ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress

Question 1.
Evaluate the following:
(i) (-7) × (-9) × (-11)
(ii) (-5) × 7 × (-6) × (-8)
(iii) (-1024) ÷ 32
(iv) (-216) ÷ (-12)
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress 1

Question 2.
What will be the sign of the product if we multiply 39 negative integers and 98 positive integers?
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress 2

Question 3.
Use the sign >, < or = in the box to make the following statements true:
(i) (-15) + 38 ……… 27 + (-50)
(ii) (-13) × 0 × (-5) …….. (-7) × (-6) × 14
(iii) (-18) ÷ (-3) …….. (-10) + (-15) + 31
(iv) (-5) × (-7) × (-10) …….. (-1400) ÷ (-4)
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress 3
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress 4

Question 4.
Is {(-45) ÷ (-15)} ÷ (-3) = (-45) ÷ [(-15) ÷ (-3)]?
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress 5

Question 5.
A cement company earns a profit of ₹ 8 per bag of white cement sold and a loss of ₹ 5 per bag of grey cement sold.
(i) The company sells 3000 bags of white cement and 5000 bags of grey cement in a month. What is its profit or loss?
(ii) What is the number of white cement bags it must sell to have neither profit nor loss if the number of grey cement bags sold is 6400?
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress 6

Question 6.
Simplify the following:
(i) (-7) + (-6) ÷ 2 – {(-5) × (-4) – (3 – 5)}
(ii) 11 – [7 – (5 – 3 (9 – \(\bar { 3-6 }\))}].
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress 7

ML Aggarwal Class 7 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in One Variable Check Your Progress

Question 1.
Solve the following equations:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 1
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 3
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 4
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 5

Question 2.
The sum of three consecutive multiples of 11 is 363. Find these multiples.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 6

Question 3.
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 7

Question 4.
One-half of a number is equal to one-third of its succeeding number. Find the first number.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 8

Question 5.
The numerator of a rational number is 8 less than its denominator. If the numerator is increased by 2 and denominator is decreased by 1, the number obtained is \(\frac{1}{2}\). Find the number.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 9

Question 6.
The present ages of Rohit and Mayank are in the ratio 11 : 8. 8 years later the sum of their ages will be 54 years. What are their present ages?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 10

Question 7.
A father’s age is 3 times the sum of ages of his two sons. Five years later he will be twice the sum of ages of his two sons. Find the present age of the father.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 11

Question 8.
The digits of a two-digit number differ by 7. If the digits are interchanged and the resulting number is added to the original number we get 121. Find the original number.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 12

Question 9.
The ten’s digit of a two-digit number exceeds it’s unit’s digit by 5. When digits are reversed, the new number added to the original number becomes 99. Find the original number.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 13

Question 10.
Sonia went to a bank with ₹2,00,000. She asked the cashier to give her ₹500 and ₹2000 currency notes in return. She got 250 currency notes in all. Find the number of each kind of currency notes.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 14

Question 11.
Ajay covers a distance of 240 km in \(4 \frac{1}{4}\) hours. Some part of the journey was covered at the speed of 45 km/h and the remaining at 60 km/h. Find the distance covered by him at the rate of 60 km/h.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 15
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 16

Question 12.
If x ϵ {even integers), represent the solution set of the inequation -5 ≤ x < 5 on a number line.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 17

Question 13.
Solve the following inequality and graph its solution on a number line:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 18
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 19
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Check Your Progress 20

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in One Variable Ex 12.2

Question 1.
Three more than twice a number is equal to four less than the number. Find the number.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 1

Linear Equations and Inequalities in one Variable

Question 2.
When four consecutive integers are added, the sum is 46. Find the integers.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 2

Linear Equations and Inequalities in one Variable Solution

Question 3.
Manjula thinks a number and subtracts \(\frac{7}{3}\) from it. She multiplies the result by 6. The result now obtained is 2 less than twice the same number she thought of. What is the number?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 3

Question 4.
A positive number is 7 times another number. If 15 is added to both the numbers, then one of the new numbers becomes \(\frac{5}{2}\) times the other new number. What are the numbers?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 4

Question 5.
When three consecutive even integers are added, the sum is zero. Find the integers.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 5

Question 6.
Find two consecutive odd integers such that two-fifth of the smaller exceeds two-ninth of the greater by 4.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 6
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 7

