Number System Quizzes

Online MCQs from Chapter 1 Number System of Intermediate Mathematics with Questions and Answers

Number System Test 3

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The Post is about the Number System Test from Mathematics of Intermediate Part-I (First Year). Let us start with the Online Number System Quiz with Answers. MCQs are about the number system Test for the preparation of mathematics.

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

1. The factors of $3(x^2+y^2)$ are

 
 
 
 

2. $(0, 1)^2$ is equal to

 
 
 
 

3. If $z$ is any real number then its conjugate is

 
 
 
 

4. $(0, 1)^4$ is equal to

 
 
 
 

5. If $a+ib$ is a complex number then its conjugate is

 
 
 
 

6. The product of two conjugate complex numbers is

 
 
 
 

7. The additive identity in a set of complex numbers is

 
 
 
 

8. The multiplicative inverse of $(a, -b)$ is

 
 
 
 

9. The real part of $\frac{2+i}{i}$ is equal to

 
 
 
 

10. If $k$ is any real number and $a+ib$ is a complex number then

 
 
 
 

11. The additive inverse of $(a, -b)$ is

 
 
 
 

12. $(0, 1)^3$ is equal to

 
 
 
 

13. The multiplicative identity of a complex number is

 
 
 
 

14. The sum of two conjugate complex numbers is

 
 
 
 

15. The multiplicative inverse of $(-4, 7)$ is

 
 
 
 

16. $(-i)^{19}$ is equal to

 
 
 
 

17. (0, 3) (0, 5) is equal to

 
 
 
 

18. If $a+ib$ is a complex number then its conjugate is

 
 
 
 

19. $(-1)^{-\frac{21}{2}}$ is equal to

 
 
 
 

20. (0, 1) is equal 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

Decimal 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.

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 Test

  • If $a+ib$ is a complex number then its conjugate is
  • If $a+ib$ is a complex number then its conjugate is
  • If $z$ is any real number then its conjugate is
  • If $k$ is any real number and $a+ib$ is a complex number then
  • The additive identity in a set of complex numbers is
  • The multiplicative identity of a complex number is
  • The additive inverse of $(a, -b)$ is
  • The multiplicative inverse of $(a, -b)$ is
  • (0, 1) is equal to
  • $(0, 1)^2$ is equal to
  • $(0, 1)^3$ is equal to
  • $(0, 1)^4$ is equal to
  • $(-i)^{19}$ is equal to
  • $(-1)^{-\frac{21}{2}}$ is equal to
  • (0, 3) (0, 5) is equal to
  • The sum of two conjugate complex numbers is
  • The product of two conjugate complex numbers is
  • The multiplicative inverse of $(-4, 7)$ is
  • The factors of $3(x^2+y^2)$ are
  • The real part of $\frac{2+i}{i}$ is equal to

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Important MCQs Number System 1

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The Post is about the MCQs Number System from Mathematics of Intermediate Part-I (First Year). Let us start with the Online MCQS Number System with Answers.

Please go to Important MCQs Number System 1 to view the test

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.

MCQs Number System with Answers

Decimal 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. In the decimal number system, there are a total of ten numbers/symbols. All other numbers such as 10, 11, 12, …, are all made from these 10 symbols/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 (Ten symbols or numbers), (ii) The binary number system (two symbols or numbers), (iii) The octal number system (eighth numbers of symbols) and, (iv) The hexadecimal number system (sixteen numbers or symbols).

MCQs Number System

  • For any complex number $z$, it is always true that $|z|$ is equal to
  • If $z_1$ and $z_2$ are any two complex numbers, then
  • If $z_1$ and $z_2$ are two complex number then
  • The numbers which can be put in the form $\frac{p}{q}\,\,$ $p, q \in Z$, $q \ne 0$ are
  • The numbers that cannot be written in the form of $\frac{p}{q}\,\,$ $p,q\in Z\,$, $q\ne 0$ are
  • A decimal which has only finite numbers of digits in its decimal part is called
  • A decimal in which one or more digits repeat indefinitely in its decimal part is called
  • Every recurring decimal is
  • A Non terminating and a non-recurring decimal is
  • 5.333 is
  • $\pi$ is
  • $\frac{22}{7}$ is
  • $\pi$ is the ratio
  • Every Integer is also a
  • If $n$ is a Prime Number, then $\sqrt{n}$ is
  • If $n$ is a negative number then $\sqrt{n}$ is
  • The Number ‘0’ is
  • The Number ‘0’ is
  • If $a, b \in R$ and $(a+b)\in R$ then this property of real numbers is
  • For $a,b\in R$ if $a+b=b+a$, then this property is called

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MCQs about Basic Statistics

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.

Please go to Number System Quiz 2 to view the test

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