NCERT Solutions Class 7 Mathematics Chapter 1

NCERT Solutions for Class 7 Mathematics Chapter 1 Integers

The two important aspects of improving Mathematics are  understanding concepts and practising problems on a daily basis. To make room in a highly competitive environment, students must lay a strong foundation of the subject in their early years.

NCERT Class 7 Mathematics Chapter 1 deals with integers. We learned about whole digits and integers in previous classes. We'll now move further into integers, their properties, and operations. Similarly, we will also learn about integer addition and subtraction, integer addition and subtraction properties, integer multiplication and division, and integer multiplication and division properties.

NCERT Solutions for Class 7 Mathematics Chapter 1 

Access NCERT Solutions for Mathematics Chapter 1 – Integers

Chapter 1 encourages students in gaining a better understanding of the number system and solving complex problems  with ease in subsequent classes. As a result, students should be familiar with every topic and practise in-text and end-text questions to erase ‘maths phobia’  and develop interest in Mathematics. Meanwhile, let’s review the key topics covered in Class 7 Mathematics Chapter 1:

Section Number Section Title
1 Introduction to Integers
2 Properties of Addition and Subtraction of Integers
3 Multiplication of Integers
4 Multiplication of a Positive and Negative Integer
5 Multiplication of two negative integers
6 Properties of Multiplication of Integers
7 Division of Integers
8 Properties of Division of Integers

1.1 Introduction of Integers

Integers are part of a larger collection of numbers that includes both whole and negative numbers. The student will learn more about integers, their properties, and operations in this chapter. They will also learn about number concepts similar to those covered in the previous class, such as the number line, in this section.

1.2 Properties of Addition and Subtraction of Integers

Children will learn the addition and subtraction of integers, which will make it easier for them to perform simple calculations in day-to-day life. 

1.3 Multiplication of Integers

Multiplying numbers may be a simple concept. It is important to remember the positive or negative  number sign while multiplying the integers. This is most useful when simplifying an equation. 

1.4 Multiplication of a Positive and Negative Integer

This topic demonstrates with examples how we always get a negative integer by multiplying a positive integer and a negative integer. 

1.5 Multiplication of two negative integers

This topic explains how we always get a positive integer by multiplying a negative integer and a negative integer. 

1.6 Properties of Multiplication of Integers

  • By multiplying two positive integers and two negative integers, we get a positive integer.
  • We get a negative integer by multiplying a positive integer with a negative integer
  • We get  zero by multiplying any integer with zero

1.7 Division of Integers

It means division in which the fractional part(remainder) is discarded is called integer division.

1.8 Properties of Division of Integers

  • We get a positive integer by dividing two positive integers and two negative integers.
  • We get a negative integer by dividing a positive integer with a negative integer.
  •  Zero divided  by any number is zero.
  •  Any number divided by zero is infinite.

NCERT Solutions for Class 7 Chapter 1 Mathematics Integers –

Integers are numbers that are not fractions and can be positive, negative, or zero. These numbers can be used for addition, subtraction, multiplication, and division. Integers help evaluate efficiency in both positive and negative numbers in every field. For example   temperature, sea level, and other real-life integers. 

Exercise 1.1 will refresh your memory on the number line, how to present integers on the number line, how to arrange integers in ascending and descending order, what is a positive and negative integer, how to add and subtract positive and negative integers, and how to represent them on the number line. 

The properties  of Addition and Subtraction of Integers is covered in Exercise 1.2. You'll see how integer addition is commutative for integers but not for integer subtraction. 

In Exercise 1.3, you will learn about the properties of  multiplication of integers. 

Topics related to the division of integers are covered in Exercise 1.4. Multiplication is the inverse operation of division and its properties 

Students will explore the negative set of whole number values, as well as how they are represented on a number line. By understanding the number system, students can easily be acquainted with newly introduced number terminology in higher classes, such as rational numbers, irrational numbers, and so on. Keeping this in mind, Extramarks has designed NCERT Solutions Class 7 Mathematics Chapter 1 in such a way that students can quickly revise these basic Mathematical concepts before moving on to the next academic year.  

Properties of Integers

Numbers for addition and multiplication through patterns are  a part of the properties of integers. They also take into account the whole numbers. Integers involve expression of communicative and associative properties in a general form.

Facts:

  • Natural numbers are the counting numbers such as 1, 2, 3, 4, 5, and so on, whereas whole numbers are the set of natural numbers plus zero, such as 0, 1, 2, 3, 4, 5, and so on.
  • On a number line, negative integers are represented by points to the left of zero, and positive integers are represented by points to the right of zero.
  • For negative integers to the left of zero and positive integers to the right of zero, the integer 0 serves as an additive identity.
  • 0 is neither a positive nor a negative integer.
  • The numerical value of an integer, regardless of its sign, is its absolute value. | a | denotes the absolute value of an integer a.

Number Line

Natural numbers, negative and positive numbers, and whole numbers are all represented on a number line. To determine numerical operations, the identities are marked at equal intervals on a line. Number lines are significant because they represent numbers that we use every day.

How to Draw a Number Line: 

  1. Draw  a straight line of any length.
  2. To divide the drawn line into the required number, mark points at fixed distances on it.
  3. Any of the points marked on the line in step 2 should be marked as 0. 
  4. Starting at 0, write the positive numbers + 1, + 2, + 3, and so on on the right-hand side of the line. Similarly, starting at 0, mark the negative integers -1, -2, -3, and so on on the left side.
  5. The numbers continue to infinity on both sides of the drawn line, as indicated by the arrowheads on both sides of the drawn line. 

NCERT Solutions for Class 7 Mathematics

In CBSE Class 7, integers, algebraic expressions, fractions, and decimals are all part of the solved exercises. As a result, learning this challenging subject and clarifying their doubts  will aid students in their preparation for  higher classes as well. Extramarks offers CBSE Class 7 Mathematics study materials that will help students achieve higher marks in the exam. Sample papers, past years’ question papers, and NCERT Solutions are all part of our study materials.  Students must practice and revise NCERT solutions to build a strong foundation.

You can use our NCERT textbook solutions to bridge the knowledge gap and stay motivated.  Extramarks subject matter experts have created study materials for CBSE Class 7 Mathematics. They are available  on Extramarks official website. 

Chapter 1 - Integers

Chapter 2 - Fractions and Decimals

Chapter 3 - Data Handling

Chapter 4 - Simple Equations

Chapter 5 - Lines and Angles

Chapter 6 - The Triangle and Its Properties

Chapter 7 - Congruence of Triangles

Chapter 8 - Comparing Quantities

Chapter 9 - Rational Numbers

Chapter 10 - Practical Geometry

Chapter 11 - Perimeter and Area

Chapter 12 - Algebraic Expressions

Chapter 13 - Exponents and Powers

Chapter 14 - Symmetry

Chapter 15 - Visualising Solid Shapes

NCERT Solutions for Class 7

In CBSE Class 7, learning the fundamentals is crucial  because the fundamentals learned now will come handy later. Students require solid training and study materials that will assist them in achieving high exam scores and simplifying all of their concepts. Extramarks provides CBSE Class 7 study materials to help students prepare for their exams. 

Our CBSE Class 7 study materials are created by experienced faculty . We have textbook solutions, especially NCERT Solutions Class 7, which have simplified solutions to the textbook questions for each chapter.Our textbook solutions also assist students in completing home assignments and  mastering all concepts. 

Extramarks offers study materials that are updated regularly to reflect the most recent CBSE Syllabus. The systemic and well-laid-out balanced study plan boosts their performance naturally and effortlessly.

Q.1

Following number line shows the temperature in degreecelsius (°C) at different places on a particular day(a) Observe this number line and write thetemperature of the places marked on it.(b) What is the temperature difference between thehottest and the coldest places among the above?(c) What is the temperature difference between Lahulspitiand Srinagar?(d) Can we say temperature of Srinagar and Shimla takentogether is less than the temperature at Shimla?Is it also less than the temperature at Srinagar?

Ans.

(a)By observing the number line, the temprature of the places marked are as follows: Lahulspiti:8°C Srinagar:2°C Shimla: 5°C Ooty: 14°C Banglore: 22°C (b)The hottest place is Banglore with temprature 22°C and coldest place is Lahulspitiwith temprature 8°C. So,the temperature difference between the hottest and the coldest places is =22°C( 8°C ) =22°C+8°C = 30°C (c)The temperature difference between Lahulspiti and Srinagar =2°C( 8°C ) =2°C+8°C = 6°C (d)The temprature of Srinagar and Shimla are 2°C and 5°C. So, together their temprature would be 2°C+5°C=3°C, which is less than temprature of Shimla Thus, temprature of Srinagar and Shimla taken together is less than the temprature at Shimla. But, it is not less than temprature at Srinagar. 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Q.2

In a quiz, positive marks are given for correct answersand negative marks are given for in correct answers.If Jacks scores in five successive rounds were25,5,10,15 and 10,what was his total at the end?

Ans.

Jack’s scores in five successive rounds were 25,5,10, 15 and and 10. His total at the end would be =25+( 5 )+( 10 )+15+10 =5015 = 35 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGkbGaaeyyaiaabogacaqGRbGaae4j aiaabohacaqGGaGaae4CaiaabogacaqGVbGaaeOCaiaabwgacaqGZb GaaeiiaiaabMgacaqGUbGaaeiiaiaabAgacaqGPbGaaeODaiaabwga caqGGaGaae4CaiaabwhacaqGJbGaae4yaiaabwgacaqGZbGaae4Cai aabMgacaqG2bGaaeyzaiaabccacaqGYbGaae4BaiaabwhacaqGUbGa aeizaiaabohacaqGGaGaae4DaiaabwgacaqGYbGaaeyzaiaabccaca qGYaGaaeynaiaabYcacqGHsislcaaI1aGaaiilaiabgkHiTiaaigda caaIWaGaaiilaaqaaiaabgdacaqG1aGaaeiiaiaabggacaqGUbGaae izaiaabccacaqGHbGaaeOBaiaabsgacaqGGaGaaeymaiaabcdacaqG UaaabaGaaeisaiaabMgacaqGZbGaaeiiaiaabshacaqGVbGaaeiDai aabggacaqGSbGaaeiiaiaabggacaqG0bGaaeiiaiaabshacaqGObGa aeyzaiaabccacaqGLbGaaeOBaiaabsgacaqGGaGaae4Daiaab+gaca qG1bGaaeiBaiaabsgacaqGGaGaaeOyaiaabwgaaeaacaqG9aGaaeOm aiaabwdacaqGRaWaaeWaaeaacqGHsislcaaI1aaacaGLOaGaayzkaa Gaey4kaSYaaeWaaeaacqGHsislcaaIXaGaaGimaaGaayjkaiaawMca aiabgUcaRiaaigdacaaI1aGaey4kaSIaaGymaiaaicdaaeaacqGH9a qpcaaI1aGaaGimaiabgkHiTiaaigdacaaI1aaabaGaeyypa0ZaauIh aeaacaaIZaGaaGynaaaaaaaa@A7AB@

Q.3

At Srinagar temperature was-5°C on Monday and thenit dropped by2°C on Tuesday. What was the temperatureof Srinagar on Tuesday? On Wednesday, it rose by 4°C.What was the temperature on this day?

Ans.

Temprature on Monday= 5°CSince, temperature dropped by 2°C on Tuesday.So, the temperature of Srinagar on Tuesday was=5°C2°C= 7°COn Wednesday, temperature rose by 4°C,so temperature ofSrinagar on Wednesday was=7°C+4°C=3°CThus, Temperature on Tuesday and Wednesday was7°Cand3°C respectively.

Q.4

A plane is flying at the height of 5000 m above the sealevel. At a particular point, it is exactly above a submarinefloating 1200 m below the sea level. What is the verticaldistance between them?

Ans.

Height of the plane = 5000 m Depth of the submarine = 1200 m So, the distance between plane and submarine =5000 m ( 1200m ) =5000 m+1200 m = 6200 m Thus, the vertical distance between them is 6200 m. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGibGaaeyzaiaabMgacaqGNbGaaeiA aiaabshacaqGGaGaae4BaiaabAgacaqGGaGaaeiDaiaabIgacaqGLb GaaeiiaiaabchacaqGSbGaaeyyaiaab6gacaqGLbGaaeiiaiaab2da caqGGaGaaeynaiaabcdacaqGWaGaaeimaiaabccacaqGTbaabaGaae iraiaabwgacaqGWbGaaeiDaiaabIgacaqGGaGaae4BaiaabAgacaqG GaGaaeiDaiaabIgacaqGLbGaaeiiaiaabohacaqG1bGaaeOyaiaab2 gacaqGHbGaaeOCaiaabMgacaqGUbGaaeyzaiaabccacqGH9aqpcaqG GaGaeyOeI0IaaGymaiaaikdacaaIWaGaaGimaiaabccacaqGTbaaba Gaae4uaiaab+gacaqGSaGaaeiiaiaabshacaqGObGaaeyzaiaabcca caqGKbGaaeyAaiaabohacaqG0bGaaeyyaiaab6gacaqGJbGaaeyzai aabccacaqGIbGaaeyzaiaabshacaqG3bGaaeyzaiaabwgacaqGUbGa aeiiaiaabchacaqGSbGaaeyyaiaab6gacaqGLbGaaeiiaiaabggaca qGUbGaaeizaiaabccacaqGZbGaaeyDaiaabkgacaqGTbGaaeyyaiaa bkhacaqGPbGaaeOBaiaabwgaaeaacaqG9aGaaeynaiaabcdacaqGWa GaaeimaiaabccacaqGTbGaaeiiaiabgkHiTiaabccadaqadaqaaiab gkHiTiaaigdacaaIYaGaaGimaiaaicdacaaMe8UaaeyBaaGaayjkai aawMcaaaqaaiabg2da9iaaiwdacaaIWaGaaGimaiaaicdacaqGGaGa aeyBaiaabUcacaqGXaGaaeOmaiaabcdacaqGWaGaaeiiaiaab2gaae aacaqG9aWaauIhaeaacaqG2aGaaeOmaiaabcdacaqGWaGaaeiiaiaa b2gaaaaabaGaaeivaiaabIgacaqG1bGaae4CaiaabYcacaqGGaGaae iDaiaabIgacaqGLbGaaeiiaiaabAhacaqGLbGaaeOCaiaabshacaqG PbGaae4yaiaabggacaqGSbGaaeiiaiaabsgacaqGPbGaae4Caiaabs hacaqGHbGaaeOBaiaabogacaqGLbGaaeiiaiaabkgacaqGLbGaaeiD aiaabEhacaqGLbGaaeyzaiaab6gacaqGGaGaaeiDaiaabIgacaqGLb GaaeyBaiaabccacaqGPbGaae4CaiaabccacaqG2aGaaeOmaiaabcda caqGWaGaaeiiaiaab2gacaqGUaaaaaa@E107@

Q.5

Mohan deposits Rs 2,000 in his bank account andwithdraws Rs 1,642 from it, the next day. If withdrawalof amount from the account is represented by a negativeinteger, then how will you represent the amount deposited?Find the balance in Mohan’s account after the withdraw.