Question 7.
The denominator of a fraction is 1 more than twice its numerator. If the numerator and denominator are both increased by 5, it becomes \(\frac{3}{5}\). Find the original fraction.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 8

Question 8.
Find two positive numbers in the ratio 2 : 5 such that their difference is 15.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 9

Question 9.
What number should be added to each of the numbers 12, 22, 42 and 72 so that the resulting numbers may be in proportion?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 10

Question 10.
The digits of a two-digit number differ by 3. If the digits are interchanged and the resulting number is added to the original number, we get 143. What can be the original number?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 11

Question 11.
Sum of the digits of a two-digit number is 11. When we interchange the digits, it is found that the resulting new number is greater than the original number by 63. Find the two-digit number.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 12

Question 12.
Ritu is now four times as old as his brother Raju. In 4 years time, her age will be twice of Raju’s age. What are their present ages?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 13

Question 13.
A father is 7 times as old as his son. Two years ago, the father was 13 times as old as his son. How old are they now?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 14

Question 14.
The ages of Sona and Sonali are in the ratio 5 : 3. Five years hence, the ratio of their ages will be 10 : 7. Find their present ages.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 15

Question 15.
An employee works in a company on a contract of 30 days on the condition that he will receive ₹200 for each day he works and he will be fined ₹20 for each day he is absent. If he receives ₹3800 in all, for how many days did he remain absent?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 16

Question 16.
I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 17

Question 17.
A local bus is carrying 40 passengers, some with ₹5 tickets and the remaining with ₹7.50 tickets. If the total receipts from these passengers are ₹230, find the number of passengers with ₹5 tickets.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 18

Question 18.
On a school picnic, a group of students agree to pay equally for the use of a full boat and pay ₹10 each. If there had been 3 more students in the group, each would have paid ₹2 less. How many students were there in the group?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 19

Question 19.
Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 20

Question 20.
Sakshi takes some flowers in a basket and visits three temples one by one. At each temple, she offers one-half of the flowers from the basket. If she is left with 6 flowers at the end, find the number of flowers she had in the beginning.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 21

Question 21.
Two supplementary angles differ by 50°. Find the measure of each angle.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 22

Question 22.
If the angles of a triangle are in the ratio 5 : 6 : 7, find the angles.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 23

Question 23.
Two equal sides of an isosceles triangle are 3x – 1 and 2x + 2 units. The third side is 2x units. Find x and the perimeter of the triangle.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 24

Question 24.
If each side of a triangle is increased by 4 cm, the ratio of the perimeters of the new triangle and the given triangle is 7 : 5. Find the perimeter of the given triangle.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 25

Question 25.
The length of a rectangle is 5 cm less than twice its breadth. If the length is decreased by 3 cm and breadth increased by 2 cm, the perimeter of the resulting rectangle is 72 cm. Find the area of the original rectangle.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 26

Question 26.
A rectangle is 10 cm long and 8 cm wide. When each side of the rectangle is increased by x cm, its perimeter is doubled. Find the equation in x and hence find the area of the new rectangle.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 27

Question 27.
A steamer travels 90 km downstream in the same time as it takes to travel 60 km upstream. If the speed of the stream is 5 km/hr, find the speed of the streamer in still water.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 28

Question 28.
A steamer goes downstream and covers the distance between two ports in 5 hours while it covers the same distance upstream in 6 hours. If the speed of the stream is 1 km/h, find the speed of the streamer in still water and the distance between two ports.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 29

Question 29.
Distance between two places A and B is 350 km. Two cars start simultaneously from A and B towards each other and the distance between them after 4 hours is 62 km. If the speed of one car is 8 km/h less than the speed of other cars, find the speed of each car.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in one Variable Ex 12.2 30

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths

Understanding ICSE Mathematics Class 10 ML Aggarwal Solved Solutions 2020

Get Latest Edition of ML Aggarwal Class 10 Solutions for ICSE Maths PDF Download 2020-2021 on LearnCram.com. It provides step by step solutions for ML Aggarwal Maths for Class 10 ICSE Solutions Pdf Download. You can download the Understanding ICSE Mathematics Class 10 ML Aggarwal Solved Solutions with Free PDF download option, which contains chapter-wise solutions. APC Maths Class 10 ICSE Solutions all questions are solved and explained by expert Mathematics teachers as per ICSE board guidelines.

APC Understanding ICSE Mathematics Class 10 ML Aggarwal Solutions 2019 Edition for 2020 Examinations

ICSE Class 10 Maths Solutions ML Aggarwal Chapter 1 Value Added Tax

Understanding Mathematics Class 10 Chapter 2 Banking

ML Aggarwal Class 10 ICSE Solutions Solutions Chapter 3 Shares and Dividends

ICSE 10th Maths Solutions Chapter 4 Linear Inequations

ICSE Class 10 Maths Solution Chapter 5 Quadratic Equations in One Variable

Maths ICSE Class 10 Solutions Chapter 6 Factorization

Class 10 ML Aggarwal SolutionsChapter 7 Ratio and Proportion

Class 10 ICSE Maths Solutions Chapter 8 Matrices

ML Aggarwal Class 10 Maths Solutions Chapter 9 Arithmetic and Geometric Progressions

ML Aggarwal Class 10 Solution Chapter 10 Reflection

ICSE Solutions For Class 10 Maths Chapter 11 Section Formula

Class 10 ICSE Maths Solution Chapter 12 Equation of a Straight Line

ML Aggarwal Solutions For Class 10 Chapter 13 Similarity

ML Aggarwal Class 10 ICSE Chapter 14 Locus

ML Aggarwal Class 10 Solutions Chapter 15 Circles

ICSE Mathematics Class 10 Solutions Chapter 16 Constructions

M L Aggarwal Class 10 Solutions Chapter 17 Mensuration

Class 10 ICSE ML Aggarwal Solutions Trigonometric Identities

Maths Solutions Class 10 ICSE ML Aggarwal Chapter 19 Trigonometric Tables

ML Aggarwal Class 10 Maths Chapter 20 Heights and Distances

ML Aggarwal Class 10 Maths Chapter 21 Measures of Central Tendency

ML Aggarwal Class 10 Maths Chapter 22 Probability

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ML Aggarwal Class 9 Solutions for ICSE Maths

Understanding ICSE Mathematics Class 9 ML Aggarwal Solved Solutions

Get Latest Edition of ML Aggarwal Class 9 Solutions for ICSE Maths PDF Download 2019-2020 on LearnCram.com. It provides step by step solutions for ML Aggarwal Maths for Class 9 ICSE Solutions Pdf Download. You can download the Understanding ICSE Mathematics Class 9 ML Aggarwal Solved Solutions with Free PDF download option, which contains chapter wise solutions. APC Maths Class 9 ICSE Solutions all questions are solved and explained by expert Mathematics teachers as per ICSE board guidelines.

APC Understanding ICSE Mathematics Class 9 ML Aggarwal Solutions 2019 Edition for 2020 Examinations

Icse Mathematics Class 9 SolutionsChapter 1 Rational and Irrational Numbers

  • Chapter 1 Rational and Irrational Numbers Ex 1.1
  • Chapter 1 Rational and Irrational Numbers Ex 1.2
  • Chapter 1 Rational and Irrational Numbers Ex 1.3
  • Chapter 1 Rational and Irrational Numbers Ex 1.4
  • Chapter 1 Rational and Irrational Numbers Ex 1.5
  • Chapter 1 Rational and Irrational Numbers Multiple Choice Questions
  • Chapter 1 Rational and Irrational Numbers Chapter Test

ML Aggarwal Class 9 Maths Chapter 2 Compound Interest

  • Chapter 2 Compound Interest Ex 2.1
  • Chapter 2 Compound Interest Ex 2.2
  • Chapter 2 Compound Interest Ex 2.3
  • Chapter 2 Compound Interest Multiple Choice Questions
  • Chapter 2 Compound Interest Chapter Test

ML Aggarwal Class 9 Icse Chapter 3 Expansions

  • Chapter 3 Expansions Ex 3.1
  • Chapter 3 Expansions Ex 3.2
  • Chapter 3 Expansions Multiple Choice Questions
  • Chapter 3 Expansions Chapter Test

Icse Maths Class 9 Chapter 4 Factorisation

  • Chapter 4 Factorisation Ex 4.1
  • Chapter 4 Factorisation Ex 4.2
  • Chapter 4 Factorisation Ex 4.3
  • Chapter 4 Factorisation Ex 4.4
  • Chapter 4 Factorisation Ex 4.5
  • Chapter 4 Factorisation Multiple Choice Questions
  • Chapter 4 Factorisation Chapter Test

