Mathematics Part1

Online MCQs about First Year Mathematics Part1 and Part2, Intermediate Mathematics Part1 multiple choice questions with answers

Number System Quiz 2

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The Post is about the Number System Quiz from Mathematics of Intermediate Part-I (First Year). There are 20 multiple-choice questions about the Number System. Let us start with the Online Number System Quiz with Answers.

MCQs Mathematics covering the topic of the Number system for the preparation of Intermediate mathematics.

1. For $a,b,c \in R$, $a=b\Rightarrow ac=bc$, then it is _______ property

 
 
 
 

2. For $a,b,c \in R$, $a=b \Rightarrow a+c=b+c$, then it is ______ property

 
 
 
 

3. For $a,b,c \in R$, and $a>b, b>c \Rightarrow a>c$, then it is ________ property

 
 
 
 

4. If $ a < b $ then

 
 
 
 

5. If $n$ is an even integer, then $(i)^n$ is equal to

 
 
 
 

6. If $a$ is any non-zero real number, then its multiplicative inverse is

 
 
 
 

7. For $a,b,c \in R$, if $a>b$ and $c<0$, then

 
 
 
 

8. For $a,b,c \in R$ if $a=b, b=c \Rightarrow a=c$, then it is ______ property

 
 
 
 

9. If $n$ is an odd number then $(i)^n$ is equal to

 
 
 
 

10. For all $a,b \in R$, $a=b \Rightarrow b=a$ is called ________ property

 
 
 
 

11. If $\frac{a}{b}=\frac{ka}{kb}$, $k\ne 0$, this rule is called

 
 
 
 

12. For all $a\in R$, $a=a$ is ____________ property

 
 
 
 

13. For $a,b,c \in R$, $a+c=b+c \Rightarrow a=b$, then it is ______ property

 
 
 
 

14. For $a,b,c \in R$, if $a<b$ and $c>0$, then which one is true

 
 
 
 

15. $a(b+c-d)=ab+ac-ad$ is _______ property

 
 
 
 

16. The multiplicative inverse of 0 is

 
 
 
 

17. If $n$ is an integral multiple of 4, then $(i)^n$ is equal to

 
 
 
 

18. The set $\{1\}$ has closure property with respect to

 
 
 
 

19. If $a>0$ and $b<0$, then

 
 
 
 

20. The set $\{1,-1\}$ is closed with respect to

 
 
 
 

A numeral system is a way of expressing numbers; that is, it is a mathematical writing system or notation used to represent the numbers of a given set consistently by using either digits or other symbols. The same sequence of symbols may represent different numbers in different numeral systems.

Number System Quiz

Number System as Decimal System

The commonly used number system is the decimal positional numeral system. The decimal refers to 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to construct all numbers.

In mathematics courses you have heard about number systems of whole numbers and real numbers, however, in the context of computer systems, the other types of number systems are (i) The decimal number system, (ii) The binary number system, (iii) The octal number system and, (iv) The hexadecimal number system.

MCQs Number System Quiz

  • The multiplicative inverse of 0 is
  • If $a$ is any non-zero real number, then its multiplicative inverse is
  • For all $a\in R$, $a=a$ is _________ property
  • For all $a,b \in R$, $a=b \Rightarrow b=a$ is called property
  • For $a,b,c \in R$ if $a=b, b=c \Rightarrow a=c$, then it is property
  • For $a,b,c \in R$, $a=b \Rightarrow a+c=b+c$, then it is property
  • For $a,b,c \in R$, $a+c=b+c \Rightarrow a=b$, then it is property
  • For $a,b,c \in R$, $a=b\Rightarrow ac=bc$, then it is _ property
  • For $a,b,c \in R$, and $a>b, b>c \Rightarrow a>c$, then it is property
  • For $a,b,c \in R$, if $a0$, then which one is true
  • For $a,b,c \in R$, if $a>b$ and $c<0$, then If $a>0$ and $b<0$, then
  • The set ${1,-1}$ is closed with respect to
  • The set ${1}$ has closure property with respect to
  • $a(b+c-d)=ab+ac-ad$ is property
  • If $ a < b $ then
  • If $\frac{a}{b}=\frac{ka}{kb}$, $k\ne 0$, this rule is called
  • If $n$ is an even integer, then $(i)^n$ is equal to
  • If $n$ is an odd number then $(i)^n$ is equal to
  • If $n$ is an integral multiple of 4, then $(i)^n$ is equal to

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Number System: Complete Guide

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Introduction to Number System

In early civilizations, the number of animals (sheep, goats, camels, etc.) or children people had was tracked by using different methods such as people matching the number of animals with the number of stones. Similarly, they count the number of children with the number of notches tied on a string or marks on a piece of wood, leather, or wall. With the development of humans, other uses for numerals were found and this led to the invention of the number system.

Commonly used Number System

The commonly used number system is the decimal positional numeral system. The decimal refers to 10 symbols: $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ to construct all numbers.

Number System: Real Number Line

Natural Numbers

Natural numbers are used to count the number of subjects or objects. Natural numbers are also called counting numbers. The numbers $1, 2, 3, \cdots$ are all natural numbers.

Whole Numbers

The numbers $0, 1, 2, \cdots$ are called whole numbers. It can be observed that whole numbers except $0$ are natural numbers.

Number Line

Whole numbers can be represented by points on a line called the number line. For this purpose, a straight line is drawn and a point is chosen on the line and labeled as $0$. Starting with $0$, mark off equal intervals of any suitable length. Marked points are labeled as $1, 2, \cdots$ as shown in Figure below. The figure below represents real numbers since it includes the negative number (numbers on the left of $0$ in this diagram are called negative numbers).

The arrow on the extreme (right-hand side in case of while numbers or negative numbers) indicates that the list of numbers continues in the same way indefinitely.

A whole number can be even or odd. An even number is a number that can be divided by 2 without leaving any remainder. The numbers $0, 2, 4, 6, 8, \cdots$ are all even numbers. An odd number is a number which cannot be divided by 2 without leaving any remainder. The numbers $1, 3, 5, 7, 9, \cdots$ are all odd.

It is interesting to know that any two numbers can be added in any order and it will not affect the results. For example, $3+5 = 5+3$. This is called the commutative law of addition. Similarly, the order of grouping the numbers does not affect the result. For example, $2+3+5=(2+3)+5 = 2+ (3+5)=(2+5)+3$. This is called the associative law of addition. The subtraction and division of numbers are not commutative as $5-7\ne7-5$ and $6\div2 \ne 2\div 6$ in general.

Like addition and multiplication, whole numbers also follow commutative law and it is called commutative law of multiplication, for example, $2\times 8 = 8 \times 2$. Like addition and multiplication, whole numbers also follow the associative law of multiplications. For example, $2 \times (3 \times 4) = (2 \times 3) \times 4 =  (2 \times 4)\times 3$. Similarly, multiplication is distributive over addition and subtraction, for example, (i) $5\times (6 + 7) = (5 \times 6) + (5 \times 7)$ or $(6+7) \times 5=(6 \times 5)+(7 \times 5)$. (ii) $3 \times (6-2) = (3 \times 6) – (3 \times 2)$ or $(6-2) \times 3 = (6 \times 3) – (2 \times 3)$.

Take any two-digit number say 57, and reverse the digits to obtain 75. Now subtract the smaller number from the bigger number, we have $75-57=18$. Now reverse the digits of 18 and add 18 to its reverse (81), that is, $18+81$, and you will get 99.

Statistics and Data Analysis

Online MCQs Number System