Number System


Last Updated : 28-03-2024 21:20:57
Share this :

Natural Numbers: {1,2,3,4,5,……..}

Whole Numbers: { 0,1,2,3,4,…….}

Set of Integers: {…….,-3,-2,-1,0,1,2,3,4,………}

Sum of First n Natural Numbers: n(n+1)/2

Sum of Square of First n Natural Numbers: n(n+1)(2n+1)/6

Sum of Cube of First n Natural Numbers: [n(n+1)/2]²

Even Numbers: {2,4,6,8,…..}

Odd Numbers: { 1,3,5,7,9,…….}

Sum of First n Even Numbers: n(n+1)

Sum of First n Odd Numbers: n²

Prime Numbers

Numbers Divisible by 1 & itself

Eg. 2,3,5,7,11,13,…….

Test to Decide Prime Numbers 

Steps: For Number n

  1. Take whole number x such that x <= √n
  2. Take all Prime Numbers <= x
  3. If none of the above numbers divide n exactly then n is Prime else n is Nonprime.

Two numbers having only 1 as a common factor are called co-prime numbers.

Thus, 4 and 15 are co-prime numbers.

Note :

If a number is divisible by another number then it is divisible by each of the factors of that number.

If a number is divisible by two co-prime numbers then it is divisible by their product also.

If two given numbers are divisible by a number, then their sum is also divisible by that number.

If two given numbers are divisible by a number, then their difference is also divisible by that number.

Twin Prime Numbers: Two prime numbers which differs by 2 Eg. (3,5), (11,13), ……..

Composite Numbers: Numbers divisible by at least one number other than 1 Eg. 4,6,9,15,……

Rational Numbers: Expressed as p/q

Irrational Numbers:

  • Non recurring & non terminating decimals
  • can not be expressed in p/q form
  • eg. √3, √5, …….

Note : Rational & Irrational numbers together make Real Numbers

Formula : Dividend = ( Divisor * Quotient) + Remainder

VBODMAS Rule :

V – Vernacular or Bar “¯”

B – Brackets Removing order (), {},[]

O – Of

D – Division

M – Multiplication

A – Addition

S – Subtraction

Tests for Divisibility of Numbers

Divisibility by 10 :

if a number has 0 in the ones place then it is divisible by 10.

eg. 10, 1030,15000,etc

Divisibility by 5 :

a number which has either 0 or 5 in its ones place is divisible by 5

eg. 25, 1020, etc

Divisibility by 2 :

a number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place.

eg. 2410, 4356, 1358, 2972, 5974

Divisibility by 3 :

if the sum of the digits is a multiple of 3, then the number is divisible by 3.

eg. 21, 27, 36, 54, 219

Divisibility by 6 :

if a number is divisible by 2 and 3 both then it is divisible by 6 also.

eg. 18

Divisibility by 4 :

a number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

eg. 212, 1936

Divisibility by 8 :

a number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.

eg. 2112, 10240

Divisibility by 9 :

if the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.

eg. 981, 2754,

Divisibility by 11 :

find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.

image

Leave a Reply

Your email address will not be published. Required fields are marked *

Online Test Series for Students

Each Test

Rs. 100
Solve Online Test At Moreques Authorized Exam Center

Each Test

Rs. 50
Solve Online Test on Own PC/Laptop/Mobile

UPSC Exams | Union Public Services Commission Examinations


Last Updated : 28-03-2024 21:20:57
Share this :

Civil Services Examination (IAS,IPS,IFS,IRS)

UPSC Civil Services Pre Examination 2016 Notification

last date to apply : 27 May 2016

Preliminary Exam : 07 Aug 2016

UPSC Civil Services Preliminary Exam

UPSC Civil Services Mains Exam

General Studies GS 1 Study Material

General Studies GS 2 Study Material

General Studies GS 3 Study Material

General Studies GS 4 Study Material

Optional Subject

History

UPSC Mains History Optional Paper 1 Syllabus

UPSC Mains History optional Paper 2 Syllabus

Optional Subject :

History

UPSC Previous Year Question Papers Download FREE for Prelims and Mains Exam

Indian Forest Service examination

Engineering Services Examination

Combined Defence Services Examination

National Defence Academy Examination And Naval Academy Examination

Combined Medical Services Examination

Special Class Railway Apprentice

Indian Economic Service/Indian Statistical Service Examination

Combined Geoscientist and Geologist Examination

Central Armed Police Forces(Assistant Commandant) Examination

State PSC Exams | State Public Services Commission Examinations


Last Updated : 28-03-2024 21:20:57
Share this :