Class 9 Maths Icse Solutions Chapter 5 Simultaneous Linear Equations

  • Chapter 5 Simultaneous Linear Equations Ex 5.1
  • Chapter 5 Simultaneous Linear Equations Ex 5.2
  • Chapter 5 Simultaneous Linear Equations Ex 5.3
  • Chapter 5 Simultaneous Linear Equations Ex 5.4
  • Chapter 5 Simultaneous Linear Equations Multiple Choice Questions
  • Chapter 5 Simultaneous Linear Equations Chapter Test

ML Aggarwal Class 9 Icse Solutions Chapter 6 Problems on Simultaneous Linear Equations

  • Chapter 6 Problems on Simultaneous Linear Equations Ex 6
  • Chapter 6 Problems on Simultaneous Linear Equations Multiple Choice Questions
  • Chapter 6 Problems on Simultaneous Linear Equations Chapter Test

Understanding Mathematics Class 9 Chapter 7 Quadratic Equations

  • Chapter 7 Quadratic Equations Ex 7
  • Chapter 7 Quadratic Equations Multiple Choice Questions
  • Chapter 7 Quadratic Equations Chapter Test

ML Aggarwal Class 9 Indices Chapter 8

  • Chapter 8 Indices Ex 8
  • Chapter 8 Indices Multiple Choice Questions
  • Chapter 8 Indices Chapter Test

ML Aggarwal Class 9 Logarithm Chapter 9

  • Chapter 9 Logarithms Ex 9.1
  • Chapter 9 Logarithms Ex 9.2
  • Chapter 9 Logarithms Multiple Choice Questions
  • Chapter 9 Logarithms Chapter Test

Icse Mathematics Class 9 Chapter 10 Triangles

  • Chapter 10 Triangles Ex 10.1
  • Chapter 10 Triangles Ex 10.2
  • Chapter 10 Triangles Ex 10.3
  • Chapter 10 Triangles Ex 10.4
  • Chapter 10 Triangles Multiple Choice Questions
  • Chapter 10 Triangles Chapter Test

ML Aggarwal Class 9 Maths Chapter 11 Mid Point Theorem

  • Mid Point Theorem Ex 11
  • Mid Point Theorem Multiple Choice Questions
  • Mid Point Theorem Chapter Test

ML Aggarwal Class 9 Maths Chapter 12 Pythagoras Theorem

  • Chapter 12 Pythagoras Theorem Ex 12
  • Chapter 12 Pythagoras Theorem Multiple Choice Questions
  • Chapter 12 Pythagoras Theorem Chapter Test

ML Aggarwal Class 9 Rectilinear Figures Chapter 13 Rectilinear Figures

  • Chapter 13 Rectilinear Figures Ex 13.1
  • Chapter 13 Rectilinear Figures Ex 13.2
  • Chapter 13 Rectilinear Figures Multiple Choice Questions
  • Chapter 13 Rectilinear Figures Chapter Test

ML Aggarwal Class 9 Maths Chapter 14 Theorems on Area

  • Chapter 14 Theorems on Area Ex 14
  • Chapter 14 Theorems on Area Multiple Choice Questions
  • Chapter 14 Theorems on Area Chapter Test

ML Aggarwal Class 9 Maths Chapter 15 Circle

  • Chapter 15 Circle Ex 15.1
  • Chapter 15 Circle Ex 15.2
  • Chapter 15 Circle Multiple Choice Questions
  • Chapter 15 Circle Chapter Test

ML Aggarwal Class 9 Solutions Icse Chapter 16 Mensuration

  • Chapter 16 Mensuration Ex 16.1
  • Chapter 16 Mensuration Ex 16.2
  • Chapter 16 Mensuration Ex 16.3
  • Chapter 16 Mensuration Ex 16.4
  • Chapter 16 Mensuration Multiple Choice Questions
  • Chapter 16 Mensuration Chapter Test

ML Aggarwal Class 9 Maths Chapter 17 Trigonometric Ratios

  • Chapter 17 Trigonometric Ratios Ex 17
  • Chapter 17 Trigonometric Ratios Multiple Choice Questions
  • Chapter 17 Trigonometric Ratios Chapter Test

ML Aggarwal Class 9 Maths Chapter 18 Trigonometric Ratios and Standard Angles

  • Chapter 18 Trigonometric Ratios and Standard Angles Ex 18.1
  • Chapter 18 Trigonometric Ratios and Standard Angles Ex 18.2
  • Chapter 18 Trigonometric Ratios and Standard Angles Multiple Choice Questions
  • Chapter 18 Trigonometric Ratios and Standard Angles Chapter Test

