## 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

LearnCram.com also covered previous Year argumentative essay topics asked in ICSE board exams.

## 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

## 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

## 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

## 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

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 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:

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 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:

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 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:

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 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 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:

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 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:

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:

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:

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:

Higher Order Thinking Skills (HOTS)

Question 1.
In the given figure, ABDE is a parallelogram, find the area of the trapezium ACDE.

Solution:

Question 2.
In the given figure, the length of the rectangle is 28 cm. Find the area of the shaded region.

Solution:

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.

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 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:

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:

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

Question 5.
Determine the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Solution:

Question 6.
In a GP., the third term is 24 and 6th term is 192. Find the 10th term
Solution:

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:

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:

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:

Question 10.
The 5th, 8th and 11th terms of a G.P. are p, q, and s respectively. Show that q² = ps.
Solution:

Question 11.
If a, b, c are in G.P., then show that a², b², c² are also in G.P.
Solution:

Question 12.
If a, b, c are in A.P., then show that 3a, 3b, 3c are in G.P.
Solution:

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:

Question 14.
If a, a2+ 2 and a3 + 10 are in G.P., then find the values(s) of a.
Solution:

Question 15.
If k, 2k + 2, 3k + 3, … are in G.P., then find the common ratio of the G.P.
Solution:

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:

Question 17.
Find the geometric progression whose 4th term is 54 and the 7th Term is 1458.
Solution:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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

## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Take π = $$\\ \frac { 22 }{ 7 }$$, unless stated otherwise.

ML Aggarwal Class 10 Mensuration Question 1. The adjoining figure shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block.

Solution:

LearnCram.com also covered previous Year argumentative essay topics asked in ICSE board exams.

ML Aggarwal Class 9 Mensuration Solutions Question 2. The given figure shows a solid trophy made of shining glass. If one cubic centimetre of glass costs Rs 0.75, find the cost of the glass for making the trophy.

Solution:

ICSE Class 10 Maths Mensuration Solutions Question 3. From a cube of edge 14 cm, a cone of maximum size is carved out. Find the volume of the remaining material.
Solution:

Mensuration Class 10 ML Aggarwal Question 4. A cone of maximum volume is curved out of a block of wood of size 20 cm × 10 cm × 10 cm. Find the volume of the remaining wood.
Solution:

ML Aggarwal Class 9 Solutions Mensuration Question 5. 16 glass spheres each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of the water filled in the box.
Solution:

Mensuration ML Aggarwal Class 9 Question 6. A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm. Find the volume of the wood in the entire stand, correct to 2 decimal places.

Solution:

ML Aggarwal Class 9 Mensuration Solution Question 7. A cuboidal block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter that the hemisphere can have? Also find the surface area of the solid.
Solution:

ML Aggarwal Mensuration Question 8. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder (as shown in the given figure). If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article.

Solution:

ML Aggarwal Mensuration Class 10 Question 9. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. If the total height of the toy is 15.5 cm, find the total surface area of the toy.
Solution:

Class 10 ML Aggarwal Mensuration Solutions Question 10. A circus tent is in the shape of a cylinder surmounted by a cone. The diameter of the cylindrical portion is 24 m and its height is 11 m. If the vertex of the cone is 16 m above the ground, find the area of the canvas used to make the tent.
Solution:

ML Aggarwal Class 10 Solutions Mensuration Question 11. An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and the height of the cylindrical part is 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for folds and stitching. Give your answer to the nearest m².
Solution:

Mensuration ML Aggarwal Class 10 Solutions Question 12. From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out. Find the volume and the total surface of the remaining solid.
Solution:

ML Aggarwal Class 10 Mensuration Solutions Question 13. The given figure shows a wooden toy rocket which is in the shape of a circular cone mounted on a circular cylinder. The total height of the rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted green and the cylindrical portion red, find the area of the rocket painted with each of these colours. Also, find the volume of the wood in the rocket. Use π = 3.14 and give answers correct to 2 decimal places.

Solution:

Question 14.
The given figure shows a hemisphere of radius 5 cm surmounted by a right circular cone of base radius 5 cm. Find the volume of the solid if the height of the cone is 7 cm. Give your answer correct to two places of decimal.
Solution:

Question 15.
A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 metres and its volume is $$\\ \frac { 2 }{ 3 }$$ of the hemisphere. Calculate the height of the cone and the surface area of the buoy correct to 2 places of decimal
Solution:

Question 16.
A circular hall (big room) has a hemispherical roof. The greatest height is equal to the inner diameter, find the area of the floor, given that the capacity of the hall is 48510 m³.
Solution:

Question 17.
A building is in the form of a cylinder surmounted by a hemisphere valted dome and contains $$41 \frac { 19 }{ 21 }$$ m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building
Solution:

Question 18.
A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and the height of the cylinder are 6 cm and 12 cm respectively. If the slant height of the conical portion is 5 cm, find the total surface area and the volume of the rocket. (Use π = 3.14).
Solution:

Question 19.
A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. Their common diameter is 3.5 cm and the height of the cylindrical and conical portions are 10 cm and 6 cm respectively. Find the volume of the solid. (Take π = 3.14)
Solution:

Question 20.
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of the conical part is 12 cm.
Solution:

Question 21.
The given figure shows a model of a solid consisting of a cylinder surmounted by a hemisphere at one end. If the model is drawn to a scale of 1 : 200, find
(i) the total surface area of the solid in π m².
(ii) the volume of the solid in π litres.