Ans.

Since, withdrawal of amount from the account is represented by a negative integer, so we take amount deposited as a positive integer Amount deposited = Rs 2000 Amount withdrawn =Rs 1642 Balance left in Mohan’s account = Rs 2000Rs 1642 = Rs 358 Thus, the balance in Mohan’s account after withdrawal is Rs 358. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGtbGaaeyAaiaab6gacaqGJbGaaeyz aiaabYcacaqGGaGaae4DaiaabMgacaqG0bGaaeiAaiaabsgacaqGYb GaaeyyaiaabEhacaqGHbGaaeiBaiaabccacaqGVbGaaeOzaiaabcca caqGHbGaaeyBaiaab+gacaqG1bGaaeOBaiaabshacaqGGaGaaeOzai aabkhacaqGVbGaaeyBaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGa aeyyaiaabogacaqGJbGaae4BaiaabwhacaqGUbGaaeiDaiaabccaca qGPbGaae4CaiaabccacaqGYbGaaeyzaiaabchacaqGYbGaaeyzaiaa bohacaqGLbGaaeOBaiaabshacaqGLbGaaeizaaqaaiaabkgacaqG5b GaaeiiaiaabggacaqGGaGaaeOBaiaabwgacaqGNbGaaeyyaiaabsha caqGPbGaaeODaiaabwgacaqGGaGaaeyAaiaab6gacaqG0bGaaeyzai aabEgacaqGLbGaaeOCaiaabYcacaqGGaGaae4Caiaab+gacaqGGaGa ae4DaiaabwgacaqGGaGaaeiDaiaabggacaqGRbGaaeyzaiaabccaca qGHbGaaeyBaiaab+gacaqG1bGaaeOBaiaabshacaqGGaGaaeizaiaa bwgacaqGWbGaae4BaiaabohacaqGPbGaaeiDaiaabwgacaqGKbGaae iiaiaabggacaqGZbGaaeiiaiaabggacaqGGaGaaeiCaiaab+gacaqG ZbGaaeyAaiaabshacaqGPbGaaeODaiaabwgaaeaacaqGPbGaaeOBai aabshacaqGLbGaae4zaiaabwgacaqGYbaabaGaaeyqaiaab2gacaqG VbGaaeyDaiaab6gacaqG0bGaaeiiaiaabsgacaqGLbGaaeiCaiaab+ gacaqGZbGaaeyAaiaabshacaqGLbGaaeizaiaabccacaqG9aGaaeii aiaabkfacaqGZbGaaeiiaiaabkdacaqGWaGaaeimaiaabcdaaeaaca qGbbGaaeyBaiaab+gacaqG1bGaaeOBaiaabshacaqGGaGaae4Daiaa bMgacaqG0bGaaeiAaiaabsgacaqGYbGaaeyyaiaabEhacaqGUbGaae iiaiabg2da9iabgkHiTiaabkfacaqGZbGaaeiiaiaabgdacaqG2aGa aeinaiaabkdaaeaacaqGcbGaaeyyaiaabYgacaqGHbGaaeOBaiaabo gacaqGLbGaaeiiaiaabYgacaqGLbGaaeOzaiaabshacaqGGaGaaeyA aiaab6gacaqGGaGaaeytaiaab+gacaqGObGaaeyyaiaab6gacaqGNa Gaae4CaiaabccacaqGHbGaae4yaiaabogacaqGVbGaaeyDaiaab6ga caqG0baabaGaaeypaiaabccacaqGsbGaae4CaiaabccacaqGYaGaae imaiaabcdacaqGWaGaeyOeI0IaaeOuaiaabohacaqGGaGaaeymaiaa bAdacaqG0aGaaeOmaaqaaiaab2dadaqjEaqaaiaabkfacaqGZbGaae iiaiaabodacaqG1aGaaeioaaaaaeaacaqGubGaaeiAaiaabwhacaqG ZbGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeOyaiaabg gacaqGSbGaaeyyaiaab6gacaqGJbGaaeyzaiaabccacaqGPbGaaeOB aiaabccacaqGnbGaae4BaiaabIgacaqGHbGaaeOBaiaabEcacaqGZb GaaeiiaiaabggacaqGJbGaae4yaiaab+gacaqG1bGaaeOBaiaabsha caqGGaGaaeyyaiaabAgacaqG0bGaaeyzaiaabkhacaqGGaGaae4Dai aabMgacaqG0bGaaeiAaiaabsgacaqGYbGaaeyyaiaabEhacaqGHbGa aeiBaaqaaiaabMgacaqGZbGaaeiiaiaabkfacaqGZbGaaeiiaiaabo dacaqG1aGaaeioaiaab6caaaaa@4035@

Q.6

Rita goes 20 km towards east from a point A to the point B.From B, she moves 30 km towards west along the same road.If the distance towards east is represented by a positiveinteger then, how will you represent the distance travelledtowards west? By which integer will you represent her finalposition from A?

Ans.

Here, the distance towards east is represented by a positive integer and the distance travelled towards west will be represented by a negative integer. So, distance travelled in east direction = 20 km distance travelled in west direction =30 km Distance travelled from A = 20 km+ ( 30 km ) =10km Thus, Rita’s distance travelled from point A will be represented by a negative integer( 10km ). Rita is in west direction. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGibGaaeyzaiaabkhacaqGLbGaaeil aiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeizaiaabMgacaqGZb GaaeiDaiaabggacaqGUbGaae4yaiaabwgacaqGGaGaaeiDaiaab+ga caqG3bGaaeyyaiaabkhacaqGKbGaae4CaiaabccacaqGLbGaaeyyai aabohacaqG0bGaaeiiaiaabMgacaqGZbGaaeiiaiaabkhacaqGLbGa aeiCaiaabkhacaqGLbGaae4CaiaabwgacaqGUbGaaeiDaiaabwgaca qGKbGaaeiiaiaabkgacaqG5bGaaeiiaiaabggacaqGGaGaaeiCaiaa b+gacaqGZbGaaeyAaiaabshacaqGPbGaaeODaiaabwgaaeaacaqGPb GaaeOBaiaabshacaqGLbGaae4zaiaabwgacaqGYbGaaeiiaiaabgga caqGUbGaaeizaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeizai aabMgacaqGZbGaaeiDaiaabggacaqGUbGaae4yaiaabwgacaqGGaGa aeiDaiaabkhacaqGHbGaaeODaiaabwgacaqGSbGaaeiBaiaabwgaca qGKbGaaeiiaiaabshacaqGVbGaae4DaiaabggacaqGYbGaaeizaiaa bohacaqGGaGaae4DaiaabwgacaqGZbGaaeiDaiaabccacaqG3bGaae yAaiaabYgacaqGSbGaaeiiaiaabkgacaqGLbaabaGaaeOCaiaabwga caqGWbGaaeOCaiaabwgacaqGZbGaaeyzaiaab6gacaqG0bGaaeyzai aabsgacaqGGaGaaeOyaiaabMhacaqGGaGaaeyyaiaabccacaqGUbGa aeyzaiaabEgacaqGHbGaaeiDaiaabMgacaqG2bGaaeyzaiaabccaca qGPbGaaeOBaiaabshacaqGLbGaae4zaiaabwgacaqGYbGaaeOlaaqa aiaabofacaqGVbGaaeilaiaabccacaqGKbGaaeyAaiaabohacaqG0b Gaaeyyaiaab6gacaqGJbGaaeyzaiaabccacaqG0bGaaeOCaiaabgga caqG2bGaaeyzaiaabYgacaqGSbGaaeyzaiaabsgacaqGGaGaaeyAai aab6gacaqGGaGaaeyzaiaabggacaqGZbGaaeiDaiaabccacaqGKbGa aeyAaiaabkhacaqGLbGaae4yaiaabshacaqGPbGaae4Baiaab6gaca qGGaGaaeypaiaabccacaqGYaGaaeimaiaabccacaqGRbGaaeyBaaqa aiaabsgacaqGPbGaae4CaiaabshacaqGHbGaaeOBaiaabogacaqGLb GaaeiiaiaabshacaqGYbGaaeyyaiaabAhacaqGLbGaaeiBaiaabYga caqGLbGaaeizaiaabccacaqGPbGaaeOBaiaabccacaqG3bGaaeyzai aabohacaqG0bGaaeiiaiaabsgacaqGPbGaaeOCaiaabwgacaqGJbGa aeiDaiaabMgacaqGVbGaaeOBaiaabccacaqG9aGaeyOeI0Iaae4mai aabcdacaqGGaGaae4Aaiaab2gaaeaacaqGebGaaeyAaiaabohacaqG 0bGaaeyyaiaab6gacaqGJbGaaeyzaiaabccacaqG0bGaaeOCaiaabg gacaqG2bGaaeyzaiaabYgacaqGSbGaaeyzaiaabsgacaqGGaGaaeOz aiaabkhacaqGVbGaaeyBaiaabccacaqGbbGaaeiiaiaab2dacaqGGa GaaeOmaiaabcdacaqGGaGaae4Aaiaab2gacaqGRaGaaeiiamaabmaa baGaeyOeI0IaaG4maiaaicdacaqGGaGaae4Aaiaab2gaaiaawIcaca GLPaaaaeaacqGH9aqpcqGHsislcaaIXaGaaGimaiaaysW7caqGRbGa aeyBaaqaaiaabsfacaqGObGaaeyDaiaabohacaqGSaGaaeiiaiaabk facaqGPbGaaeiDaiaabggacaqGNaGaae4CaiaabccacaqGKbGaaeyA aiaabohacaqG0bGaaeyyaiaab6gacaqGJbGaaeyzaiaabccacaqG0b GaaeOCaiaabggacaqG2bGaaeyzaiaabYgacaqGSbGaaeyzaiaabsga caqGGaGaaeOzaiaabkhacaqGVbGaaeyBaiaabccacaqGWbGaae4Bai aabMgacaqGUbGaaeiDaiaabccacaqGbbGaaeiiaiaaygW7caqG3bGa aeyAaiaabYgacaqGSbGaaeiiaiaabkgacaqGLbGaaeiiaiaabkhaca qGLbGaaeiCaiaabkhacaqGLbGaae4CaiaabwgacaqGUbGaaeiDaiaa bwgacaqGKbaabaGaaeOyaiaabMhacaqGGaGaaeyyaiaabccacaqGUb GaaeyzaiaabEgacaqGHbGaaeiDaiaabMgacaqG2bGaaeyzaiaabcca caqGPbGaaeOBaiaabshacaqGLbGaae4zaiaabwgacaqGYbWaaeWaae aacqGHsislcaaIXaGaaGimaiaaysW7caqGRbGaaeyBaaGaayjkaiaa wMcaaiaab6caaeaacaqGsbGaaeyAaiaabshacaqGHbGaaeiiaiaabM gacaqGZbGaaeiiaiaabMgacaqGUbGaaeiiaiaabEhacaqGLbGaae4C aiaabshacaqGGaGaaeizaiaabMgacaqGYbGaaeyzaiaabogacaqG0b GaaeyAaiaab+gacaqGUbGaaeOlaaaaaa@A6C5@

Q.7

In a magic square each row, column and diagonal have thesame sum. Check which of the following is a magic square.

Ans.

In a magic square, each row, column and diagonal have the same sum. So, in square (i), every row and column sum up to 0. However sum of one of its diagonal is not zero. 42=60 So, (i) is not a magic square. Similarly, in square (ii) every row, column and diagonal sum up to 9. Thus, (ii) is a magic square. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGjbGaaeOBaiaabccacaqGHbGaaeii aiaab2gacaqGHbGaae4zaiaabMgacaqGJbGaaeiiaiaabohacaqGXb GaaeyDaiaabggacaqGYbGaaeyzaiaabYcacaqGGaGaaeyzaiaabgga caqGJbGaaeiAaiaabccacaqGYbGaae4BaiaabEhacaqGSaGaaeiiai aabogacaqGVbGaaeiBaiaabwhacaqGTbGaaeOBaiaabccacaqGHbGa aeOBaiaabsgacaqGGaGaaeizaiaabMgacaqGHbGaae4zaiaab+gaca qGUbGaaeyyaiaabYgacaqGGaGaaeiAaiaabggacaqG2bGaaeyzaaqa aiaabshacaqGObGaaeyzaiaabccacaqGZbGaaeyyaiaab2gacaqGLb GaaeiiaiaabohacaqG1bGaaeyBaiaab6caaeaacaqGtbGaae4Baiaa bYcacaqGGaGaaeyAaiaab6gacaqGGaGaae4CaiaabghacaqG1bGaae yyaiaabkhacaqGLbGaaeiiaiaabIcacaqGPbGaaeykaiaabYcacaqG GaGaaeyzaiaabAhacaqGLbGaaeOCaiaabMhacaqGGaGaaeOCaiaab+ gacaqG3bGaaeiiaiaabggacaqGUbGaaeizaiaabccacaqGJbGaae4B aiaabYgacaqG1bGaaeyBaiaab6gacaqGGaGaae4CaiaabwhacaqGTb GaaeiiaiaabwhacaqGWbGaaeiiaiaabshacaqGVbGaaeiiaiaabcda caqGUaaabaGaaeisaiaab+gacaqG3bGaaeyzaiaabAhacaqGLbGaae OCaiaabccacaqGZbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqG GaGaae4Baiaab6gacaqGLbGaaeiiaiaab+gacaqGMbGaaeiiaiaabM gacaqG0bGaae4CaiaabccacaqGKbGaaeyAaiaabggacaqGNbGaae4B aiaab6gacaqGHbGaaeiBaiaabccacaqGPbGaae4CaiaabccacaqGUb Gaae4BaiaabshacaqGGaGaaeOEaiaabwgacaqGYbGaae4Baiaab6ca aeaacqGHsislcaaI0aGaeyOeI0IaaGOmaiabg2da9iabgkHiTiaaiA dacqGHGjsUcaqGWaaabaGaae4uaiaab+gacaqGSaGaaeiiaiaabIca caqGPbGaaeykaiaabccacaqGPbGaae4CaiaabccacaqGUbGaae4Bai aabshacaqGGaGaaeyyaiaabccacaqGTbGaaeyyaiaabEgacaqGPbGa ae4yaiaabccacaqGZbGaaeyCaiaabwhacaqGHbGaaeOCaiaabwgaca qGUaaabaGaae4uaiaabMgacaqGTbGaaeyAaiaabYgacaqGHbGaaeOC aiaabYgacaqG5bGaaeilaiaabccacaqGPbGaaeOBaiaabccacaqGZb GaaeyCaiaabwhacaqGHbGaaeOCaiaabwgacaqGGaGaaeikaiaabMga caqGPbGaaeykaiaabccacaqGLbGaaeODaiaabwgacaqGYbGaaeyEai aabccacaqGYbGaae4BaiaabEhacaqGSaGaaeiiaiaabogacaqGVbGa aeiBaiaabwhacaqGTbGaaeOBaiaabccacaqGHbGaaeOBaiaabsgaca qGGaGaaeizaiaabMgacaqGHbGaae4zaiaab+gacaqGUbGaaeyyaiaa bYgaaeaacaqGGaGaae4CaiaabwhacaqGTbGaaeiiaiaabwhacaqGWb GaaeiiaiaabshacaqGVbGaaeiiaiabgkHiTiaabMdacaqGUaaabaGa aeivaiaabIgacaqG1bGaae4CaiaabYcacaqGGaGaaeikaiaabMgaca qGPbGaaeykaiaabccacaqGPbGaae4CaiaabccacaqGHbGaaeiiaiaa b2gacaqGHbGaae4zaiaabMgacaqGJbGaaeiiaiaabohacaqGXbGaae yDaiaabggacaqGYbGaaeyzaiaab6caaaaa@41AF@

Q.8

Verifya b = a + b for the following values of a and b.i  a = 21,b = 18 ii  a = 118, b = 125iii a = 75,b = 84 iv a = 28, b = 11

Ans.

(i) a=21, b=18a(b)=21(18)=21+18=39a+b=21+18=39Thus, a(b)=a+b(ii) a=118, b=125a(b)=118(125)=118+125=243a+b=118+125=243Thus,a(b)=a+b(iii) a=75, b=84a(b)=75(84)=75+84=159a+b=75+84=39Thus, a(b)=a+b(iv) a=28, b=11a(b)=28(11)=28+11=39a+b=28+11=39Thus, a(b)=a+b

Q.9

Use the sign of >,< or = in the box to make the statementtrue.a8+484(b)(3)+7(19)158+(9)(c)2341+11234111(d)39+(24)(15)36+(52)(36)(e)231+79+51399+159+81

Ans.

(a) (8) + (4) < (8)(4) (b) (3) +7 (19) < 158+(9) (c) 2341+11 > 234111 (d) 39+(24) (15) < 36+(52)(36) (e) 231+79+51 > 399 + 159 + 81 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyyaiaabMcacaqGGaGaaeik aiabgkHiTiaabIdacaqGPaGaaeiiaiaabUcacaqGGaGaaeikaiabgk HiTiaabsdacaqGPaGaaeiiaiaaxMaadaqjEaqaaiabgYda8aaacaqG GaGaaCzcaiaaxMaacaqGOaGaeyOeI0IaaeioaiaabMcacqGHsislca qGOaGaeyOeI0IaaeinaiaabMcaaeaacaqGOaGaaeOyaiaabMcacaqG GaGaaeikaiabgkHiTiaabodacaqGPaGaaeiiaiaabUcacaqG3aGaey OeI0IaaeiiaiaabIcacaqGXaGaaeyoaiaabMcacaqGGaGaaCzcamaa L4babaGaeyipaWdaaiaabccacaWLjaGaaCzcaiaabgdacaqG1aGaey OeI0IaaeioaiaabUcacaqGOaGaeyOeI0IaaeyoaiaabMcaaeaacaqG OaGaae4yaiaabMcacaqGGaGaaeOmaiaabodacqGHsislcaqG0aGaae ymaiaabUcacaqGXaGaaeymaiaabccacaWLjaGaaCzcamaaL4babaGa eyOpa4daaiaabccacaWLjaGaaCzcaiaaikdacaaIZaGaeyOeI0IaaG inaiaaigdacqGHsislcaaIXaGaaGymaaqaaiaabIcacaqGKbGaaeyk aiaabccacaqGZaGaaeyoaiaabUcacaqGOaGaeyOeI0IaaeOmaiaabs dacaqGPaGaaeiiaiabgkHiTiaabccacaqGOaGaaeymaiaabwdacaqG PaWaauIhaeaacqGH8aapaaGaaeiiaiaaxMaacaWLjaGaaG4maiaaiA dacqGHRaWkcaqGOaGaeyOeI0IaaeynaiaabkdacaqGPaGaeyOeI0Ia aeikaiabgkHiTiaabodacaqG2aGaaeykaaqaaiaabIcacaqGLbGaae ykaiaabccacqGHsislcaqGYaGaae4maiaabgdacaqGRaGaae4naiaa bMdacaqGRaGaaeynaiaabgdacaqGGaGaaeiiaiaabccacaqGGaGaae iiaiaabccadaqjEaqaaiabg6da+aaacaqGGaGaaCzcaiaaxMaacqGH sislcaqGZaGaaeyoaiaabMdacaqGRaGaaeymaiaabwdacaqG5aGaae 4kaiaabIdacaqGXaaaaaa@B3CA@

Q.10

A water tank has steps inside it. A monkey is sitting onthe topmost step i.e., the first step. The water level isat the ninth step. i He jumps 3 steps down and then jumps back 2 stepsup.In how many jumps will he reach the water level? ii After drinking water, he wants to go back. For this,he jumps 4 steps up and then jumps back 2steps down in every move. In how many jumps will hereach back the top step? iii If the number of steps moved down is representedby negative integers and the number of steps moved upby positive integers, represent his moves in part i and ii by completing the following; a – 3 + 2 – =- 8 b 4 – 2 + = 8.In a the sum – 8 represents going down by eightsteps. So, what will the sum 8 in b represent?

Ans.

Consider the steps moved down be represented by positive integers and steps moved up be represented by negative integers. (i)Initially, the monkey was at step = 1 After 1st jump, monkey will be at step = 1+3=4 After 2nd jump, monkey will be at step = 4+( 2 )=2 After 3rd jump, monkey will be at step = 2+3=5 After 4th jump, monkey will be at step = 5+( 2 )=3 After 5th jump, monkey will be at step = 3+3=6 After 6th jump, monkey will be at step = 6+( 2 )=4 After 7th jump, monkey will be at step = 4+3=7 After 8th jump, monkey will be at step = 7+( 2 )=5 After 9th jump, monkey will be at step = 5+3=8 After 10th jump, monkey will be at step = 8+( 2 )=6 After 11th jump, monkey will be at step = 6+3=9 Clearly, the monkey will be at water level (i.e., 9th step) after 11 jumps. (ii) Initiall, the monkey was at step = 9 After 1st jump, monkey will be at step = 9+( 4 )=5 After 2nd jump, monkey will be at step = 5+2=7 After 3rd jump, monkey will be at step = 7+( 4 )=3 After 4th jump, monkey will be at step = 3+2=5 After 5th jump, monkey will be at step = 5+( 4 )=1 Clearly,the will reach back at the top step after 5 jumps. (iii) If steps moved down are represented by a negative integers and steps moved up are represented bya positive integers, then his moves will be as follows: Moves in part (i): 3+23+23+23+23+23=8 Moves in part (ii): 42+42+4=8 Moves in part (ii) represent goin up 8 steps. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGdbGaae4Baiaab6gacaqGZbGaaeyA aiaabsgacaqGLbGaaeOCaiaabccacaqG0bGaaeiAaiaabwgacaqGGa Gaae4CaiaabshacaqGLbGaaeiCaiaabohacaqGGaGaaeyBaiaab+ga caqG2bGaaeyzaiaabsgacaqGGaGaaeizaiaab+gacaqG3bGaaeOBai aabccacaqGIbGaaeyzaiaabccacaqGYbGaaeyzaiaabchacaqGYbGa aeyzaiaabohacaqGLbGaaeOBaiaabshacaqGLbGaaeizaiaabccaca qGIbGaaeyEaiaabccacaqGWbGaae4BaiaabohacaqGPbGaaeiDaiaa bMgacaqG2bGaaeyzaaqaaiaabMgacaqGUbGaaeiDaiaabwgacaqGNb GaaeyzaiaabkhacaqGZbGaaeiiaiaabggacaqGUbGaaeizaiaabcca caqGZbGaaeiDaiaabwgacaqGWbGaae4CaiaabccacaqGTbGaae4Bai aabAhacaqGLbGaaeizaiaabccacaqG1bGaaeiCaiaabccacaqGIbGa aeyzaiaabccacaqGYbGaaeyzaiaabchacaqGYbGaaeyzaiaabohaca 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Q.11

Write down a pair of integers whose:a sumis -7b differenceis -10c sumis 0

Ans.

(a) 8+(+1) =8+1=7 So, the pair is (8, 1) (b) 12(2)=12+2=10 So, the pair is (12,2) (c) 5+(5)=55=0 So, the pair is (5,5) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyyaiaabMcacaqGGaGaeyOe I0IaaeioaiaabUcacaqGOaGaae4kaiaabgdacaqGPaGaaeiiaiaab2 dacqGHsislcaqG4aGaae4kaiaabgdacaqG9aGaeyOeI0Iaae4naaqa aiaabofacaqGVbGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqGGa GaaeiCaiaabggacaqGPbGaaeOCaiaabccacaqGPbGaae4Caiaabcca caqGOaGaeyOeI0IaaeioaiaabYcacaqGGaGaaeymaiaabMcaaeaaca qGOaGaaeOyaiaabMcacaqGGaGaeyOeI0IaaeymaiaabkdacqGHsisl caqGOaGaeyOeI0IaaeOmaiaabMcacaqG9aGaeyOeI0Iaaeymaiaabk dacaqGRaGaaeOmaiaab2dacqGHsislcaqGXaGaaeimaaqaaiaabofa caqGVbGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeiCai aabggacaqGPbGaaeOCaiaabccacaqGPbGaae4CaiaabccacaqGOaGa eyOeI0IaaeymaiaabkdacaqGSaGaeyOeI0IaaeOmaiaabMcaaeaaca qGOaGaae4yaiaabMcacaqGGaGaaeynaiaabUcacaqGOaGaeyOeI0Ia aeynaiaabMcacaqG9aGaaeynaiabgkHiTiaabwdacaqG9aGaaeimaa qaaiaabofacaqGVbGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqG GaGaaeiCaiaabggacaqGPbGaaeOCaiaabccacaqGPbGaae4Caiaabc cacaqGOaGaeyOeI0IaaeynaiaabYcacqGHsislcaqG1aGaaeykaaaa aa@A10D@

Q.12 

a Write a pair of negative integers whose differencegives 8.b Write an egative integer and a positive integer whosesumis -5.c Write an egative integer and a positive integer whosedifferenceis -3.

Ans.

(a) To write a pair of negative integers whose difference is 8 So, 2(10)=2+10=8 So, pair of negative integers is (2,10) . (b)To write a negative integer and a positive integer whose sum is 5. 8+3=5 So, a negative integer and a positive integeris (8,3) . (c)To write a negative integer and a positive integer whose difference is 3 2(+1)=21=3 So, a negative integer and a positive integeris (2,1) . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyyaiaabMcacaqGGaGaaeiv aiaab+gacaqGGaGaae4DaiaabkhacaqGPbGaaeiDaiaabwgacaqGGa GaaeyyaiaabccacaqGWbGaaeyyaiaabMgacaqGYbGaaeiiaiaab+ga caqGMbGaaeiiaiaab6gacaqGLbGaae4zaiaabggacaqG0bGaaeyAai aabAhacaqGLbGaaeiiaiaabMgacaqGUbGaaeiDaiaabwgacaqGNbGa aeyzaiaabkhacaqGZbGaaeiiaiaabEhacaqGObGaae4Baiaabohaca qGLbGaaeiiaiaabsgacaqGPbGaaeOzaiaabAgacaqGLbGaaeOCaiaa bwgacaqGUbGaae4yaiaabwgacaqGGaGaaeyAaiaabohacaqGGaGaae ioaaqaaiaabofacaqGVbGaaeilaiaabccacqGHsislcaqGYaGaeyOe I0IaaeikaiabgkHiTiaabgdacaqGWaGaaeykaiaab2dacqGHsislca qGYaGaae4kaiaabgdacaqGWaGaaeypaiaabIdaaeaacaqGtbGaae4B aiaabYcacaqGGaGaaeiCaiaabggacaqGPbGaaeOCaiaabccacaqGVb GaaeOzaiaabccacaqGUbGaaeyzaiaabEgacaqGHbGaaeiDaiaabMga caqG2bGaaeyzaiaabccaciGGPbGaaiOBaiaacshacaqGLbGaae4zai aabwgacaqGYbGaae4CaiaabccacaqGPbGaae4CaiaabccadaqjEaqa aiaacIcacqGHsislcaaIYaGaaiilaiabgkHiTiaaigdacaaIWaGaai ykaaaacaGGUaaabaGaaiikaiaadkgacaGGPaGaaeivaiaab+gacaqG GaGaae4DaiaabkhacaqGPbGaaeiDaiaabwgacaqGGaGaaeyyaiaabc cacaqGUbGaaeyzaiaabEgacaqGHbGaaeiDaiaabMgacaqG2bGaaeyz aiaabccacaqGPbGaaeOBaiaabshacaqGLbGaae4zaiaabwgacaqGYb GaaeiiaiaabggacaqGUbGaaeizaiaabccacaqGHbGaaeiiaiaabcha caqGVbGaae4CaiaabMgacaqG0bGaaeyAaiaabAhacaqGLbGaaeiiai aabMgacaqGUbGaaeiDaiaabwgacaqGNbGaaeyzaiaabkhacaqGGaGa ae4DaiaabIgacaqGVbGaae4CaiaabwgaaeaacaqGZbGaaeyDaiaab2 gacaqGGaGaaeyAaiaabohacaqGGaGaeyOeI0Iaaeynaiaab6caaeaa cqGHsislcaqG4aGaae4kaiaabodacaqG9aGaeyOeI0Iaaeynaaqaai aabofacaqGVbGaaeilaiaabccacaqGHbGaaeiiaiaab6gacaqGLbGa ae4zaiaabggacaqG0bGaaeyAaiaabAhacaqGLbGaaeiiaiaabMgaca qGUbGaaeiDaiaabwgacaqGNbGaaeyzaiaabkhacaqGGaGaaeyyaiaa b6gacaqGKbGaaeiiaiaabggacaqGGaGaaeiCaiaab+gacaqGZbGaae yAaiaabshacaqGPbGaaeODaiaabwgacaqGGaGaciyAaiaac6gacaGG 0bGaaeyzaiaabEgacaqGLbGaaeOCaiaaysW7caqGPbGaae4Caiaabc cadaqjEaqaaiaacIcacqGHsislcaaI4aGaaiilaiaaiodacaGGPaaa aiaac6caaeaacaGGOaGaam4yaiaacMcacaaMe8Uaaeivaiaab+gaca qGGaGaae4DaiaabkhacaqGPbGaaeiDaiaabwgacaqGGaGaaeyyaiaa bccacaqGUbGaaeyzaiaabEgacaqGHbGaaeiDaiaabMgacaqG2bGaae yzaiaabccacaqGPbGaaeOBaiaabshacaqGLbGaae4zaiaabwgacaqG YbGaaeiiaiaabggacaqGUbGaaeizaiaabccacaqGHbGaaeiiaiaabc hacaqGVbGaae4CaiaabMgacaqG0bGaaeyAaiaabAhacaqGLbGaaeii aiaabMgacaqGUbGaaeiDaiaabwgacaqGNbGaaeyzaiaabkhacaqGGa Gaae4DaiaabIgacaqGVbGaae4CaiaabwgaaeaacaqGKbGaaeyAaiaa bAgacaqGMbGaaeyzaiaabkhacaqGLbGaaeOBaiaabogacaqGLbGaae iiaiaabMgacaqGZbGaaeiiaiabgkHiTiaabodaaeaacqGHsislcaaI YaGaeyOeI0IaaeikaiaabUcacaqGXaGaaeykaiaab2dacqGHsislca qGYaGaeyOeI0Iaaeymaiaab2dacqGHsislcaqGZaaabaGaae4uaiaa b+gacaqGSaGaaeiiaiaabggacaqGGaGaaeOBaiaabwgacaqGNbGaae yyaiaabshacaqGPbGaaeODaiaabwgacaqGGaGaaeyAaiaab6gacaqG 0bGaaeyzaiaabEgacaqGLbGaaeOCaiaabccacaqGHbGaaeOBaiaabs gacaqGGaGaaeyyaiaabccacaqGWbGaae4BaiaabohacaqGPbGaaeiD aiaabMgacaqG2bGaaeyzaiaabccaciGGPbGaaiOBaiaacshacaqGLb Gaae4zaiaabwgacaqGYbGaaGjbVlaabMgacaqGZbGaaeiiamaaL4ba baGaaiikaiabgkHiTiaaikdacaGGSaGaaGymaiaacMcaaaGaaiOlaa aaaa@9822@

