Number System Notes for RRB NTPC Exam 2022

NTPC is an abbreviation for Non-Technical Popular Categories. The RRB NTPC test is administered by the Railway Recruitment Board (RRB) to select applicants for various non-technical roles in the Indian Railways. Applicants who have completed their degree or passed class XII are eligible for RRB NTPC posts. The RRB NTPC 2022 examination is divided into four stages: CBT 1, CBT 2, Typing Skill Test/Computer Based Aptitude Test (where applicable), and Document Verification. The highlights of the RRB NTPC 2022 test are as follows:

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RRB NTPC CBT 1 Exam Pattern 2022

The following is a detailed overview of the RRB NTPC CBT -1 exams:

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RRB NTPC CBT 2 Exam Pattern 2022

A computer-based examination will be used to administer the recruiting exam at testing centres around the country. The test will consist of 120 multiple-choice questions, with each question worth one point. The duration of the NTPC Computer Based Test – 2 is 90 minutes i.e. 30 minutes and one hour. The exam will have 35 MCQs from Mathematics and General Intelligence, and Reasoning each as well as 50 questions from General Awareness. The table below contains more information about the RRB NTPC CBT-2 Exam Pattern 2022.

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RRB NTPC Exam Syllabus 2022 for Mathematics

In this section, we will go through the RRB NTPC 2022 syllabus for mathematics.

1. Ratio and Proportions
2. Trigonometry
3. Mensuration
4. LCM
5. Elementary Algebra
6. Fractions
7. Geometry
8. HCF
9. Profit and Loss
10. Time and Distance
11. Time and Work
12. Number system
13. Simple and Compound Interest
14. Elementary Statistics
15. Decimals

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Number System Notes for RRB NTPC Exam 2022

A number is a mathematical entity that is used to count, measure, and label. A number system, also known as a system of numeration, is a method of writing numbers or symbols consistently. In simplified terms, the number system is concerned with the writing of numbers. The number system may be categorised into the following types based on the numbers utilised in the system:

• Binary Number System
• Octal Number System
• Decimal Number System
• Hexadecimal Number System

These number systems are often utilised in computers nowadays. However, in “Mathematics,” we employ the Decimal Number System. “Deci” indicates ten, hence the “Decimal number system” employs 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Using these digits, we can create any number. This system’s base is also ten. We have two words for numbers when we represent them.

• Face Value: The face value of a digit in a number is its true value.

Ex. 1: The face value of 7 in 38786 is merely 7.

• Place Value: The value of a digit concerning its position in the number is referred to as its place value.

Ex-2: The place value of 7 in 38786 is 700, which equals 7×100.