ML Aggarwal Class 9 Maths Chapter 19 Coordinate Geometry

  • Chapter 19 Coordinate Geometry Ex 19.1
  • Chapter 19 Coordinate Geometry Ex 19.2
  • Chapter 19 Coordinate Geometry Ex 19.3
  • Chapter 19 Coordinate Geometry Ex 19.4
  • Chapter 19 Coordinate Geometry Multiple Choice Questions
  • Chapter 19 Coordinate Geometry Chapter Test

ML Aggarwal Class 9 Maths Chapter 20 Statistics

  • Chapter 20 Statistics Ex 20.1
  • Chapter 20 Statistics Ex 20.2
  • Chapter 20 Statistics Ex 20.3
  • Chapter 20 Statistics Multiple Choice Questions
  • Chapter 20 Statistics Chapter Test

ML Aggarwal Class 8 Solutions for ICSE Maths

Understanding ICSE Mathematics Class 8 ML Aggarwal Solved Solutions

Get Latest Edition of ML Aggarwal Class 8 Solutions for ICSE Maths PDF Download 2018-2020 on LearnCram.com. It provides step by step solutions for ML Aggarwal Maths for Class 8 ICSE Solutions Pdf Download. You can download the Understanding ICSE Mathematics Class 8 ML Aggarwal Solved Solutions with Free PDF download option, which contains chapter wise solutions. APC Maths Class 8 ICSE Solutions all questions are solved and explained by expert Mathematics teachers as per ICSE board guidelines.

APC Understanding ICSE Mathematics Class 8 ML Aggarwal Solutions 2019 Edition for 2020 Examinations

ML Aggarwal Class 8 Maths Chapter 1 Rational Numbers

ML Aggarwal Class 8 Maths Chapter 2 Exponents and Powers

ML Aggarwal Class 8 Maths Chapter 3 Squares and Square Roots

ML Aggarwal Class 8 Maths Chapter 4 Cubes and Cube Roots

ML Aggarwal Class 8 Maths Chapter 5 Playing with Numbers

ML Aggarwal Class 8 Maths Chapter 6 Operation on sets Venn Diagrams

ML Aggarwal Class 8 Maths Chapter 7 Percentage

ML Aggarwal Class 8 Maths Chapter 8 Simple and Compound Interest

ML Aggarwal Class 8 Maths Chapter 9 Direct and Inverse Variation

ML Aggarwal Class 8 Maths Chapter 10 Algebraic Expressions and Identities

ML Aggarwal Class 8 Maths Chapter 11 Factorisation

ML Aggarwal Class 8 Maths Chapter 12 Linear Equations and Inequalities in one Variable

ML Aggarwal Class 8 Maths Chapter 13 Understanding Quadrilaterals

ML Aggarwal Class 8 Maths Chapter 14 Constructions of Quadrilaterals

ML Aggarwal Class 8 Maths Chapter 15 Circle

ML Aggarwal Class 8 Maths Chapter 16 Symmetry Reflection and Rotation

ML Aggarwal Class 8 Maths Chapter 17 Visualising Solid Shapes

ML Aggarwal Class 8 Maths Chapter 18 Mensuration

ML Aggarwal Class 8 Maths Chapter 19 Data Handling

ML Aggarwal Class 8 Maths Model Question Papers

ML Aggarwal Class 7 Solutions for ICSE Maths

Understanding ICSE Mathematics Class 7 ML Aggarwal Solved Solutions

Get Latest Edition of ML Aggarwal Class 7 Solutions for ICSE Maths PDF Download 2017-2020 on LearnCram.com. It provides step by step solutions for ML Aggarwal Maths for Class 7 ICSE Solutions Pdf Download. You can download the Understanding ICSE Mathematics Class 7 ML Aggarwal Solved Solutions with Free PDF download option, which contains chapter wise solutions. APC Maths Class 7 ICSE Solutions all questions are solved and explained by expert Mathematics teachers as per ICSE board guidelines.

APC Understanding ICSE Mathematics Class 7 ML Aggarwal Solutions 2019 Edition for 2020 Examinations

ML Aggarwal Class 7 Maths Chapter 1 Integers

ML Aggarwal Class 7 Maths Chapter 2 Fractions and Decimals

ML Aggarwal Class 7 Maths Chapter 3 Rational Numbers

ML Aggarwal Class 7 Maths Chapter 4 Exponents and Powers

ML Aggarwal Class 7 Maths Chapter 5 Sets

ML Aggarwal Class 7 Maths Chapter 6 Ratio and Proportion

ML Aggarwal Class 7 Maths Chapter 7 Percentage and Its applications

ML Aggarwal Class 7 Maths Chapter 8 Algebraic Expressions

ML Aggarwal Class 7 Maths Chapter 9 Linear Equations and Inequalities

ML Aggarwal Class 7 Maths Chapter 10 Lines and Angles

ML Aggarwal Class 7 Maths Chapter 11 Triangles and its Properties

ML Aggarwal Class 7 Maths Chapter 12 Congruence of Triangles

ML Aggarwal Class 7 Maths Chapter 13 Practical Geometry

ML Aggarwal Class 7 Maths Chapter 14 Symmetry

ML Aggarwal Class 7 Maths Chapter 15 Visualising Solid Shapes

ML Aggarwal Class 7 Maths Chapter 16 Perimeter and Area

ML Aggarwal Class 7 Maths Chapter 17 Data Handling

ML Aggarwal Class 7 Maths Model Question Papers

ML Aggarwal Class 6 Solutions for ICSE Maths

Understanding ICSE Mathematics Class 6 ML Aggarwal Solved Solutions

Get Latest Edition of ML Aggarwal Class 6 Solutions for ICSE Maths PDF Download 2016-2020 on LearnCram.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 ICSE Solutions all questions are solved and explained by expert Mathematics 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

ML Aggarwal Class 6 Maths Chapter 2 Whole Numbers

ML Aggarwal Class 6 Maths Chapter 3 Integers

ML Aggarwal Class 6 Maths Chapter 4 Playing with Numbers

ML Aggarwal Class 6 Maths Chapter 5 Sets

ML Aggarwal Class 6 Maths Chapter 6 Fractions

ML Aggarwal Class 6 Maths Chapter 7 Decimals

ML Aggarwal Class 6 Maths Chapter 8 Ratio and Proportion

ML Aggarwal Class 6 Maths Chapter 9 Algebra

ML Aggarwal Class 6 Maths Chapter 10 Basic Geometrical Concept

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

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions

Mental Maths

Class 7 Maths Chapter 16 Perimeter and Area Question 1. Fill in the blanks:
(i) The perimeter of a regular polygon = ……….. × length of a side.
(ii) The unit of measurement of the area is ……….
(iii) The perimeter of a rhombus is = 4 × ………
(iv) An area of 1 km2 = ……… hectare
(v) If the perimeter of a parallelogram is 40 cm and the length of one side is 12 cm, then the length of the adjacent side is ……
(vi) To find the cost of polishing a table-top, we need to find the ………. of the table-top.
(vii) The ratio of circumference to the diameter of a circle is ………..
(viii) If the area of a triangular piece of cardboard is 90 cm2, then the length of the altitude corresponding to 20 cm long base is ………. cm.
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 1

ML Aggarwal Class 7 Solutions Chapter 16 Question 2. State whether the following statements are true (T) or false (F):
(i) A diagonal of a rectangle divides it into two right-angled triangles of equal areas.
(ii) A diagonal of a parallelogram divides it into two triangles of equal areas.
(iii) If the perimeter of two parallelograms is equal, then their areas are also equal.
(iv) All parallelogram having equal areas have the same perimeters.
(v) The area of a circle of diameter d is πd2.
(vi) Area of a parallelogram = product of lengths of its two adjacent sides.
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 2

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 14):
Question 3.
If the perimeter of a square is 24 cm, then its area is
(a) 16 cm2
(b) 24 cm2
(c) 36 cm2
(d) 36 m2
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 3

ML Aggarwal Class 7 Chapter 16 Question 4. If the area of a parallelogram is 54 cm2 and the length of one side is 7.5 cm, then the corresponding height is
(a) 7.2 cm
(b) 14.4 cm
(c) 3.6 cm
(d) 13.5 cm
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 4

Perimeter and Area Class 7 Question 5.
If the base of a triangle is doubled and its height is halved, then the area of the resulting triangle
(a) decreases
(b) increases
(c) doubles
(d) remains the same
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 5

ML Aggarwal Class 7 Question 6. If the height of a parallelogram is doubled and base tripled, then its area becomes
(a) 2 times
(b) 3 times
(c) 6 times
(d) 12 times
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 6

Perimeter and Area Class 7 Question 7. The circumference of the circle with diameter 28 cm is
(a) 44 cm
(b) 88 cm
(c) 176 cm
(d) 616 cm
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 7

ML Aggarwal Class 7 Perimeter and Area Question 8. The ratio of circumference to the area of a circle of radius r units is
(a) 2 : r
(b) r : 2
(c) 1 : r
(d) π : r
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 8

ML Aggarwal Class 9 Solutions ICSE Chapter 16 Question 9. If the area of a circle is numerically equal to its circumference, then the radius of the circle is
(a) 1 unit
(b) 2 units
(c) 3 units
(d) 4 units
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 9

Question 10.
The area of a circle of diameter d is
(a) 2πd2
(b) πd2
(c) \(\frac { \pi { d }^{ 2 } }{ 2 }\)
(d) \(\frac { \pi { d }^{ 2 } }{ 4 }\)
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 10

ML Aggarwal Maths for Class 7 Solutions Pdf Question 11. If the ratio of the radii of two circles is 2 then the ratio of their circumferences is
(a) 2 : 3
(b) 3 : 2
(c) 4 : 9
(d) 9 : 4
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 11

Question 12.
If the ratio of the radii of two circles is 3 : 5, then the ratio of their areas is
(a) 3 : 5
(b) 5 : 3
(c) 25 : 9
(d) 9 : 25
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 12

Question 13.
The perimeter of a semicircle (including its diameter) of radius 7 cm is
(a) 22 cm
(b) 29 cm
(c) 36 cm
(d) 44 cm
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 13

Question 14.
Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are 14 cm × 11 cm, then the radius of the circle is
(a) 21 cm
(b) 14 cm
(c) 10.5 cm
(d) 7 cm
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 14

Higher Order Thinking Skills (HOTS)

Question 1.
In the given figure, ABDE is a parallelogram, find the area of the trapezium ACDE.
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 15
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 16

Question 2.
In the given figure, the length of the rectangle is 28 cm. Find the area of the shaded region.
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 17
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 18
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 19

Question 3.
In the given figure, ABCD is a square of side 14 cm. A, B, C, and D are centers of circular arcs of equal radius. Find the perimeter and the area of the shaded region.
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 20
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions 21

ML Aggarwal Class 7 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

ML Aggarwal Class 10 Solutions Arithmetic and Geometric Progression Question 1. Can 0 be a term of a geometric progression?
Solution:
No, 0 is not a term of geometric progression.

ML Aggarwal Class 10 Solutions Question 2.
(i) Find the next term of the list of numbers \(\frac { 1 }{ 6 } ,\frac { 1 }{ 3 } ,\frac { 2 }{ 3 } ,… \)
(ii) Find the next term of the list of numbers \(\frac { 3 }{ 16 } ,-\frac { 3 }{ 8 } ,\frac { 3 }{ 4 } ,-\frac { 3 }{ 2 } ,…\)
(iii) Find the 15th term of the series \(\sqrt { 3 } +\frac { 1 }{ \sqrt { 3 } } +\frac { 1 }{ 3\sqrt { 3 } } +…\)
(iv) Find the nth term of the list of numbers \(\frac { 1 }{ \sqrt { 2 } } ,-2,4\sqrt { 2 } ,-16,…\)
(v) Find the 10th and nth terms of the list of numbers 5, 25, 125, …
(vi) Find the 6th and the nth terms of the list of numbers \(\frac { 3 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 3 }{ 8 } ,…\)
(vii) Find the 6th term from the end of the list of numbers 3, – 6, 12, – 24, …, 12288.
Solution:
Ap Gp ML Aggarwal Class 10 Solutions
Ap Gp ML Aggarwal
Arithmetic Progression Class 10 ICSE Solutions ML Aggarwal
ML Aggarwal Class 10 Gp Solutions

Question 3.
Which term of the G.P.
(i) 2, 2√2, 4, … is 128?
(ii) \(1,\frac { 1 }{ 3 } ,\frac { 1 }{ 9 } ,…is\quad \frac { 1 }{ 243 } ?\)
(iii) \(\frac { 1 }{ 3 } ,\frac { 1 }{ 9 } ,\frac { 1 }{ 27 } ,…is\quad \frac { 1 }{ 19683 } ? \)
Solution:
ML Aggarwal Ap Gp Solution
ML Aggarwal Class 10 Ap Gp
ML Aggarwal Ap Gp Solutions