Q.13

In a quiz, team A scored – 40,10,0 and team B scored10, 0, -40 in three successive rounds.Which team scoredmore? Can we say that we can add integers in any order?

Ans.

Sum of team A scored = 40+10+0=30 Sum of team B scored = 10+040=30 Both teams scored equal. Yes, we can add integers in any order. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4B aiaabAgacaqGGaGaaeiDaiaabwgacaqGHbGaaeyBaiaabccacaqGbb GaaeiiaiaabohacaqGJbGaae4BaiaabkhacaqGLbGaaeizaiaabcca cqGH9aqpcaqGGaGaeyOeI0IaaGinaiaaicdacqGHRaWkcaaIXaGaaG imaiabgUcaRiaaicdacqGH9aqpcqGHsislcaaIZaGaaGimaaqaaiaa bofacaqG1bGaaeyBaiaabccacaqGVbGaaeOzaiaabccacaqG0bGaae yzaiaabggacaqGTbGaaeiiaiaabkeacaqGGaGaae4CaiaabogacaqG VbGaaeOCaiaabwgacaqGKbGaaeiiaiabg2da9iaabccacaaIXaGaaG imaiabgUcaRiaaicdacqGHsislcaaI0aGaaGimaiabg2da9iabgkHi TiaaiodacaaIWaaabaGaaeOqaiaab+gacaqG0bGaaeiAaiaabccaca qG0bGaaeyzaiaabggacaqGTbGaae4CaiaabccacaqGZbGaae4yaiaa b+gacaqGYbGaaeyzaiaabsgacaqGGaGaaeyzaiaabghacaqG1bGaae yyaiaabYgacaqGUaaabaGaaeywaiaabwgacaqGZbGaaeilaiaabcca caqG3bGaaeyzaiaabccacaqGJbGaaeyyaiaab6gacaqGGaGaaeyyai aabsgacaqGKbGaaeiiaiaabMgacaqGUbGaaeiDaiaabwgacaqGNbGa aeyzaiaabkhacaqGZbGaaeiiaiaabMgacaqGUbGaaeiiaiaabggaca qGUbGaaeyEaiaabccacaqGVbGaaeOCaiaabsgacaqGLbGaaeOCaiaa b6caaaaa@ACA4@

Q.14

Fillintheblankstomakethefollowingstatementstrue:(i) (5)+(.………..)=(8)+(.………..)(ii)53+.………..=53(iii) 17+.………..=0(iv)[13+(12)]+(.………..)=.………..+[(12)+(7)](v)(4)+[.………..+(3)]=[.………..+15]+.………..

Ans.

( i ) ( 5 ) + ( 8 ) = ( 8 ) + ( 5 ) ( ii ) 53 + 0 = 53 ( iii ) 17 + 17 = 0 ( iv ) [ 13 + ( 12 ) ] + ( 7 ) = 13 + [ ( 12 ) + ( 7 ) ] ( v ) ( 4 ) + [ 15 + ( 3 ) ] = [ 4 + 15 ] + 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaGGGcWaaeWaaeaacaqGPbaacaGLOaGa ayzkaaGaaeiiamaabmaabaGaeyOeI0IaaeynaaGaayjkaiaawMcaai aabccacqGHRaWkcaqGGaWaaeWaaeaadaqjEaqaaiabgkHiTiaaiIda aaaacaGLOaGaayzkaaGaaeiiaiabg2da9iaabccadaqadaqaaiabgk HiTiaabccacaqG4aaacaGLOaGaayzkaaGaaeiiaiabgUcaRiaabcca daqadaqaamaaL4babaGaeyOeI0IaaGynaaaaaiaawIcacaGLPaaaae aadaqadaqaaiaabMgacaqGPbaacaGLOaGaayzkaaGaaeiiaiabgkHi TiaabwdacaqGZaGaaeiiaiabgUcaRiaabccadaqjEaqaaiaaicdaaa Gaaeiiaiabg2da9iaabccacqGHsislcaqG1aGaae4maaqaamaabmaa baGaaeyAaiaabMgacaqGPbaacaGLOaGaayzkaaGaaiiOaiaaysW7ca qGXaGaae4naiaabccacqGHRaWkcaqGGaWaauIhaeaacqGHsislcaaI XaGaaG4naaaacaqGGaGaeyypa0Jaaeiiaiaaicdaaeaadaqadaqaai aabMgacaqG2baacaGLOaGaayzkaaGaaeiiamaadmaabaGaaeymaiaa bodacaqGGaGaey4kaSIaaeiiamaabmaabaGaeyOeI0Iaaeymaiaabk daaiaawIcacaGLPaaaaiaawUfacaGLDbaacaqGGaGaey4kaSIaaeii amaabmaabaWaauIhaeaacqGHsislcaaI3aaaaaGaayjkaiaawMcaai aabccacqGH9aqpcaqGGaWaauIhaeaacaaIXaGaaG4maaaacaqGGaGa ey4kaSIaaeiiamaadmaabaWaaeWaaeaacqGHsislcaqGXaGaaeOmaa GaayjkaiaawMcaaiaabccacqGHRaWkcaqGGaWaaeWaaeaacqGHsisl caqG3aaacaGLOaGaayzkaaaacaGLBbGaayzxaaaabaWaaeWaaeaaca qG2baacaGLOaGaayzkaaGaaeiiamaabmaabaGaeyOeI0IaaeinaaGa ayjkaiaawMcaaiaabccacqGHRaWkcaqGGaWaamWaaeaadaqjEaqaai aaigdacaaI1aaaaiaabccacqGHRaWkcaqGGaWaaeWaaeaacqGHsisl caqGZaaacaGLOaGaayzkaaaacaGLBbGaayzxaaGaaeiiaiabg2da9i aabccadaWadaqaamaaL4babaGaeyOeI0IaaGinaaaacqGHRaWkcaqG GaGaaeymaiaabwdaaiaawUfacaGLDbaacaqGGaGaey4kaSYaauIhae aacqGHsislcaaIZaaaaaaaaa@B725@

Q.15

Findeachofthefollowingproducts: (a)3×(1) (b)(1)×225 (c)(21)×(30) (d)(316)×(1) (e)(15)×0×(18) (f)(12)×(11)×(10)(g) 9×(3)×(6) (h) (18)×(5)×(4)(i) (1)×(2)×(3)×4(j)(3)×(6)×(2)×(1)

Ans.

( a ) 3 × ( 1 )= 3 ( b ) ( 1 ) × 225= 225 ( c ) ( 21 ) × ( 30 ) = 630 ( d ) ( 316 ) × ( 1 )= 316 ( e ) ( 15 ) × 0 × ( 18 )= 0 ( f ) ( 12 ) × ( 11 ) × ( 10 )= 1320 ( g ) 9 × ( 3 ) × ( 6 )= 162 ( h ) ( 18 ) × ( 5 ) × ( 4 )= 360 ( i ) ( 1 ) × ( 2 ) × ( 3 ) × 4= 24 ( j ) ( 3 ) × ( 6 ) × ( 2 ) × ( 1 )= 36 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa caqGGaGaae4maiaabccacqGHxdaTcaqGGaWaaeWaaeaacqGHsislca qGXaaacaGLOaGaayzkaaGaeyypa0ZaauIhaeaacqGHsislcaaIZaaa aaqaamaabmaabaGaaeOyaaGaayjkaiaawMcaaiaabccadaqadaqaai abgkHiTiaabgdaaiaawIcacaGLPaaacaqGGaGaey41aqRaaeiiaiaa bkdacaqGYaGaaeynaiabg2da9iaabccadaqjEaqaaiabgkHiTiaaik dacaaIYaGaaGynaaaaaeaadaqadaqaaiaabogaaiaawIcacaGLPaaa caqGGaWaaeWaaeaacqGHsislcaqGYaGaaeymaaGaayjkaiaawMcaai aabccacqGHxdaTcaqGGaWaaeWaaeaacqGHsislcaqGZaGaaGimaaGa ayjkaiaawMcaaiaacckacqGH9aqpdaqjEaqaaiaaiAdacaaIZaGaaG imaaaacaGGGcaabaWaaeWaaeaacaqGKbaacaGLOaGaayzkaaGaaeii amaabmaabaGaeyOeI0Iaae4maiaabgdacaqG2aaacaGLOaGaayzkaa GaaeiiaiabgEna0kaabccadaqadaqaaiabgkHiTiaabgdaaiaawIca caGLPaaacqGH9aqpdaqjEaqaaiaaiodacaaIXaGaaGOnaaaaaeaada qadaqaaiaabwgaaiaawIcacaGLPaaacaqGGaWaaeWaaeaacqGHsisl caqGXaGaaeynaaGaayjkaiaawMcaaiaabccacqGHxdaTcaqGGaGaaG imaiaabccacqGHxdaTcaqGGaWaaeWaaeaacqGHsislcaqGXaGaaeio aaGaayjkaiaawMcaaiabg2da9maaL4babaGaaGimaaaacaGGGcaaba WaaeWaaeaacaqGMbaacaGLOaGaayzkaaGaaeiiamaabmaabaGaeyOe I0IaaeymaiaabkdaaiaawIcacaGLPaaacaqGGaGaey41aqRaaeiiam aabmaabaGaeyOeI0IaaeymaiaabgdaaiaawIcacaGLPaaacaqGGaGa ey41aqRaaeiiamaabmaabaGaaeymaiaaicdaaiaawIcacaGLPaaacq GH9aqpdaqjEaqaaiaaigdacaaIZaGaaGOmaiaaicdaaaaabaWaaeWa aeaacaqGNbaacaGLOaGaayzkaaGaaeiiaiaabMdacaqGGaGaey41aq RaaeiiamaabmaabaGaeyOeI0Iaae4maaGaayjkaiaawMcaaiaabcca cqGHxdaTcaqGGaWaaeWaaeaacqGHsislcaqGGaGaaeOnaaGaayjkai aawMcaaiabg2da9maaL4babaGaaGymaiaaiAdacaaIYaaaaaqaamaa bmaabaGaaeiAaaGaayjkaiaawMcaaiaabccadaqadaqaaiabgkHiTi aabgdacaqG4aaacaGLOaGaayzkaaGaaeiiaiabgEna0kaabccadaqa daqaaiabgkHiTiaabwdaaiaawIcacaGLPaaacaqGGaGaey41aqRaae iiamaabmaabaGaeyOeI0IaaeiiaiaabsdaaiaawIcacaGLPaaacqGH 9aqpdaqjEaqaaiabgkHiTiaaiodacaaI2aGaaGimaaaaaeaacaGGGc WaaeWaaeaacaqGPbaacaGLOaGaayzkaaGaaeiiamaabmaabaGaeyOe I0IaaeymaaGaayjkaiaawMcaaiaabccacqGHxdaTcaqGGaWaaeWaae aacqGHsislcaqGYaaacaGLOaGaayzkaaGaaeiiaiabgEna0kaabcca daqadaqaaiabgkHiTiaabodaaiaawIcacaGLPaaacaqGGaGaey41aq RaaeiiaiaabsdacqGH9aqpdaqjEaqaaiabgkHiTiaaikdacaaI0aaa aaqaamaabmaabaGaaeOAaaGaayjkaiaawMcaaiaabccadaqadaqaai abgkHiTiaabodaaiaawIcacaGLPaaacaqGGaGaey41aqRaaeiiamaa bmaabaGaeyOeI0IaaeOnaaGaayjkaiaawMcaaiaabccacqGHxdaTca qGGaWaaeWaaeaacqGHsislcaqGYaaacaGLOaGaayzkaaGaaeiiaiab gEna0kaabccadaqadaqaaiabgkHiTiaabgdaaiaawIcacaGLPaaacq GH9aqpdaqjEaqaaiaaiodacaaI2aaaaaaaaa@166C@

Q.16

Verifythefollowing:(a)18×[7+(3)]=[18×7]+[18×(3)](b)(21)×[(4)+(6)]=[(21)×(4)]+[(21)×(6)]

Ans.

( a ) 18 × [ 7 + ( 3 ) ]=18×[ 4 ]=72 and [ 18 × 7 ] + [ 18 × ( 3 ) ]=[ 126 ]+[ 56 ]=70 So, 18 × [ 7 + ( 3 ) ][ 18 × 7 ] + [ 18 × ( 3 ) ] ( b ) ( 21 ) × [ ( 4 ) + ( 6 ) ]=( 21 )×[ 10 ]=210 and [ ( 21 ) × ( 4 ) ] + [ ( 21 ) × ( 6 ) ]=[ 84 ]+[ 126 ]=210 So, ( 21 ) × [ ( 4 ) + ( 6 ) ]=[ ( 21 ) × ( 4 ) ] + [ ( 21 ) × ( 6 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa aeaacaqGXaGaaeioaiaabccacqGHxdaTcaqGGaWaamWaaeaacaqG3a GaaeiiaiabgUcaRiaabccadaqadaqaaiaacobicaqGZaaacaGLOaGa ayzkaaaacaGLBbGaayzxaaGaeyypa0JaaGymaiaaiIdacqGHxdaTda WadaqaaiaaisdaaiaawUfacaGLDbaacqGH9aqpcaaI3aGaaGOmaaqa aiaabggacaqGUbGaaeizaaqaamaadmaabaGaaeymaiaabIdacaqGGa Gaey41aqRaaeiiaiaabEdaaiaawUfacaGLDbaacaqGGaGaey4kaSIa aeiiamaadmaabaGaaeymaiaabIdacaqGGaGaey41aqRaaeiiamaabm aabaGaai4eGiaabodaaiaawIcacaGLPaaaaiaawUfacaGLDbaacqGH 9aqpdaWadaqaaiaaigdacaaIYaGaaGOnaaGaay5waiaaw2faaiabgU caRmaadmaabaGaeyOeI0IaaGynaiaaiAdaaiaawUfacaGLDbaacqGH 9aqpcaaI3aGaaGimaaqaaiaabofacaqGVbGaaiilamaaL4babaGaae ymaiaabIdacaqGGaGaey41aqRaaeiiamaadmaabaGaae4naiaabcca cqGHRaWkcaqGGaWaaeWaaeaacaGGtaIaae4maaGaayjkaiaawMcaaa Gaay5waiaaw2faaiabgcMi5oaadmaabaGaaeymaiaabIdacaqGGaGa ey41aqRaaeiiaiaabEdaaiaawUfacaGLDbaacaqGGaGaey4kaSIaae iiamaadmaabaGaaeymaiaabIdacaqGGaGaey41aqRaaeiiamaabmaa baGaai4eGiaabodaaiaawIcacaGLPaaaaiaawUfacaGLDbaaaaaaba WaaeWaaeaacaqGIbaacaGLOaGaayzkaaaabaWaaeWaaeaacqGHsisl caqGYaGaaeymaaGaayjkaiaawMcaaiaabccacqGHxdaTcaqGGaWaam WaaeaadaqadaqaaiabgkHiTiaabsdaaiaawIcacaGLPaaacaqGGaGa ey4kaSIaaeiiamaabmaabaGaeyOeI0IaaeOnaaGaayjkaiaawMcaaa Gaay5waiaaw2faaiabg2da9maabmaabaGaeyOeI0IaaGOmaiaaigda aiaawIcacaGLPaaacqGHxdaTdaWadaqaaiabgkHiTiaaigdacaaIWa aacaGLBbGaayzxaaGaeyypa0JaaGOmaiaaigdacaaIWaaabaGaaeyy aiaab6gacaqGKbaabaWaamWaaeaadaqadaqaaiabgkHiTiaabkdaca qGXaaacaGLOaGaayzkaaGaaeiiaiabgEna0kaabccadaqadaqaaiab gkHiTiaabsdaaiaawIcacaGLPaaaaiaawUfacaGLDbaacaqGGaGaey 4kaSIaaeiiamaadmaabaWaaeWaaeaacqGHsislcaqGYaGaaeymaaGa ayjkaiaawMcaaiaabccacqGHxdaTcaqGGaWaaeWaaeaacqGHsislca qG2aaacaGLOaGaayzkaaaacaGLBbGaayzxaaGaeyypa0ZaamWaaeaa caaI4aGaaGinaaGaay5waiaaw2faaiabgUcaRmaadmaabaGaaGymai aaikdacaaI2aaacaGLBbGaayzxaaGaeyypa0JaaGOmaiaaigdacaaI WaaabaGaae4uaiaab+gacaGGSaaabaWaauIhaeaadaqadaqaaiaaco bicaqGYaGaaeymaaGaayjkaiaawMcaaiaabccacqGHxdaTcaqGGaWa amWaaeaadaqadaqaaiaacobicaqGGaGaaeinaaGaayjkaiaawMcaai aabccacqGHRaWkcaqGGaWaaeWaaeaacaGGtaIaaeiiaiaabAdaaiaa wIcacaGLPaaaaiaawUfacaGLDbaacqGH9aqpdaWadaqaamaabmaaba Gaai4eGiaabkdacaqGXaaacaGLOaGaayzkaaGaaeiiaiabgEna0kaa bccadaqadaqaaiaacobicaqGGaGaaeinaaGaayjkaiaawMcaaaGaay 5waiaaw2faaiaabccacqGHRaWkcaqGGaWaamWaaeaadaqadaqaaiaa cobicaqGYaGaaeymaaGaayjkaiaawMcaaiaabccacqGHxdaTcaqGGa WaaeWaaeaacaGGtaIaaeiiaiaabAdaaiaawIcacaGLPaaaaiaawUfa caGLDbaaaaaaaaa@1C03@

Q.17

(i) For any integera, what is (1)×a equal to ?(ii) Determine the integer whose product with (1) is(a)22 (b) 37 (c) 0

Ans.

( i )( 1 )×a=a (ii) (a) 22 ×( 1 )=22 (b) 37 ×( 1 )=37 (c) 0 ×( 1 )=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabMgaaiaawIcacaGLPaaa caaMe8+aaeWaaeaacqGHsislcaqGXaaacaGLOaGaayzkaaGaey41aq Raaeyyaiaab2dacqGHsislcaqGHbaabaGaaeikaiaabMgacaqGPbGa aeykaiaabccacaqGOaGaaeyyaiaabMcacaqGGaWaauIhaeaacaaIYa GaaGOmaaaacqGHxdaTdaqadaqaaiabgkHiTiaaigdaaiaawIcacaGL PaaacqGH9aqpcqGHsislcaaIYaGaaGOmaaqaaiaabIcacaqGIbGaae ykaiaabccadaqjEaqaaiabgkHiTiaabodacaqG3aaaaiabgEna0oaa bmaabaGaeyOeI0IaaGymaaGaayjkaiaawMcaaiabg2da9iaaiodaca aI3aaabaGaaeikaiaabogacaqGPaGaaeiiamaaL4babaGaaeimaaaa cqGHxdaTdaqadaqaaiabgkHiTiaaigdaaiaawIcacaGLPaaacqGH9a qpcaaIWaaaaaa@7353@

Q.18

Starting from (1)×5, write various products showing somepattern to show (1)×(1)=1

Ans.

1×5=5 1×4=4=5+1 1×3=3=4+1 1×2=2=3+1 1×1=1=2+1 1×0=0=1+1 Thus, 1×( 1 )=0+1=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacqGHsislcaaIXaGaey41aqRaaGynaiab g2da9iabgkHiTiaaiwdaaeaacqGHsislcaaIXaGaey41aqRaaGinai abg2da9iabgkHiTiaaisdacqGH9aqpcqGHsislcaaI1aGaey4kaSIa aGymaaqaaiabgkHiTiaaigdacqGHxdaTcaaIZaGaeyypa0JaeyOeI0 IaaG4maiabg2da9iabgkHiTiaaisdacqGHRaWkcaaIXaaabaGaeyOe I0IaaGymaiabgEna0kaaikdacqGH9aqpcqGHsislcaaIYaGaeyypa0 JaeyOeI0IaaG4maiabgUcaRiaaigdaaeaacqGHsislcaaIXaGaey41 aqRaaGymaiabg2da9iabgkHiTiaaigdacqGH9aqpcqGHsislcaaIYa Gaey4kaSIaaGymaaqaaiabgkHiTiaaigdacqGHxdaTcaaIWaGaeyyp a0JaaGimaiabg2da9iabgkHiTiaaigdacqGHRaWkcaaIXaaabaGaae ivaiaabIgacaqG1bGaae4CaiaabYcadaqjEaqaaiabgkHiTiaabgda cqGHxdaTdaqadaqaaiabgkHiTiaaigdaaiaawIcacaGLPaaacqGH9a qpcaaIWaGaey4kaSIaaGymaiabg2da9iaaigdaaaaaaaa@8D8E@

Q.19 

Find the product, using suitable properties: ( a ) 26 × ( 48 ) + ( 48 ) × ( 36 ) ( b ) 8 × 53 × ( 125 ) ( c ) 15 × ( 25 ) × ( 4 ) × ( 10 ) ( d ) ( 41 ) × 102 ( e ) 625 × ( 35 ) + ( 625 ) × 65 ( f ) 7 × ( 50 2 ) ( g ) ( 17 ) × ( 29 ) ( h ) ( 57 ) × ( 19 ) + 57 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaaieqacaWFgbGaa8xAaiaa=5gacaWFKbGa a8hiaiaa=rhacaWFObGaa8xzaiaa=bcacaWFWbGaa8NCaiaa=9gaca WFKbGaa8xDaiaa=ngacaWF0bGaa8hlaiaa=bcacaWF1bGaa83Caiaa =LgacaWFUbGaa83zaiaa=bcacaWFZbGaa8xDaiaa=LgacaWF0bGaa8 xyaiaa=jgacaWFSbGaa8xzaiaa=bcacaWFWbGaa8NCaiaa=9gacaWF WbGaa8xzaiaa=jhacaWF0bGaa8xAaiaa=vgacaWFZbGaa8Noaaqaai aa=bkadaqadaqaaiaa=fgaaiaawIcacaGLPaaacaWFGaGaa8Nmaiaa =zdacaWFGaGaa831aiaa=bcadaqadaqaaiaa=nbicaWFGaGaa8hnai aa=HdaaiaawIcacaGLPaaacaWFGaGaa83kaiaa=bcadaqadaqaaiaa =nbicaWFGaGaa8hnaiaa=HdaaiaawIcacaGLPaaacaWFGaGaa831ai aa=bcadaqadaqaaiaa=nbicaWFZaGaa8NnaaGaayjkaiaawMcaaiaa =bcadaqadaqaaiaa=jgaaiaawIcacaGLPaaacaWFGaGaa8hoaiaa=b cacaWFxdGaa8hiaiaa=vdacaWFZaGaa8hiaiaa=DnacaWFGaWaaeWa aeaacaWFtaIaa8xmaiaa=jdacaWF1aaacaGLOaGaayzkaaaabaGaa8 hOamaabmaabaGaa83yaaGaayjkaiaawMcaaiaa=bcacaWFXaGaa8xn aiaa=bcacaWFxdGaa8hiamaabmaabaGaa83eGiaa=jdacaWF1aaaca GLOaGaayzkaaGaa8hiaiaa=DnacaWFGaWaaeWaaeaacaWFtaIaa8hi aiaa=rdaaiaawIcacaGLPaaacaWFGaGaa831aiaa=bcadaqadaqaai aa=nbicaWFXaGaa8hmaaGaayjkaiaawMcaaiaa=bcacaWLjaWaaeWa aeaacaWFKbaacaGLOaGaayzkaaGaa8hiamaabmaabaGaa83eGiaa=b cacaWF0aGaa8xmaaGaayjkaiaawMcaaiaa=bcacaWFxdGaa8hiaiaa =fdacaWFWaGaa8Nmaaqaaiaa=bkadaqadaqaaiaa=vgaaiaawIcaca GLPaaacaWFGaGaa8Nnaiaa=jdacaWF1aGaa8hiaiaa=DnacaWFGaWa aeWaaeaacaWFtaIaa83maiaa=vdaaiaawIcacaGLPaaacaWFGaGaa8 3kaiaa=bcadaqadaqaaiaa=nbicaWFGaGaa8Nnaiaa=jdacaWF1aaa caGLOaGaayzkaaGaa8hiaiaa=DnacaWFGaGaa8Nnaiaa=vdacaWFGa WaaeWaaeaacaWFMbaacaGLOaGaayzkaaGaa8hiaiaa=DdacaWFGaGa a831aiaa=bcadaqadaqaaiaa=vdacaWFWaGaa8hiaiaa=nbicaWFGa Gaa8NmaaGaayjkaiaawMcaaaqaaiaa=bkadaqadaqaaiaa=Dgaaiaa wIcacaGLPaaacaWFGaWaaeWaaeaacaWFtaIaa8xmaiaa=DdaaiaawI cacaGLPaaacaWFGaGaa831aiaa=bcadaqadaqaaiaa=nbicaWFYaGa a8xoaaGaayjkaiaawMcaaiaa=bcacaWLjaGaaCzcaiaaxMaacaWLja WaaeWaaeaacaWFObaacaGLOaGaayzkaaGaa8hiamaabmaabaGaa83e Giaa=vdacaWF3aaacaGLOaGaayzkaaGaa8hiaiaa=DnacaWFGaWaae WaaeaacaWFtaIaa8xmaiaa=LdaaiaawIcacaGLPaaacaWFGaGaa83k aiaa=bcacaWF1aGaa83naaaaaa@F7B5@

Ans.

( a ) 26 × ( 48 ) + ( 48 ) × ( 36 ) =( 48 )×26+( 48 )×( 36 ) =( 48 )[ 2636 ] =( 48 )[ 10 ] = 480 ( b ) 8 × 53 × ( 125 ) =424×( 125 ) = 53000 ( c ) 15 × ( 25 ) × ( 4 ) × ( 10 ) =( 15×25 )×( 4×10 ) =( 375 )×40 = 15000 ( d ) ( 41 ) × 102 = 4182 ( e ) 625 × ( 35 ) + ( 625 ) × 65 =21875+( 40625 ) = 62500 ( f ) 7 × ( 50 2 ) =7×( 48 ) = 336 ( g ) ( 17 ) × ( 29 ) = 493 ( h ) ( 57 ) × ( 19 ) + 57 =1083+57 = 1140 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa caqGGaGaaeOmaiaabAdacaqGGaGaey41aqRaaeiiamaabmaabaGaey OeI0IaaeiiaiaabsdacaqG4aaacaGLOaGaayzkaaGaaeiiaiabgUca RiaabccadaqadaqaaiabgkHiTiaabccacaqG0aGaaeioaaGaayjkai aawMcaaiaabccacqGHxdaTcaqGGaWaaeWaaeaacqGHsislcaqGZaGa aeOnaaGaayjkaiaawMcaaaqaaiabg2da9maabmaabaGaeyOeI0IaaG inaiaaiIdaaiaawIcacaGLPaaacqGHxdaTcaaIYaGaaGOnaiabgUca RmaabmaabaGaeyOeI0IaaGinaiaaiIdaaiaawIcacaGLPaaacqGHxd aTdaqadaqaaiabgkHiTiaaiodacaaI2aaacaGLOaGaayzkaaaabaGa eyypa0ZaaeWaaeaacqGHsislcaaI0aGaaGioaaGaayjkaiaawMcaam aadmaabaGaaGOmaiaaiAdacqGHsislcaaIZaGaaGOnaaGaay5waiaa w2faaaqaaiabg2da9maabmaabaGaeyOeI0IaaGinaiaaiIdaaiaawI cacaGLPaaadaWadaqaaiabgkHiTiaaigdacaaIWaaacaGLBbGaayzx aaaabaGaeyypa0ZaauIhaeaacaaI0aGaaGioaiaaicdaaaaabaWaae WaaeaacaqGIbaacaGLOaGaayzkaaGaaeiiaiaabIdacaqGGaGaey41 aqRaaeiiaiaabwdacaqGZaGaaeiiaiabgEna0kaabccadaqadaqaai abgkHiTiaabgdacaqGYaGaaeynaaGaayjkaiaawMcaaaqaaiabg2da 9iaaisdacaaIYaGaaGinaiabgEna0oaabmaabaGaeyOeI0IaaGymai aaikdacaaI1aaacaGLOaGaayzkaaaabaGaeyypa0ZaauIhaeaacaaI 1aGaaG4maiaaicdacaaIWaGaaGimaaaaaeaacaGGGcWaaeWaaeaaca qGJbaacaGLOaGaayzkaaGaaeiiaiaabgdacaqG1aGaaeiiaiabgEna 0kaabccadaqadaqaaiabgkHiTiaabkdacaqG1aaacaGLOaGaayzkaa GaaeiiaiabgEna0kaabccadaqadaqaaiabgkHiTiaabccacaqG0aaa caGLOaGaayzkaaGaaeiiaiabgEna0kaabccadaqadaqaaiabgkHiTi aabgdacaaIWaaacaGLOaGaayzkaaaabaGaeyypa0ZaaeWaaeaacaaI XaGaaGynaiabgEna0kabgkHiTiaaikdacaaI1aaacaGLOaGaayzkaa Gaey41aq7aaeWaaeaacqGHsislcaaI0aGaey41aqRaeyOeI0IaaGym aiaaicdaaiaawIcacaGLPaaaaeaacqGH9aqpdaqadaqaaiabgkHiTi aaiodacaaI3aGaaGynaaGaayjkaiaawMcaaiabgEna0kaaisdacaaI WaaabaGaeyypa0ZaauIhaeaacqGHsislcaaIXaGaaGynaiaaicdaca aIWaGaaGimaaaaaeaadaqadaqaaiaabsgaaiaawIcacaGLPaaacaqG GaWaaeWaaeaacqGHsislcaqGGaGaaeinaiaabgdaaiaawIcacaGLPa aacaqGGaGaey41aqRaaeiiaiaabgdacaaIWaGaaeOmaaqaaiabg2da 9maaL4babaGaeyOeI0IaaeinaiaabgdacaqG4aGaaeOmaaaaaeaada qadaqaaiaabwgaaiaawIcacaGLPaaacaqGGaGaaeOnaiaabkdacaqG 1aGaaeiiaiabgEna0kaabccadaqadaqaaiabgkHiTiaabodacaqG1a aacaGLOaGaayzkaaGaaeiiaiabgUcaRiaabccadaqadaqaaiabgkHi TiaabccacaqG2aGaaeOmaiaabwdaaiaawIcacaGLPaaacaqGGaGaey 41aqRaaeiiaiaabAdacaqG1aaabaGaeyypa0JaeyOeI0IaaGOmaiaa igdacaaI4aGaaG4naiaaiwdacqGHRaWkdaqadaqaaiabgkHiTiaais dacaaIWaGaaGOnaiaaikdacaaI1aaacaGLOaGaayzkaaaabaGaeyyp a0ZaauIhaeaacqGHsislcaaI2aGaaGOmaiaaiwdacaaIWaGaaGimaa aaaeaaaeaadaqadaqaaiaabAgaaiaawIcacaGLPaaacaqGGaGaae4n aiaabccacqGHxdaTcaqGGaWaaeWaaeaacaqG1aGaaGimaiaabccacq GHsislcaqGGaGaaeOmaaGaayjkaiaawMcaaaqaaiabg2da9iaaiEda cqGHxdaTdaqadaqaaiaaisdacaaI4aaacaGLOaGaayzkaaaabaGaey ypa0ZaauIhaeaacaaIZaGaaG4maiaaiAdaaaaabaGaaiiOamaabmaa baGaae4zaaGaayjkaiaawMcaaiaabccadaqadaqaaiabgkHiTiaabg dacaqG3aaacaGLOaGaayzkaaGaaeiiaiabgEna0kaabccadaqadaqa aiabgkHiTiaabkdacaqG5aaacaGLOaGaayzkaaaabaGaeyypa0Zaau IhaeaacaaI0aGaaGyoaiaaiodaaaaabaWaaeWaaeaacaqGObaacaGL OaGaayzkaaGaaeiiamaabmaabaGaeyOeI0IaaeynaiaabEdaaiaawI cacaGLPaaacaqGGaGaey41aqRaaeiiamaabmaabaGaeyOeI0Iaaeym aiaabMdaaiaawIcacaGLPaaacaqGGaGaey4kaSIaaeiiaiaabwdaca qG3aaabaGaeyypa0JaaGymaiaaicdacaaI4aGaaG4maiabgUcaRiaa iwdacaaI3aaabaGaeyypa0ZaauIhaeaacaaIXaGaaGymaiaaisdaca aIWaaaaaaaaa@6377@

Q.20

i For any integer a, what is –1 × a equal to?ii Determine the integer whose product with –1 isa –22 b 37 c 0

Ans.

( i )( 1 )×a=a (ii) (a) 22 ×( 1 )=22 (b) 37 ×( 1 )=37 (c) 0 ×( 1 )=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabMgaaiaawIcacaGLPaaa caaMe8+aaeWaaeaacqGHsislcaqGXaaacaGLOaGaayzkaaGaey41aq Raaeyyaiaab2dacqGHsislcaqGHbaabaGaaeikaiaabMgacaqGPbGa aeykaiaabccacaqGOaGaaeyyaiaabMcacaqGGaWaauIhaeaacaaIYa GaaGOmaaaacqGHxdaTdaqadaqaaiabgkHiTiaaigdaaiaawIcacaGL PaaacqGH9aqpcqGHsislcaaIYaGaaGOmaaqaaiaabIcacaqGIbGaae ykaiaabccadaqjEaqaaiabgkHiTiaabodacaqG3aaaaiabgEna0oaa bmaabaGaeyOeI0IaaGymaaGaayjkaiaawMcaaiabg2da9iaaiodaca aI3aaabaGaaeikaiaabogacaqGPaGaaeiiamaaL4babaGaaeimaaaa cqGHxdaTdaqadaqaaiabgkHiTiaaigdaaiaawIcacaGLPaaacqGH9a qpcaaIWaaaaaa@7353@

Q.21

Starting from -1×5, write various products showing some pattern to show -1×-1=1

Ans.

1×5=5 1×4=4=5+1 1×3=3=4+1 1×2=2=3+1 1×1=1=2+1 1×0=0=1+1 Thus , 1×( 1 )=0+1=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacqGHsislcaaIXaGaey41aqRaaGynaiab g2da9iabgkHiTiaaiwdaaeaacqGHsislcaaIXaGaey41aqRaaGinai abg2da9iabgkHiTiaaisdacqGH9aqpcqGHsislcaaI1aGaey4kaSIa aGymaaqaaiabgkHiTiaaigdacqGHxdaTcaaIZaGaeyypa0JaeyOeI0 IaaG4maiabg2da9iabgkHiTiaaisdacqGHRaWkcaaIXaaabaGaeyOe I0IaaGymaiabgEna0kaaikdacqGH9aqpcqGHsislcaaIYaGaeyypa0 JaeyOeI0IaaG4maiabgUcaRiaaigdaaeaacqGHsislcaaIXaGaey41 aqRaaGymaiabg2da9iabgkHiTiaaigdacqGH9aqpcqGHsislcaaIYa Gaey4kaSIaaGymaaqaaiabgkHiTiaaigdacqGHxdaTcaaIWaGaeyyp a0JaaGimaiabg2da9iabgkHiTiaaigdacqGHRaWkcaaIXaaabaGaae ivaiaabIgacaqG1bGaae4CaiaabYcadaqjEaqaaiabgkHiTiaabgda cqGHxdaTdaqadaqaaiabgkHiTiaaigdaaiaawIcacaGLPaaacqGH9a qpcaaIWaGaey4kaSIaaGymaiabg2da9iaaigdaaaaaaaa@8D8E@

Q.22

Find the product, using suitable properties: a 26 × – 48 + – 48 × –36 b 8 × 53 × –125 c 15 × –25 × – 4 × –10 d – 41 × 102 e 625 × –35 + – 625 × 65 f 7 × 50 – 2 g –17 × –29 h –57 × –19 + 57

Ans.

( a ) 26 × ( 48 ) + ( 48 ) × ( 36 ) =( 48 )×26+( 48 )×( 36 ) =( 48 )[ 2636 ] =( 48 )[ 10 ] = 480 ( b ) 8 × 53 × ( 125 ) =424×( 125 ) = 53000 ( c ) 15 × ( 25 ) × ( 4 ) × ( 10 ) =( 15×25 )×( 4×10 ) =( 375 )×40 = 15000 ( d ) ( 41 ) × 102 = 4182 ( e ) 625 × ( 35 ) + ( 625 ) × 65 =21875+( 40625 ) = 62500 ( f ) 7 × ( 50 2 ) =7×( 48 ) = 336 ( g ) ( 17 ) × ( 29 ) = 493 ( h ) ( 57 ) × ( 19 ) + 57 =1083+57 = 1140 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa caqGGaGaaeOmaiaabAdacaqGGaGaey41aqRaaeiiamaabmaabaGaey OeI0IaaeiiaiaabsdacaqG4aaacaGLOaGaayzkaaGaaeiiaiabgUca RiaabccadaqadaqaaiabgkHiTiaabccacaqG0aGaaeioaaGaayjkai aawMcaaiaabccacqGHxdaTcaqGGaWaaeWaaeaacqGHsislcaqGZaGa aeOnaaGaayjkaiaawMcaaaqaaiabg2da9maabmaabaGaeyOeI0IaaG inaiaaiIdaaiaawIcacaGLPaaacqGHxdaTcaaIYaGaaGOnaiabgUca RmaabmaabaGaeyOeI0IaaGinaiaaiIdaaiaawIcacaGLPaaacqGHxd aTdaqadaqaaiabgkHiTiaaiodacaaI2aaacaGLOaGaayzkaaaabaGa eyypa0ZaaeWaaeaacqGHsislcaaI0aGaaGioaaGaayjkaiaawMcaam aadmaabaGaaGOmaiaaiAdacqGHsislcaaIZaGaaGOnaaGaay5waiaa w2faaaqaaiabg2da9maabmaabaGaeyOeI0IaaGinaiaaiIdaaiaawI cacaGLPaaadaWadaqaaiabgkHiTiaaigdacaaIWaaacaGLBbGaayzx aaaabaGaeyypa0ZaauIhaeaacaaI0aGaaGioaiaaicdaaaaabaWaae WaaeaacaqGIbaacaGLOaGaayzkaaGaaeiiaiaabIdacaqGGaGaey41 aqRaaeiiaiaabwdacaqGZaGaaeiiaiabgEna0kaabccadaqadaqaai abgkHiTiaabgdacaqGYaGaaeynaaGaayjkaiaawMcaaaqaaiabg2da 9iaaisdacaaIYaGaaGinaiabgEna0oaabmaabaGaeyOeI0IaaGymai aaikdacaaI1aaacaGLOaGaayzkaaaabaGaeyypa0ZaauIhaeaacaaI 1aGaaG4maiaaicdacaaIWaGaaGimaaaaaeaacaGGGcWaaeWaaeaaca qGJbaacaGLOaGaayzkaaGaaeiiaiaabgdacaqG1aGaaeiiaiabgEna 0kaabccadaqadaqaaiabgkHiTiaabkdacaqG1aaacaGLOaGaayzkaa GaaeiiaiabgEna0kaabccadaqadaqaaiabgkHiTiaabccacaqG0aaa caGLOaGaayzkaaGaaeiiaiabgEna0kaabccadaqadaqaaiabgkHiTi aabgdacaaIWaaacaGLOaGaayzkaaaabaGaeyypa0ZaaeWaaeaacaaI XaGaaGynaiabgEna0kabgkHiTiaaikdacaaI1aaacaGLOaGaayzkaa Gaey41aq7aaeWaaeaacqGHsislcaaI0aGaey41aqRaeyOeI0IaaGym aiaaicdaaiaawIcacaGLPaaaaeaacqGH9aqpdaqadaqaaiabgkHiTi aaiodacaaI3aGaaGynaaGaayjkaiaawMcaaiabgEna0kaaisdacaaI WaaabaGaeyypa0ZaauIhaeaacqGHsislcaaIXaGaaGynaiaaicdaca aIWaGaaGimaaaaaeaadaqadaqaaiaabsgaaiaawIcacaGLPaaacaqG GaWaaeWaaeaacqGHsislcaqGGaGaaeinaiaabgdaaiaawIcacaGLPa aacaqGGaGaey41aqRaaeiiaiaabgdacaaIWaGaaeOmaaqaaiabg2da 9maaL4babaGaeyOeI0IaaeinaiaabgdacaqG4aGaaeOmaaaaaeaada qadaqaaiaabwgaaiaawIcacaGLPaaacaqGGaGaaeOnaiaabkdacaqG 1aGaaeiiaiabgEna0kaabccadaqadaqaaiabgkHiTiaabodacaqG1a aacaGLOaGaayzkaaGaaeiiaiabgUcaRiaabccadaqadaqaaiabgkHi TiaabccacaqG2aGaaeOmaiaabwdaaiaawIcacaGLPaaacaqGGaGaey 41aqRaaeiiaiaabAdacaqG1aaabaGaeyypa0JaeyOeI0IaaGOmaiaa igdacaaI4aGaaG4naiaaiwdacqGHRaWkdaqadaqaaiabgkHiTiaais dacaaIWaGaaGOnaiaaikdacaaI1aaacaGLOaGaayzkaaaabaGaeyyp a0ZaauIhaeaacqGHsislcaaI2aGaaGOmaiaaiwdacaaIWaGaaGimaa aaaeaadaqadaqaaiaabAgaaiaawIcacaGLPaaacaqGGaGaae4naiaa bccacqGHxdaTcaqGGaWaaeWaaeaacaqG1aGaaGimaiaabccacqGHsi slcaqGGaGaaeOmaaGaayjkaiaawMcaaaqaaiabg2da9iaaiEdacqGH xdaTdaqadaqaaiaaisdacaaI4aaacaGLOaGaayzkaaaabaGaeyypa0 ZaauIhaeaacaaIZaGaaG4maiaaiAdaaaaabaGaaiiOamaabmaabaGa ae4zaaGaayjkaiaawMcaaiaabccadaqadaqaaiabgkHiTiaabgdaca qG3aaacaGLOaGaayzkaaGaaeiiaiabgEna0kaabccadaqadaqaaiab gkHiTiaabkdacaqG5aaacaGLOaGaayzkaaaabaGaeyypa0ZaauIhae aacaaI0aGaaGyoaiaaiodaaaaabaWaaeWaaeaacaqGObaacaGLOaGa ayzkaaGaaeiiamaabmaabaGaeyOeI0IaaeynaiaabEdaaiaawIcaca GLPaaacaqGGaGaey41aqRaaeiiamaabmaabaGaeyOeI0Iaaeymaiaa bMdaaiaawIcacaGLPaaacaqGGaGaey4kaSIaaeiiaiaabwdacaqG3a aabaGaeyypa0JaaGymaiaaicdacaaI4aGaaG4maiabgUcaRiaaiwda caaI3aaabaGaeyypa0ZaauIhaeaacaaIXaGaaGymaiaaisdacaaIWa aaaaaaaa@6376@

Q.23

A certain freezing process requires that room temperaturebe lowered from 40°C at the rate of 5°C every hour. What willbe the room temperature 10 hours after the process begins?

Ans.

Given initial temprature=40°C Change in temprature per hour =5°C Change in temprature after 10 hours=5°C×10=50°C Final temprature=40°C50°C= 10°C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGhbGaaeyAaiaabAhacaqGLbGaaeOB aiaabccacaqGPbGaaeOBaiaabMgacaqG0bGaaeyAaiaabggacaqGSb GaaeiiaiaabshacaqGLbGaaeyBaiaabchacaqGYbGaaeyyaiaabsha caqG1bGaaeOCaiaabwgacqGH9aqpcaaI0aGaaGimaiabgclaWkaado eaaeaacaqGdbGaaeiAaiaabggacaqGUbGaae4zaiaabwgacaqGGaGa aeyAaiaab6gacaqGGaGaaeiDaiaabwgacaqGTbGaaeiCaiaabkhaca qGHbGaaeiDaiaabwhacaqGYbGaaeyzaiaabccacaqGWbGaaeyzaiaa bkhacaqGGaGaaeiAaiaab+gacaqG1bGaaeOCaiaabccacqGH9aqpcq GHsislcaaI1aGaeyiSaaRaam4qaaqaaiaaboeacaqGObGaaeyyaiaa b6gacaqGNbGaaeyzaiaabccacaqGPbGaaeOBaiaabccacaqG0bGaae yzaiaab2gacaqGWbGaaeOCaiaabggacaqG0bGaaeyDaiaabkhacaqG LbGaaeiiaiaabggacaqGMbGaaeiDaiaabwgacaqGYbGaaeiiaiaabg dacaqGWaGaaeiiaiaabIgacaqGVbGaaeyDaiaabkhacaqGZbGaeyyp a0JaeyOeI0IaaGynaiabgclaWkaadoeacqGHxdaTcaaIXaGaaGimai abg2da9iabgkHiTiaaiwdacaaIWaGaeyiSaaRaam4qaaqaaiaabAea caqGPbGaaeOBaiaabggacaqGSbGaaeiiaiaabshacaqGLbGaaeyBai aabchacaqGYbGaaeyyaiaabshacaqG1bGaaeOCaiaabwgacqGH9aqp caaI0aGaaGimaiabgclaWkaadoeacqGHsislcaaI1aGaaGimaiabgc laWkaadoeacqGH9aqpdaqjEaqaaiabgkHiTiaaigdacaaIWaGaeyiS aaRaam4qaaaaaaaa@C4D0@

Q.24

In a class test containing 10 questions, 5 marks areawarded for every correct answer and -2 marks areawarded forevery incorrect answer and 0 for questionsnot attempted. i Mohan gets four correct and six incorrect answers.What is his score? ii Reshma gets five correct answers and five incorrectanswers, what is her score? iii Heena gets two correct and five incorrect answersout of seven questions she attempts. What is her score?

Ans.

(i)Marks given for 1 correct answer =5Marks given for 4 correct answer =5×4=20Marks given for 1 wrong answer =2Marks given for 6 wrong answer =2×6=12Score obtained by Mohan =2012=8(ii)Marks given for 1 correct answer =5Marks given for 5 correct answer =5×5=25Marks given for 1 wrong answer =2Marks given for 5 wrong answer =2×5=10Scored obtained by Reshma=2510=15(iii) Similarly, Marks given for 2 correct answer =5×2Marks given for 5 correct answer =2×5=10Score btained by Heena =1010=0

Q.25

A cement company earns a profit of ₹ 8 per bag of whitecement sold and a loss of ₹ 5 per bag of grey cement sold.

a The company sells 3,000 bags of white cement and 5,000bags of grey cement in a month. What is its profit or loss? b What is the number of white cement bags it must sell tohave neither profit nor loss, if the number of grey bags soldis 6,400 bags.

Ans.

(a) Profit earned while selling 1 bag of white cement = 8 Profit earned while selling 3000 bag of white cement = 8×3000=24000 Loss incurred while selling 1 bag of grey cement = 5 Loss incurred while selling 5000 bag of grey cement = 5×5000=25000 Total profit/loss earned = Profit+loss =2400025000=1000 Thus, there will be a loss of 1000 to the company. (b) Loss incurred while selling 1 bag of grey cement = 5 Loss incurred while selling 6400 bag of grey cement = 5×6400=32000 Let the number of white bag to be sold be x. Profit earned selling 1 bag of white cement = 8 Profit earned selling x bag of white cement = 8x When there is no profit or no loss, we have Profit earned + Loss incurred = 0 8x32000=0 8x=32000 x= 32000 8 = 4000 Thus,4000bags of white cement should be sold. 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Q.26

Replace the blank with an integer to make it a truestatement. a 3 × _____ = 27 b 5 × _____ = -35c _____ × 8 = 56d _____ × 12 = 132

Ans.

( a ) ( –3 ) × –9 _ = 27 ( b ) 5 × –7 _ = –35 ( c ) 7 _ × ( –8 ) = –56 ( d ) –11 _ × ( –12 ) = 132 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa caqGGaWaaeWaaeaacaqGtaIaae4maaGaayjkaiaawMcaaiaabccaca qGxdGaaeiiamaamaaabaWaauIhaeaacaqGtaIaaeyoaaaaaaGaaeii aiaab2dacaqGGaGaaeOmaiaabEdacaqGGaaabaWaaeWaaeaacaqGIb aacaGLOaGaayzkaaGaaeiiaiaaysW7caqG1aGaaeiiaiaabEnacaqG GaWaaWaaaeaadaqjEaqaaiaabobicaqG3aaaaaaacaqGGaGaaeypai aabccacaqGtaIaae4maiaabwdaaeaadaqadaqaaiaabogaaiaawIca caGLPaaacaaMe8UaaGjbVpaamaaabaWaauIhaeaacaqG3aaaaaaaca qGGaGaae41aiaabccadaqadaqaaiaabobicaqG4aaacaGLOaGaayzk aaGaaeiiaiaab2dacaqGGaGaae4eGiaabwdacaqG2aaabaWaaeWaae aacaqGKbaacaGLOaGaayzkaaGaaGjbVlaaysW7daadaaqaamaaL4ba baGaae4eGiaabgdacaqGXaaaaaaacaqGGaGaae41aiaabccadaqada qaaiaabobicaqGXaGaaeOmaaGaayjkaiaawMcaaiaabccacaqG9aGa aeiiaiaabgdacaqGZaGaaeOmaaaaaa@7C82@

Q.27

Evaluate each of the following:(a)(30)÷10(b)50÷(5)(c)(36)÷(9)(d)(49)÷(49)(e)13÷[(2)+1](f)0÷(12)(g)(31)÷[(30)+(1)](h)[(36)÷12]÷3(i)[(6)+5)]÷[(2)+1]

Ans.

( a ) ( 30 ) ÷ 10= 3 ( b ) 50 ÷ ( 5 )= 10 ( c ) ( 36 ) ÷ ( 9 )= 4 ( d ) ( 49 ) ÷ ( 49 )= 1 ( e ) 13 ÷ [ ( 2 ) + 1 ]=13÷[ 1 ]= 13 ( f ) 0 ÷ ( 12 )= 0 ( g ) ( 31 ) ÷ [ ( 30 ) + ( 1 ) ]=( 31 )÷[ 31 ]= 1 ( h ) [ ( 36 ) ÷ 12 ] ÷ 3=[ 3 ]÷3= 1 ( i )[ ( 6 ) + 5 )] ÷ [( 2 ) + 1]=[ 1 ]÷[ 1 ]= 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa caqGGaWaaeWaaeaacqGHsislcaqGZaGaaGimaaGaayjkaiaawMcaai aabccacqGH3daUcaqGGaGaaeymaiaaicdacqGH9aqpdaqjEaqaaiab gkHiTiaaiodaaaaabaWaaeWaaeaacaqGIbaacaGLOaGaayzkaaGaae iiaiaabwdacaaIWaGaaeiiaiabgEpa4kaabccadaqadaqaaiabgkHi TiaabwdaaiaawIcacaGLPaaacqGH9aqpdaqjEaqaaiabgkHiTiaaig dacaaIWaaaaaqaamaabmaabaGaae4yaaGaayjkaiaawMcaaiaabcca daqadaqaaiabgkHiTiaabodacaqG2aaacaGLOaGaayzkaaGaaeiiai abgEpa4kaabccadaqadaqaaiabgkHiTiaabMdaaiaawIcacaGLPaaa cqGH9aqpdaqjEaqaaiaaisdaaaaabaWaaeWaaeaacaqGKbaacaGLOa GaayzkaaGaaeiiamaabmaabaGaeyOeI0IaaeiiaiaabsdacaqG5aaa caGLOaGaayzkaaGaaeiiaiabgEpa4kaabccadaqadaqaaiaabsdaca qG5aaacaGLOaGaayzkaaGaeyypa0ZaauIhaeaacqGHsislcaaIXaaa aaqaamaabmaabaGaaeyzaaGaayjkaiaawMcaaiaabccacaqGXaGaae 4maiaabccacqGH3daUcaqGGaWaamWaaeaadaqadaqaaiabgkHiTiaa bkdaaiaawIcacaGLPaaacaqGGaGaey4kaSIaaeiiaiaabgdaaiaawU facaGLDbaacqGH9aqpcaaIXaGaaG4maiabgEpa4oaadmaabaGaeyOe I0IaaGymaaGaay5waiaaw2faaiabg2da9maaL4babaGaeyOeI0IaaG ymaiaaiodaaaaabaWaaeWaaeaacaqGMbGaaeiiaaGaayjkaiaawMca aiaabccacaaIWaGaaeiiaiabgEpa4kaabccadaqadaqaaiabgkHiTi aabgdacaqGYaaacaGLOaGaayzkaaGaeyypa0ZaauIhaeaacaaIWaaa aaqaaiaacckadaqadaqaaiaabEgaaiaawIcacaGLPaaacaqGGaWaae WaaeaacqGHsislcaqGZaGaaeymaaGaayjkaiaawMcaaiaabccacqGH 3daUcaqGGaWaamWaaeaadaqadaqaaiabgkHiTiaabodacaaIWaaaca GLOaGaayzkaaGaaeiiaiabgUcaRiaabccadaqadaqaaiabgkHiTiaa bgdaaiaawIcacaGLPaaaaiaawUfacaGLDbaacqGH9aqpdaqadaqaai abgkHiTiaaiodacaaIXaaacaGLOaGaayzkaaGaey49aG7aamWaaeaa cqGHsislcaaIZaGaaGymaaGaay5waiaaw2faaiabg2da9maaL4baba GaaGymaaaaaeaacaGGGcWaaeWaaeaacaqGObaacaGLOaGaayzkaaGa aeiiamaadmaabaWaaeWaaeaacqGHsislcaqGZaGaaeOnaaGaayjkai aawMcaaiaabccacqGH3daUcaqGGaGaaeymaiaabkdaaiaawUfacaGL DbaacaqGGaGaey49aGRaaeiiaiaabodacaqG9aWaamWaaeaacqGHsi slcaaIZaaacaGLBbGaayzxaaGaey49aGRaaG4maiabg2da9maaL4ba baGaeyOeI0IaaGymaaaaaeaadaqadaqaaiaabMgaaiaawIcacaGLPa aadaqcsaqaamaabmaabaGaeyOeI0IaaeiiaiaabAdaaiaawIcacaGL PaaacaqGGaGaey4kaSIaaeiiaiaabwdaaiaawUfacaGLPaaadaqcJa qaaiaabccacqGH3daUcaqGGaaacaGLDbGaay5waaWaaeWaaeaacqGH sislcaqGYaaacaGLOaGaayzkaaGaaeiiaiabgUcaRiaabccacaqGXa Gaaiyxaiabg2da9maadmaabaGaeyOeI0IaaGymaaGaay5waiaaw2fa aiabgEpa4oaadmaabaGaeyOeI0IaaGymaaGaay5waiaaw2faaiabg2 da9maaL4babaGaaGymaaaaaaaa@0B6D@

Q.28

Verify that a÷b+c¹a÷b+a÷c for each of thefollowing.values of a, b and c.(a) a=12, b=-4, c=2(b) a=(-10), b=1, c=1

Ans.

(a)a=12,b=4,c=2a÷(b+c)=12÷(4+2)=12÷(2)=6and(a÷b)+(a÷c)=(12÷(4))+(12÷2)=(3)+6=3So,a÷(b+c)(a÷b)+(a÷c)(b)a=10,b=1,c=1a÷(b+c)=10÷(1+1)=10÷(2)=5and(a÷b)+(a÷c)=(10÷1)+(10÷1)=(10)10=20So,a÷(b+c)(a÷b)+(a÷c)

Q.29

Fill in the blanks: a 369 ÷ _____ = 369 b–75 ÷ _____ = –1c–206 ÷ _____ = 1 d – 87 ÷ _____ = 87e _____ ÷ 1 = – 87 f _____ ÷ 48 = –1g 20 ÷ _____ = –2 h _____ ÷ 4 = –3

Ans.

( a ) 369 ÷ 1 _ = 369 ( b ) ( 75 ) ÷ 75 _ = 1 ( c ) ( 206 ) ÷ 206 _ = 1 ( d )87 ÷ 1 _ = 87 ( e ) 87 _ ÷ 1 = 87 ( f ) 48 _ ÷ 48 = 1 ( g ) 20 ÷ 10 _ _ = 2 ( h ) 12 _ ÷ ( 4 ) = 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa caqGGaGaae4maiaabAdacaqG5aGaaeiiaiabgEpa4kaabccadaadaa qaamaaL4babaGaaGymaaaaaaGaaeiiaiabg2da9iaabccacaqGZaGa aeOnaiaabMdaaeaadaqadaqaaiaabkgaaiaawIcacaGLPaaacaqGGa WaaeWaaeaacqGHsislcaqG3aGaaeynaaGaayjkaiaawMcaaiaabcca cqGH3daUcaqGGaWaaWaaaeaadaqjEaqaaiaaiEdacaaI1aaaaaaaca qGGaGaeyypa0JaaeiiaiabgkHiTiaabgdaaeaadaqadaqaaiaaboga aiaawIcacaGLPaaacaqGGaWaaeWaaeaacqGHsislcaqGYaGaaGimai aabAdaaiaawIcacaGLPaaacaqGGaGaey49aGRaaeiiamaamaaabaWa auIhaeaacqGHsislcaaIYaGaaGimaiaaiAdaaaaaaiaabccacqGH9a qpcaqGGaGaaeymaaqaamaabmaabaGaaeizaaGaayjkaiaawMcaaiab gkHiTiaabIdacaqG3aGaaeiiaiabgEpa4kaabccadaadaaqaamaaL4 babaGaeyOeI0IaaGymaaaaaaGaaeiiaiabg2da9iaabccacaqG4aGa ae4naaqaamaabmaabaGaaeyzaaGaayjkaiaawMcaaiaabccadaadaa qaamaaL4babaGaeyOeI0IaaGioaiaaiEdaaaaaaiaabccacqGH3daU caqGGaGaaeymaiaabccacqGH9aqpcaqGGaGaeyOeI0IaaeioaiaabE daaeaadaqadaqaaiaabAgaaiaawIcacaGLPaaacaqGGaWaaWaaaeaa daqjEaqaaiabgkHiTiaaisdacaaI4aaaaaaacaqGGaGaey49aGRaae iiaiaabsdacaqG4aGaaeiiaiabg2da9iaabccacqGHsislcaqGXaaa baGaaiiOamaabmaabaGaae4zaaGaayjkaiaawMcaaiaabccacaqGYa GaaGimaiaabccacqGH3daUcaqGGaWaaWaaaeaadaadaaqaamaaL4ba baGaeyOeI0IaaGymaiaaicdaaaaaaaaacaqGGaGaeyypa0Jaaeiiai abgkHiTiaabkdaaeaadaqadaqaaiaabIgaaiaawIcacaGLPaaacaqG GaWaaWaaaeaadaqjEaqaaiabgkHiTiaaigdacaaIYaaaaaaacaqGGa Gaey49aGRaaeiiamaabmaabaGaaeinaaGaayjkaiaawMcaaiaabcca cqGH9aqpcaqGGaGaeyOeI0Iaae4maaaaaa@B867@

Q.30

Write five pairs of integers a,b such that a÷b =3. Onesuch pair is 6, 2 because 6÷2 =3.

Ans.

Five pair of integers are: ( 3,1 ),( 3,1 ),( 9,3 ),( 9,3 )and( 12,4 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGgbGaaeyAaiaabAhacaqGLbGaaeii aiaabchacaqGHbGaaeyAaiaabkhacaqGGaGaae4BaiaabAgacaqGGa GaaeyAaiaab6gacaqG0bGaaeyzaiaabEgacaqGLbGaaeOCaiaaboha caqGGaGaaeyyaiaabkhacaqGLbGaaeOoaaqaamaaL4babaWaaeWaae aacaaIZaGaaiilaiabgkHiTiaaigdaaiaawIcacaGLPaaacaGGSaGa aGjbVpaabmaabaGaeyOeI0IaaG4maiaacYcacaaIXaaacaGLOaGaay zkaaGaaiilaiaaysW7daqadaqaaiaaiMdacaGGSaGaeyOeI0IaaG4m aaGaayjkaiaawMcaaiaacYcacaaMe8+aaeWaaeaacqGHsislcaaI5a GaaiilaiaaiodaaiaawIcacaGLPaaacaaMe8Uaaeyyaiaab6gacaqG KbGaaGjbVpaabmaabaGaaGymaiaaikdacaGGSaGaeyOeI0IaaGinaa GaayjkaiaawMcaaaaaaaaa@78A9@

Q.31

The temperature at 12 noon was 10°C above zero. If itdecreases at the rate of 2°C per hour until midnight, atwhat time would the temperature be 8°C below zero?What would be the temperature at mid-night?

Ans.

Initial temprature =10°C Change in temprature per hour=2°C Temprature at 1:00 PM=10°C+( 2°C )=8°C Temprature at 2:00 PM=8°C+( 2°C )=6°C Temprature at 3:00 PM=6°C+( 2°C )=4°C Temprature at 4:00 PM=4°C+( 2°C )=2°C Temprature at 5:00 PM=2°C+( 2°C )=0°C Temprature at 6:00 PM=0°C+( 2°C )=2°C Temprature at 7:00 PM=2°C+( 2°C )=4°C Temprature at 8:00 PM=4°C+( 2°C )=6°C Temprature at 9:00 PM=6°C+( 2°C )=8°C Thus, the temprature will be 8°C below zero at 9:00PM It will take 12 hours to be midnight (i.e. 12:00 AM) after 12:00 noon. Change in temprature in 12 hours = 2°C×12=24°C At midnight the temprature would be =10+( 24 )=14°C Thus, the temprature at midnight will be 14°Cbelow0 . 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Q.32

In a class test + 3 marks are given for every correctanswer and -2 marks are given for every incorrectanswer and no marks for not attempting any question. i Radhika scored 20 marks. If she has got 12 correctanswers, how many questions has she attemptedincorrectly? ii Mohini scores -5 marks in this test, though she hasgot 7 correct answers. How many questions has sheattempted incorrectly? iii Rakesh scores 18 marks by attempting 16 questions.How many questions has he attempted correctly and howmany has he attempted incorrectly?

Ans.

Marks obtained for 1 right answer=+3 Marks obtained for 1 wrong answer=2 (i) Marks obtained by Radhika=20 Marks obtained for 12 correct answers=12×3=36 Marks obtained for incorrect answer=Total score-Marks obtained for 12 correct answers =20-36=–16 Marks obtained for 1 wrong answer=-2 Thus, number of incorrect answer=( 16 )÷( 2 )= 8 Thus, Radhika attempted 8 questions wrongly. (ii) Marks scored by Mohini=-5 Marks obtained for incorrect answers =Total answer-Marks obtained for 12 incorrect answer =521=26 Marks obtained for 1 wrong answer=-2 Thus, number of incorrect answer=( 26 )÷( 2 )= 13 Therefore, Mohini attempted 13 questions wrongly. (iii) Total marks scored by Rakesh =18 Number of questions attempted =16 ( Number of correct answers )( 3 ) +( Number of incorrect answers )( 2 )=18 ( Number of correct answers )( 5 )+( 32 )=18 ( Number of correct answers )= 50 5 =10 So,( Number of incorrect answers )=1610=6 Thus, Total number of correct and incorrect answers scored by Rakesh is 10 and 6 respectively. 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Q.33

An elevator descends into a mine shaft at the rateof 6 m/min. If the descent startsfrom 10 m abovethe ground level,how long will it take to reach – 350​ m.

Ans.

Distance descended is denoted by a negative integer. Initial height=+10 m Final depth =350 m Total distance to be descended by the elevator= ( 350 )( +10 )=360m Timetaken by the elevator to be descend 6 m = 1 min Thus, time taken by the elevator to descend 360 m = ( 360 )÷( 6 )= 60minutes=1hour MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGebGaaeyAaiaabohacaqG0bGaaeyy aiaab6gacaqGJbGaaeyzaiaabccacaqGKbGaaeyzaiaabohacaqGJb Gaaeyzaiaab6gacaqGKbGaaeyzaiaabsgacaqGGaGaaeyAaiaaboha caqGGaGaaeizaiaabwgacaqGUbGaae4BaiaabshacaqGLbGaaeizai aabccacaqGIbGaaeyEaiaabccacaqGHbGaaeiiaiaab6gacaqGLbGa ae4zaiaabggacaqG0bGaaeyAaiaabAhacaqGLbGaaeiiaiaabMgaca qGUbGaaeiDaiaabwgacaqGNbGaaeyzaiaabkhacaqGUaaabaGaaeys aiaab6gacaqGPbGaaeiDaiaabMgacaqGHbGaaeiBaiaabccacaqGOb GaaeyzaiaabMgacaqGNbGaaeiAaiaabshacqGH9aqpcqGHRaWkcaaI XaGaaGimaiaabccacaqGTbaabaGaaeOraiaabMgacaqGUbGaaeyyai aabYgacaqGGaGaaeizaiaabwgacaqGWbGaaeiDaiaabIgacaqGGaGa eyypa0JaeyOeI0IaaG4maiaaiwdacaaIWaGaaeiiaiaab2gaaeaaca qGubGaae4BaiaabshacaqGHbGaaeiBaiaabccacaqGKbGaaeyAaiaa bohacaqG0bGaaeyyaiaab6gacaqGJbGaaeyzaiaabccacaqG0bGaae 4BaiaabccacaqGIbGaaeyzaiaabccacaqGKbGaaeyzaiaabohacaqG JbGaaeyzaiaab6gacaqGKbGaaeyzaiaabsgacaqGGaGaaeOyaiaabM hacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabwgacaqGSbGaaeyz aiaabAhacaqGHbGaaeiDaiaab+gacaqGYbGaeyypa0Jaaeiiamaabm aabaGaeyOeI0IaaG4maiaaiwdacaaIWaaacaGLOaGaayzkaaGaeyOe I0YaaeWaaeaacqGHRaWkcaaIXaGaaGimaaGaayjkaiaawMcaaiabg2 da9iabgkHiTiaaiodacaaI2aGaaGimaiaaysW7caqGTbaabaGaaeiv aiaabMgacaqGTbGaaeyzaiaaysW7caqG0bGaaeyyaiaabUgacaqGLb GaaeOBaiaabccacaqGIbGaaeyEaiaabccacaqG0bGaaeiAaiaabwga caqGGaGaaeyzaiaabYgacaqGLbGaaeODaiaabggacaqG0bGaae4Bai aabkhacaqGGaGaaeiDaiaab+gacaqGGaGaaeOyaiaabwgacaqGGaGa aeizaiaabwgacaqGZbGaae4yaiaabwgacaqGUbGaaeizaiaabccacq GHsislcaqG2aGaaeiiaiaab2gacaqGGaGaeyypa0Jaaeiiaiaabgda caqGGaGaaeyBaiaabMgacaqGUbaabaGaaeivaiaabIgacaqG1bGaae 4CaiaabYcacaqGGaGaaeiDaiaabMgacaqGTbGaaeyzaiaabccacaqG 0bGaaeyyaiaabUgacaqGLbGaaeOBaiaabccacaqGIbGaaeyEaiaabc cacaqG0bGaaeiAaiaabwgacaqGGaGaaeyzaiaabYgacaqGLbGaaeOD aiaabggacaqG0bGaae4BaiaabkhacaqGGaGaaeiDaiaab+gacaqGGa GaaeizaiaabwgacaqGZbGaae4yaiaabwgacaqGUbGaaeizaiaabcca cqGHsislcaqGZaGaaeOnaiaabcdacaqGGaGaaeyBaiaabccacaqG9a GaaeiiamaabmaabaGaeyOeI0IaaG4maiaaiAdacaaIWaaacaGLOaGa ayzkaaGaey49aG7aaeWaaeaacqGHsislcaaI2aaacaGLOaGaayzkaa Gaeyypa0ZaauIhaeaacaaI2aGaaGimaiaaysW7caqGTbGaaeyAaiaa b6gacaqG1bGaaeiDaiaabwgacaqGZbGaaGjbVlabg2da9iaaigdaca aMe8UaaeiAaiaab+gacaqG1bGaaeOCaaaaaaaa@3FB3@

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FAQs (Frequently Asked Questions)
1. How many exercises are included in the NCERT Solutions for Class 7 Mathematics Chapter 1?

There are four exercises in Class 7 Mathematics Chapter 1 Integers.  

The first exercise consists of ten questions (Ex 1.1). 

The second exercise consists of four questions (Ex 1.2). Question 1 is divided into three sections, question 2 is divided into three sections, and question 4 is divided into five sections.

There are 9 questions in the third exercise (Ex 1.3). Question 2 is made up of two parts, question 3 is made up of two parts, and question 5 is made up of eight parts.

There are seven questions in the fourth exercise (Ex 1.4). Question 1 is divided into nine parts, while question 2 is divided into two parts.

As a result, there are a total of 30 questions in Chapter 1 (Integers) of Class 7 Mathematics.

In the CBSE Class 7 Mathematics Integers Chapter, there are a total of seven exercises.

2. Is it necessary to complete all of the problems in Chapter 1 of the NCERT Solution for Class 7 Mathematics?

Definitely! Because these questions are important from the examination point of view. . Subject matter experts have answered these questions to assist students in completing the exercise with ease.  These NCERT Solutions assist students by encouraging them to become better learners and strive to feed their insatiable curiosity.

3. How long will it take to finish NCERT Class 7 Mathematics Chapter 1?

It takes about a week to complete the NCERT Class 7 Mathematics Chapter 1, but we recommend that you practice , again and again, to significantly improve your performance.

4. Is Class 7 Mathematics chapter Integers difficult?

It is neither easy nor difficult to complete 7th Class Mathematics Chapter 1. Because some parts of this chapter are easy and others are difficult, it falls somewhere in between easy and difficult. The difficulty level of each chapter, however, varies from student to student. As a result, whether the chapter is easy or difficult depends on the individual. Some students find it difficult, while others may find it easy.

5. What are the advantages of using NCERT Solutions Class 7 Mathematics?

Because the CBSE syllabus is based on the NCERT textbooks, NCERT solutions Class 7 Mathematics assist CBSE students in preparing for their exams.  Moreover, these solutions instil a deep understanding of the subject and assist students in resolving their doubts while solving problems and motivates them to improve their performance and stay ahead of the competition.