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Types of Numbers

• These are numbers that are represented as the square root of a negative number. These numbers are often written as “ai,” where “a” is a number and ” i” is a symbol denoting the imaginary component, with the value of I equal to the root of -1. Imaginary numbers are often represented on a vertical number line plane. 2i and 7i are two examples.
• Real Numbers are numbers that can be expressed on a number line. To put it simply, any numbers other than imaginary numbers are real numbers.
• Irrational numbers are real numbers that cannot be represented because “p” or “q” are non-terminating terms. Numbers with a perfect square root are not irrational.
• Real numbers that can be represented as powers of p/q, where q is a non-zero number, are known as rational numbers. E.g. 1, -4, 2.3, etc.
• Integers are integers with a denominator of ‘1’, or numbers that are not in the form of a fraction or a decimal. Integers are further divided into the following categories: Positive Integers, Negative Integers and Zero.
• A fraction is a portion of a whole. Fractions are typically expressed as p/q, where ‘p’ is the numerator and ‘q’ is the denominator. Both “p” and “q” are non-zero terms in this case. Fraction is classified as a proper fraction, improper fraction and mixed fraction.
• A decimal is a fraction with a denominator that is a power of ten. 1.5, 2.75, and 3.873, for example.
• Natural numbers can be defined as the number we used to count or as a collection of all positive integers. For example: 1, 2, 3, …
• When zero is included in natural numbers, the set of numbers is referred to as whole numbers. this series is like 0, 1, 2, 3, 4…
• An even number is a set of natural numbers that are exactly divisible by two. 2, 4, 6, 8, etc.
• A set of natural numbers other than even numbers are referred to as odd numbers. 1, 3, 5, etc.
• Prime numbers are natural numbers that contain precisely two elements, which are ‘1’ and themselves. 2, 3, 5, 7, 11, etc.
• A composite number is a natural number that has more than two elements. 4,6,8,9,10,12…
• Because 1 has only one factor, it is neither prime nor composite and is thus categorised as a unit.
• Twin prime numbers are two prime numbers that vary by two. (3,5), (5,7), etc (11,13)
• Co-prime numbers are those numbers that have no common factor other than ‘1’. In other words, a set of numbers with H.C.F 1 is a set of co-prime numbers. As an example, (6,35), (12,25)
• The only even prime number is 2.
• There are 15 prime numbers ranging from 1 to 50, and their sum is 328.
• There are 25 prime numbers ranging from 1 to 100, and their sum is 1060.
• The only consecutive prime numbers are 2 and 3.
• The only triplet of twin prime numbers is 3, 5, and 7.
• A number is seen to be perfect if the total of its factors, except that number, equals that number. 6 and 28 as examples The factors of 6 are 1, 2, 3, and 6 and 1 + 2 + 3 = 6. The 28’s factors are 1, 2, 4, 7, 14, 28 and 1 + 2 + 4 + 7 + 14 = 28
• The sum of the reciprocals of a perfect number’s components is always 2.
• Factorial is a product of all natural numbers, starting with the first and ending with the number. In basic terms, the factorial of a number is the product of all natural numbers that are equal to or less than the number. N! = 1×2×3… (N – 1) × N.

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Dividend, Divisor, Quotient, and Remainder Relationship

• Dividend = Divisor × Quotient + Remainder
• The value of the remainder is always positive.

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Convert a Recurring Decimal Into a Fraction

When we convert a recurring decimal into a fraction, first look at how many digits are repeated. If 1 number is recurring then put the denominator as 10-1=9. If two numbers are recurring then put the denominator as 100-1=99. Then you can simplify the resulting fraction into their smallest forms.

e.g. 0.7777…= 7/ (10-1) = 7/9

To put it simply, we put as many 9s in the denominator as digits are repeating.

If the decimal includes a mixed recurring decimal, such as 0.5777…, then in the denominator, we use zero for non-repeating numbers and 9 for repeating numbers, and we subtract the non-repeating number from the full amount in the numerator.

e.g. 0.577777…= (57-5)/ 90= 52/90

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Divisibility Test

The criteria for checking divisibility for each number are given in the table below

7 and 11 can be seen as special cases.

• In the case of 7, let’s have a look at an example. Consider the number 3402

1st step: 340 –2 × 2 = 336

2nd step: 33 – 2 × 6 = 21

3rd step: Determine whether or not 21 is divisible by 7.

Because it is divisible by seven, the number is also divisible by seven.

• In the case of 11, Let’s have a look at an example. For instance, 273691

(2 + 3 + 9) – (7 + 6 + 1) = 0

As a result, the number is divisible by eleven.

The integer is divisible by 11 if the difference between the sum of digits in the even position and the sum of digits in the odd position is equal to “0 or multiple of 11.”

• When a six-digit number is generated by repeating a digit (111111, 222222, 333333, etc), it is divisible by three, seven, eleven, thirteen, and thirty-seven.
• When a six-digit number is generated by repeating a two-digit number (272727, 353535, 565656), the result is divisible by three, seven, thirteen, and thirty-seven.
• When a six-digit number is generated by repeating a three-digit number (273273, 135135, 456456) then it is divisible by seven, eleven, and thirteen.

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The post looked at how to effectively handle number system questions. Following the advice on this website, you may solve the number system questions for RRB NTPC Exam 2022. Constant practice will also help you enhance your speed. Download the Entri app to practise additional modal questions on the number system topic for the RRB NTPC Exam 2022. Detailed notes and explanations for above-mentioned theories are available in the Entri app.