  1. Andhra Pradesh Public Service Commission ( APSPSC )

    Group I

    Syllabus

    Study Notes

    Group II

    Syllabus

    Study Notes

    Group III

    Syllabus

    Study Notes

    Group IV

    Syllabus

    Study Notes

  2. Arunachal Pradesh Public Service Commission ( APPSC )

    District Statistics Officer/ Research Officer

    Steno Grade III

    Finance & Accounts Officer / Treasury Officer (FAO/TO)

  3. Assam Public Service Commission ( APSC )
  4. Bihar Public Service Commission ( BPSC )
  5. Chhattisgarh Public Service Commission ( CGPSC )
  6. Goa Public Service Commission ( GoaPSC )
  7. Gujarat Public Service Commission ( GPSC )
  8. Haryana Public Service Commission ( HPSC )
  9. Himachal Pradesh Public Service Commission ( HPPSC )
  10. Jammu & Kashmir Public Service Commission ( JKPSC )
  11. Jharkhand Public Service Commission ( JPSC )
  12. Karnataka Public Service Commission ( KPSC )
  13. Kerala Public Service Commission ( KeralaPSC )
  14. Madhya Pradesh Public Service Commission ( MPPSC )
  15. Maharashtra Public Service Commission ( MPSC )

    State Services Examination


    PSI/ STI/Assistant

  16. Manipur Public Service Commission ( ManipurPSC )
  17. Meghalaya Public Service Commission ( MeghalayaPSC )
  18. Mizoram Public Service Commission ( MizoramPSC )
  19. Nagaland Public Service Commission ( NPSC )
  20. Odisha Public Service Commission ( OPSC )
  21. Punjab Public Service Commission ( PPSC )
  22. Rajasthan Public Service Commission ( RPSC )
  23. Sikkim Public Service Commission ( SPSC )
  24. Tamil Nadu Public Service Commission ( TNPSC )
  25. Telangana state Public Service Commission ( TSPSC )
  26. Tripura Public Service Commission ( TPSC )
  27. Uttar Pradesh Public Service Commission ( UPPSC )
  28. Uttarakhand Public Service Commission ( UKPSC )
  29. West Bengal Public Service Commission ( WBPSC )

IBPS | Banking & Insurance Exam | Banking & Insurance Examinations


Last Updated : 28-03-2024 21:20:57
Share this :

Reserves Bank of India ( RBI )

Grade A & B Exams

State Bank of India ( SBI )

Probationary Officer ( PO) Exam

Junior Associate Exam

Nationalised Banks Probationary Officers

IBPS PO Exam

Bank Clerk

Bank Clerical Exams

National Bank for Agricultural & Rural Development ( NABARD )

Assistant Development Officer Grade A exam

Development Officer Grade B exam

LIC & GIC

LIC Assistant/ Steno/Typist Exam

LIC Development Officer Exam

LIC Officers Exam

GIC Assistant Exam

GIC Officers Exam

Institute Login




Register Your Institute

MoreQues for Institutes | Features

MoreQues

Create Course

MoreQues

Add students

MoreQues

Create New Tests

MoreQues

Solving Tests

MoreQues

Test Result

MoreQues

Test Rank

MoreQues

Payments Details

MoreQues

Time Table

MoreQues

Attendance

MoreQues

And Much More

Pricing

Sign Up FREE

Rs. 0
with Ads

Remove Ads

Rs. 4,000
Per Year

Remove Ads + Notification

Rs 6,000
Per Year

Customize Portal

Rs 10,000
Starting from Rs 10,000

Don't have Computer System for Online Test?

No Problem. We also provide Computer System for online test at our Test Centres. Please get in touch with us for more information. Write us at [email protected] or call us at +91-8390111719

MoreQues | How To Use it

Exam Center Login




Register as Exam Center

MoreQues for Internate Cafe | Become Authorized Exam Center

MoreQues

Add student

MoreQues

Assign Test

MoreQues

Manage Payment

Registration

Rs. 1000
Become Authorized Exam Center

Earnning

Rs. 50
for Each Test Solved at Centre

Find Coaching Classes in your City


keyboard_arrow_up