spent on sports in 2012 is ₹1,80,00,000, then find amount spent on Badminton,
(iv) If the total amount spent on sports in 2012 is ₹2,40,00,000 then find the amount spent on cricket and hockey together.
Solution:

Question 6.
The adjoining pie chart shows the number of students enrolled in class VI to class X of a school.

If 1440 students are enrolled from VI to X, then answer the following questions:
(i) How many students are enrolled in class VIII?
(ii) How many students are more in class IX than in class X?
(iii) What is the sum of students enrolled in VII and VIII?
(iv) Find the ratio of students enrolled in VI to students enrolled in X.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1

Question 1.
The result of a survey of 200 people about their favourite fruit is given below:

Represent the above data by a bar graph.
Solution:

Question 2.
Mr Khurana has two kitchen appliance stores. He compares the sales of two stores during a month and recovered as given below:

Represent the above data by a double bar graph.
Solution:

Question 3.
The number of goals scored by a football team in different matches is given below:
3, 1, 0, 4, 6, 0, 0, 1, 1, 2, 2, 3, 5, 1, 2, 0, 1, 0, 2, 3, 9, 2, 0, 1, 0, 1, 4, 1, 0, 2, 5, 1, 2, 2, 3, 1, 0, 0, 0, 1, 1, 0, 2, 3, 0, 1, 5, 2, 0
Make a frequency distribution table using tally marks.
Solution:

Question 4.
Given below a bar graph:

Read the bar graph carefully and answer the following questions:
(i) What is the information given by the bar graph?
(ii) On which item the expenditure is maximum?
(iii) On which item the expenditure is minimum?
(iv) State whether true or false:
Expenditure on education is twice the expenditure on clothing.
Solution:

Question 5.
Given below a double bar graph.

Read the double bar graph carefully and answer the following questions:
(i) What is the information given by the double graph?
(ii) Which mode of transport girls using more than the boys?
(iii) Which mode of transport boys using the most?
(iv) In which mode of transport number of girls is half the number of boys?
Solution:

Question 6.
Using class intervals 0-5, 5-10, construct the frequency distribution table for the following
data:
13, 6, 12, 9, 11, 14, 2, 8, 18, 16, 9, 13, 17, 11, 19, 6, 7, 12, 22, 21, 18, 1, 8, 12, 18.
Solution:

Question 7.
Given below are the marks secured by 35 students in a surprise test:
41, 32, 35, 21, 11, 47, 42, 00, 05, 18, 25, 24, 29, 38, 30, 04, 14, 24, 34, 44, 48, 33, 36, 38, 41, 48, 08, 34, 39, 11, 13, 27, 26, 43, 03.
Taking class intervals 0-10, 10-20, …….. construct frequency distribution table. Find the number
of students obtaining below 20 marks.
Solution:

Question 8.
The electricity bills (in ?) of 40 houses in a locality are given below:
78, 87,81,52, 59, 65, 101, 108, 115, 95, 98, 65,62, 121, 128, 63,76, 84, 89,91,65, 101,95,81, 87, 105, 129, 92, 75, 105, 78, 72, 107, 116, 127, 100, 80, 82, 61, 118 Construct a grouped frequency distribution table of class size 10.
Class intervals (Electricity bill in ?) Tally marks Frequency (Number of houses)
Solution:

Question 9.
Draw a histogram for the frequency table made for data in Question 8, and answer the following questions:
(i) Which group has the maximum number of houses?
(ii) How many houses pay less than ₹ 100?
(iii) How many houses pay ₹ 100 or more?
Solution:

Question 10.
The weights of 29 patients in a hospital were recorded as follows:

Draw a histogram to represent this data visually.
Solution:

Question 11.
In a study of diabetic patients, the following data was obtained:

Represent the above data by a histogram.
Solution:

Question 12.
The histogram showing the weekly wages (in ₹) of workers in a factory is given alongside:

Answer the following:
(i) What is the frequency of class 400-425?
(ii) What is the class having a minimum frequency?
(iii) How many workers get more than ₹425?
(iv) How many workers get less than ₹475?
(v) Number of workers whose weekly wages are more than or equal to ₹400 but less than ₹450.
Solution:

Question 13.
The number of hours for which students of a particular class watched television during holidays is shown in the histogram below.

Answer the following:
(i) For how many hours did the maximum number of students watch T.V.?
(ii) How many students watched T.V. for less than 4 hours?
(iii) How many students spent more than 5 hours in watching T.V.?
(iv) How many students spent more than 2 hours but less than 4 hours in watching T.V.?
Solution:

Question 14.
The number of literate females in the age group of 10 to 40 years in a town is shown in the histogram alongside.

Answer the following questions:
(i) Write the classes assuming all the classes are of equal width.
(ii) What is the class size?
(iii) In which age group are the literate females the least?
(iv) In which age group is the number of literate females the highest?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths