Maths Rank Scorer

By Hari Mohan Krishnatrey

This book has been written strictly according to the latest revised CBSE Syllabus for the year of 2024 and onwards for Std 10th and all type of competitive exams. This multicoloured edition will help all section of the students who are looking for better results in the cutthroat world of competition. In this age of nail biting competition, it really helps to be well equipped in subject knowledge in order to break the ice in the competition area. So, while the market is flooded with numerable repetitions ofbooks, which mars your intellectuality and competency. We have endeavoured to reach out to your wide examination needs in this edition. This book is a set of different types of tricky questions. Every question of this book has been carefully planned to make it an effective tool to arouse interest in the study and application of mathematics and to develop the art of thinking. This book has brought the new concept of time-saving quicker method in Mathemetics. This book is written keeping in mind th level of the children and it keeps the students to increase their understanding thinking and reasoning power. The style of presentation of the subject matter is so informal that the students enjoy learning. Different type of specimen examples and questions for practices are given in graded form. We are sure that this book in the present form will prove very useful to the students for whom it is written. I am confident that the book will meet the requirements and expectations of all those for whom it is meant.

• Language: English
• Publisher: Authors Click Publishing
• Release date: Apr 19, 2024
• ISBN: 9788119368075

Book preview

MATHS RANK SCORER

Krishnatrey's NUMBER SYSTEM

(The only Unique book with complete solution)

For 9th Std

––––––––

Hari Mohan Krishnatrey

(The Maths Guru)

Table of Contents

CHAPTER-ONE..................................................................................................1

CHAPTER-TWO...............................................................................................24

CHAPTER-THREE............................................................................................44

CHAPTER-FOUR..............................................................................................53

CHAPTER-FIVE................................................................................................80

CHAPTER-SIX................................................................................................108

CHAPTER-SEVEN..........................................................................................129

CHAPTER-EIGHT...........................................................................................134

CHAPTER-NINE.............................................................................................137

CHAPTER-TEN...............................................................................................145

CHAPTER-ELEVEN........................................................................................163

CHAPTER-TWELVE.......................................................................................169

CHAPTER-THIRTEEN....................................................................................174

Krishnatrey’s

CHAPTER-ONE

General introduction of Number System

LET  US  RECALL

REAL NUMBERS (R)

Rational and irrational numbers together are known as real numbers.

REAL NUMBERS (R) = Rational Numbers(Q) + Irrational Numbers(Q/)

NATURAL NUMBERS (N)

The numbers 1, 2, 3, 4, . . . are known as natural numbers

WHOLE NUMBERS (W)

The natural numbers together with O(zero) are called whole numbers.

Thus, 0, 1, 2, 3, 4, . . . are whole numbers.

INTEGERS (I OR Z)

Natural numbers, 0 and negative of natural numbers constitute the integers Thus, . . . . .  . are integers.

PRIME NUMBERS (P)

A natural numbers which is greater than 1 and divisible by 1 and by itself only, is called a prime number.

Prime numbers (P) are 2, 3, 5, 7, 11, 13, 17, . . .

Note that the smallest prime number is 2 and except 2 all other prime numbers are odd.

COMPOSITE NUMBERS

A natural number which is greater than 1 and is not prime, is called a composite number.

Composite numbers are 4, 6, 8, 9, 10, 12, . . .

Note that

(i)  the smallest even composite is 4 and the smallest odd composite is 9.

(ii) 1 has only one factor, so it is neither prime nor composite.

COPRIME NUMBERS

If two numbers do not have any factor other than 1 common then the numbers are said to be comprime.

RATIONAL NUMBERS (Q)

A number which can be expressed in the form where ‘p’ and ‘q’ are both integers and iscalled a rational number. The decimal expansion of a rational number is either

terminating or non-terminating repeating (recurring)

some examples of rational numbers are etc. 

IRRATIONAL NUMBERS (Q’)

The number which cannot be written in the form , where 'p' and ‘q’ are integers and , is called an irrational number. The decimal expansion of an irrational number is non-terminating non-recurring. Some example of rational numbers are

REAL NUMBERS

Collection of all the rational numbers and irrational numbers together, is known as Real Numbers. It is denoted by R. Thus

(i)  Every Real Number is either Rational number or irrational number.

(ii) Every Real Number in decimal form is either terminating decimal or non-terminating recurring decimal (Rationals) ornon-terminating non-repeating decimal (Irrationals). We represent this as given below.

Q1. Examine, whether the following numbers are rational or an irrational :

(i)     (ii)    (iii)

(iv)    (v)    (vi)

(vii)     (viii)    (ix)

Solution :

(i) , is a rational number

(ii) is an irrational number

(iii) is an irrational number

(iv) = 1 – 5 = -4, is a rational number.

(v)

, is an irrational number.

(vi) , is a rational number.

(vii) , is an irrational number.

(viii) is a rational number.

(ix) , is a rational number.

Q2.  Classify the following numbers as rational or irrational with