Question 4.
Which term of the G.P. 3, -3√3, 9, -9√3, … is 729?
Solution:
Maths Gp

Question 5.
Determine the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Solution:
ML Aggarwal Class 10 Ap Gp Solutions

Question 6.
In a GP., the third term is 24 and 6th term is 192. Find the 10th term
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 7.
Find the number of terms of a G.P. whose first term is \(\\ \frac { 3 }{ 4 } \), common ratio is 2 and the last term is 384.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 8.
Find the value of x such that
(i) \(-\frac { 2 }{ 7 } ,x,-\frac { 7 }{ 2 } \) are three consecutive terms of a G.P.
(ii) x + 9, x – 6 and 4 are three consecutive terms of a G.P.
(iii) x, x + 3, x + 9 are first three terms of a G.P. Find the value of x.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 9.
If the fourth, seventh and tenth terms of a G.P. are x, y, z respectively, prove that x, y, z are in G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 10.
The 5th, 8th and 11th terms of a G.P. are p, q, and s respectively. Show that q² = ps.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 11.
If a, b, c are in G.P., then show that a², b², c² are also in G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 12.
If a, b, c are in A.P., then show that 3a, 3b, 3c are in G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 13.
If a, b, c are in A.P., then show that 10ax + 10, 10bx + 10, 10cx + 10, x ≠ 0, are in G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 14.
If a, a2+ 2 and a3 + 10 are in G.P., then find the values(s) of a.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 15.
If k, 2k + 2, 3k + 3, … are in G.P., then find the common ratio of the G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 16.
The first and the second terms of a GP. are x-4 and xm. If its 8th term is x52, then find the value of m.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 17.
Find the geometric progression whose 4th term is 54 and the 7th Term is 1458.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 18.
The fourth term of a GP. is the square of its second term and the first term is -3. Determine its seventh term.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 19.
The sum of first three terms of a G.P. is \(\\ \frac { 39 }{ 10 } \) and their product is 1. Find the common ratio and the terms.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 20.
Three numbers are in A.P. and their sum is 15. If 1, 4 and 19 are added to these numbers respectively, the resulting numbers are in G.P. Find the numbers.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 21.
Three numbers form an increasing G.P. If the middle term is doubled, then the new numbers are in A.P. Find the common ratio of the G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 22.
Three numbers whose sum is 70 are in GP. If each of the extremes is multiplied by 4 and the mean by 5, the numbers will be in A.P. Find the numbers.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 23.
There are four numbers such that the first three of them form an A.P. and the last three form a GP. The sum of the first and third number is 2 and that of the second and fourth is 26. What are these numbers?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 24.
(i) If a, b, c are in A.P. as well in G.P., prove that a = b = c.
(ii) If a, b, c are in A.P as well as in G.P., then find the value of ab-c + bc-a + ca-b
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 25.
The terms of a G.P. with first term a and common ratio r are squared. Prove that resulting numbers form a G.P. Find its first term, common ratio, and the nth term.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 26.
Show that the products of the corresponding terms of two G.P.’s a, ar, ar², …, arn-1 and A, AR, AR2, …, ARn-1 form a G.P. and find the common ratio.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 27.
(i) If a, b, c are in G.P. show that \(\frac { 1 }{ a } ,\frac { 1 }{ b } ,\frac { 1 }{ c } \) are also in G.P.
(ii) If K is any positive real number and Ka, Kb Kc is three consecutive terms of a G.P., prove that a, b, c are three consecutive terms of an A.P.
(iii) If p, q, r are in A.P., show that pth, qth and rth terms of any G.P. are themselves in GP.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 28.
If a, b, c are in GP., prove that the following are also in G.P.
(i) a3, b3, c3
(ii) a2 + b2, ab + bc, b2 + c2.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 29.
If a, b, c, d are in G.P., show that
(i) a2 + b2, b2 + c2, c2 + d2 are in G.P.
(ii) (b – c)2 + (c – a)2 + (d – b)2 = (a – d)2.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 30.
The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of the 2nd hour, 4th hour and nth hour?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 31.
The length of the sides of a triangle form a G.P. If the perimeter of the triangle is 37 cm and the shortest side is of length 9 cm, find the lengths of the other two sides.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

ML Aggarwal Class 10 Solutions for ICSE Maths