Solution:

ML Aggarwal Class 10 Solutions for ICSE Maths

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress

ML Aggarwal Class 8 solutions chapter 18 Question 1. A square field of side 65 m and rectangular field of length 75 m have the same perimeter. Which field has a larger area and by how much?
Solution:

ML Aggarwal Class 8 solutions Question 2. The shape of a top surface of the table is a trapezium. Find the area if its parallel sides are 1.5 m and 2.5 m and the perpendicular distance between them is 0.8 m.
Solution:

Question 3.
The length and breadth of a hall of a school are 26 m and 22 m respectively. If one student requires 1.1 sq. m area, then find the maximum number of students to be seated in this hall.
Solution:

Question 4.
It costs ₹936 to fence a square field at ₹7·80 per metre. Find the cost of levelling the field at ₹2.50 per square metre.
Solution:

Mensuration Class 8 ML Aggarwal Question 5.
Find the area of the shaded portion in the following figures all measurements are given in cm.

Solution:

Question 6.
Area of a trapezium is 160 sq. cm. Lengths of parallel sides are in the ratio 1:3. If smaller of the parallel sides is 10 cm in length, then find the perpendicular distance between them.
Solution:

ML Aggarwal Class 8 solutions Mensuration Question 7.
The area of a trapezium is 729 cm2 and the distance between two parallel sides is 18 cm. If one of its parallel sides is 3 cm shorter than the other parallel side, find the lengths of its parallel sides.
Solution:

Question 8.
Find the area of the polygon given in the figure:

Solution:

ML Aggarwal Class 8 chapter 18 solutions Question 9. The diagonals of a rhombus are 16 m and 12 m, find:
(i) it’s area
(ii) length of a side
(iii) perimeter.
Solution:

ML Aggarwal Class 8 chapter 18 Question 10.
The area of a parallelogram is 98 cm2. If one altitude is half the corresponding base, determine the base and the altitude of the parallelogram.
Solution:

Mensuration Questions for Class 8 ICSE Question 11.
Preeti is painting the walls and ceiling of a hall whose dimensions are 18 m × 15 m × 5 m. From each can of paint 120 m2 of area is painted. How many cans of paint does she need to paint the hall?
Solution:

Question 12.
A rectangular paper is size 22 cm × 14 cm is rolled to form a cylinder of height 14 cm, find the volume of the cylinder. (Take π = $$\frac{22}{7}$$)
Solution:

Question 13.
A closed rectangular wooden box has inner dimensions 90 cm by 80 cm by 70 cm. Compute its capacity and the area of the tin foil needed to line its inner surface.
Solution:

Question 14.
The lateral surface area of a cuboid is 224 cm2. Its height is 7 cm and the base is a square. Find
(i) side of the square base
(ii) the volume of the cuboid.
Solution:

Question 15.
The inner dimensions of a closed wooden box are 2 m by 1.2 m by 0.75 m. The thickness of the wood is 2.5 cm. Find the cost of wood required to make the box if 1 m3 of wood costs ₹5400.
Solution:

Question 16.
A car has a petrol tank 40 cm long, 28 cm wide and 25 cm deep. If the ful consumption of the car averages 13.5 km per litre, how far can the car travel with a full tank of petrol?
Solution:

Question 17.
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area it will cover in 5 revolutions?
Solution:

Question 18.
The capacity of an open cylindrical tank is 2079 m3 and the diameter of its base is 21m. Find the cost of plastering its inner surface at ₹40 per square metre.
Solution:

Question 19.
A solid right circular cylinder of height 1.21 m and diameter 28 cm is melted and recast into 7 equal solid cubes. Find the edge of each cube.
Solution:

Question 20.
(i) How many cubic metres of soil must be dug out to make a well 20 m deep and 2 m in diameter?
(ii) If the inner curved surface of the well in part (i) above is to be plastered at the rate of ₹50 per m2, find the cost of plastering.
Solution:

## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 1.
Using the given information, find the value of x in each of the following figures :

Solution:

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Question 2.
If O is the centre of the circle, find the value of x in each of the following figures (using the given information):

Solution:

ML Aggarwal Class 10 Circles Solutions Question 3.
(a) In the figure (i) given below, AD || BC. If ∠ACB = 35°. Find the measurement of ∠DBC.
(b) In the figure (ii) given below, it is given that O is the centre of the circle and ∠AOC = 130°. Find∠ABC

Solution:

Circles Class 10 ICSE ML Aggarwal Solutions Question 4.
(a) In the figure (i) given below, calculate the values of x and y.
(b) In the figure (ii) given below, O is the centre of the circle. Calculate the values of x and y.

Solution:

Circles ML Aggarwal Class 10 Solutions Question 5.
(a) In the figure (i) given below, M, A, B, N are points on a circle having centre O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, find ∠MAN and the reflex angle MON.
(b) In the figure (ii) given below, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°, find
(i) ∠ACB
(ii) ∠OBC
(iii) ∠OAB
(iv) ∠CBA

Solution:

ML Aggarwal Class 10 Circle Question 6.
(a) In the figure (i) given below, O is the centre of the circle and ∠PBA = 42°. Calculate the value of ∠PQB
(b) In the figure (ii) given below, AB is a diameter of the circle whose centre is O. Given that ∠ECD = ∠EDC = 32°, calculate
(i) ∠CEF
(ii) ∠COF.

Solution:

Question 7.
(a) In the figure (i) given below, AB is a diameter of the circle APBR. APQ and RBQ are straight lines, ∠A = 35°, ∠Q = 25°. Find (i) ∠PRB (ii) ∠PBR (iii) ∠BPR.
(b) In the figure (ii) given below, it is given that ∠ABC = 40° and AD is a diameter of the circle. Calculate ∠DAC.

Solution:

ML Aggarwal Class 10 Circles Question 8.
(a) In the figure given below, P and Q are centres of two circles intersecting at B and C. ACD is an st. line. Calculate the numerical value of x.

(b) In the figure given below, O is the circumcentre of triangle ABC in which AC = BC. Given that ∠ACB = 56°, calculate
(i)∠CAB
(ii)∠OAC

Solution:

Circle ML Aggarwal Question 9.
(a) In the figure (i) given below, chord ED is parallel to the diameter AC of the circle. Given ∠CBE = 65°, calculate ∠DEC.
(b) In the figure (ii) given below, C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = p°, ∠AOB = q°, express q in terms of p. Calculate p if OACB is a parallelogram.

Solution:

ICSE Class 10 Maths Circles Solutions Question 10.
(a) In the figure (i) given below, straight lines AB and CD pass through the centre O of a circle. If ∠OCE = 40° and ∠AOD = 75°, find the number of degrees in :
(i) ∠CDE
(ii) ∠OBE.
(b) In the figure (ii) given below, I is the incentre of ∆ABC. AI produced meets the circumcircle of ∆ABC at D. Given that ∠ABC = 55° and ∠ACB = 65°, calculate
(i) ∠BCD
(ii) ∠CBD
(iii) ∠DCI
(iv) ∠BIC.

Solution:

Question 11.
O is the circumcentre of the triangle ABC and D is mid-point of the base BC. Prove that ∠BOD = ∠A.
Solution:

Question 12.
In the given figure, AB and CD are equal chords. AD and BC intersect at E. Prove that AE = CE and BE = DE.

Solution:

Question 13.
(a) In the figure (i) given below, AB is a diameter of a circle with centre O. AC and BD are perpendiculars on a line PQ. BD meets the circle at E. Prove that AC = ED.
(b) In the figure (ii) given below, O is the centre of a circle. Chord CD is parallel to the diameter AB. If ∠ABC = 25°, calculate ∠CED.

Solution:

Question 14.
In the adjoining figure, O is the centre of the given circle and OABC is a parallelogram. BC is produced to meet the circle at D.
Prove that ∠ABC = 2 ∠OAD.

Solution:

Question 15.
(a) In the figure (i) given below, P is the point of intersection of the chords BC and AQ such that AB = AP. Prove that CP = CQ

(b) In the figure (i) given below, AB = AC = CD, ∠ADC = 38°. Calculate :
(i) ∠ABC (ii) ∠BEC.

Solution:

Question 16.
(a) In the figure (i) given below, CP bisects ∠ACB. Prove that DP bisects ∠ADB.
(b) In the figure (ii) given below, BDbisects ∠ABC. Prove that $$\frac { AB }{ BD } =\frac { BE }{ BC }$$

Solution:

Question 17.
(a) In the figure (i) given below, chords AB and CD of a circle intersect at E.
(i) Prove that triangles ADE and CBE are similar.
(ii) Given DC =12 cm, DE = 4 cm and AE = 16 cm, calculate the length of BE.

(b) In the figure (ii) given below, AB and CD are two intersecting chords of a circle. Name two triangles which are similar. Hence, calculate CP given that AP = 6 cm, PB = 4 cm, and CD = 14 cm (PC > PD).

Solution:

Question 18.
In the adjoining figure, AE and BC intersect each other at point D. If ∠CDE = 90°, AB = 5 cm, BD = 4 cm and CD = 9 cm, find DE. (2008)

Solution:

Question 19.
(a) In the figure (i) given below, PR is a diameter of the circle, PQ = 7 cm, QR = 6 cm and RS = 2 cm. Calculate the perimeter of the cyclic quadrilateral PQRS.
(b) In the figure (ii) given below, the diagonals of a cyclic quadrilateral ABCD intersect in P and the area of the triangle APB is 24 cm². If AB = 8 cm and CD = 5 cm, calculate the area of ∆DPC.

Solution:

Question 20.
(a) In the figure (i) given below, QPX is the bisector of ∠YXZ of the triangle XYZ. Prove that XY : XQ = XP : XZ,
(b) In the figure (ii) given below, chords BA and DC of a circle meet at P. Prove that: