Number system short tricks with examples hindi me

Number system short tricks:
Mathsmell ( Maths tricks in Hindi) me apka swagat haj.Previous post me humne dekha number system kya hai aur number system in maths kitne types ki hote hai. Aaj iss post me hum janenge basic number theory ki important basics shortcut rules and tricks with examples in hindi.

Hum sab jante hai number system in hindi mathematics ki sabse jada important topics hai.Isliye teacher hamesa students ko sab se pehle number system in maths shikhata hai.Bahut sare competitive exams me number system in maths se questions puche jate hain. Isliye dosto iss post ko dhayan se pura padhe. Iss post pura padne ki baad aapka number system in maths se related maths short tricks ki sabhi confusion dur ho jayegi.

Number system shortcut tricks hindi me:

Dosto niche number system in hindi ki kuch important maths short tricks discuss karrahahu jiske competitive exams me bahut mahatta hai.Diye gaye tricks ki help se aap competitive exams me puche gaye sabhi questions ki answers 5 second me de payenge.Ek baat aur dosto inn sabhi fast maths tricks ko dekkar syad lagega ki time bahut jada lagegi but bar bar practice karne se aap diye gaye tricks ki help se kisi bhi questions ki solutions asani se depayenge.

Tricks:-1.

Square of every even numbers is an even numbers.
OR
Even numbers ki square hamesa even numbers hote hai.
For example, 4^2 = 16 and 6^2 = 36.Here 4 and 6 are even and 4 and 6 ki squares 16 and 36 bhi even numbers.

Tricks:-2.

Square of every odd numbers is an odd numbers.
OR
Odd numbers ki square hamesa odd numbers he hote hain.
For examples, 3^2=9, 5^2=25 and 7^2=49.Here 3, 5, and 7 odd numbers hai and inn odd numbers ki squares 9, 25, and 49 bhi odd numbers hai.

Tricks:-3.

Kisi bhi perfect squares numbers ki unit place me 2, 3, 7 and 8 digit nahi hoga.Because
1 ki square me unit digit = 1
2 ki square me unit digit = 4
3 ki square me unit digit = 9
4 ki square me unit digit = 6
5 ki square me unit digit = 5
6 ki square me unit digit = 6
7 ki square me unit digit = 9
8 ki square me unit digit = 4
9 ki square me unit digit = 1

Tricks:-4.

Sum of first n natural numbers = n(n+1)/2
OR
First n natural numbers ki sum hamesa n(n+1)/2 hoga.
For example, What is the sum of first 105 natural numbers.
Soln. Here n = 105.
So, sum = n(n+1)/2
= 105(105+1)/2
= 105*106/2
= 105*53
= 5565

Tricks:-5.

Sum of first n odd numbers = n^2.
OR
First n odd numbers ki sum hamesa n^2 hoga.
For examples,Find the sum of the following
1+3+5+..........+27.
Soln. Here n = 27.
Therefore, Sum = n^2
= (27)^2
= 729.

Tricks:-6

Sum of first n even numbers = n(n+1).
Or.
First n-even numbers ki sunlm hamesa n(n+1) hoga.
For example, Find the sum of the following numbers
2+4+6+.........+98.
Soln. Here n
Sum = n(n+1)
= 98(98+1)
= 98*99
= 9702.

Tricks:-7.

Sum of squares of first n natural numbers = n(n+1)(2n+1)/2.
Or
First n square natural numbers ki sum hamesa n(n+1)(2n+1)/2. hoga.
For example, Find the sum of the following1^2 + 2^2 +........ + 10^2.
Soln. Here n = 10.
Sum = n(n+1)(2n+1)/2
= 10(10+1)(2*10+1)/6
= (10*11*21)/6
= 365.

Tricks:-8.

First n natural numbers ke cubes ki sum hoga [n(n+1)/2]^2
For example, Find the sum of the following numbers 1^3 + 2^3 +........ + 7^3.
Soln. Here n = 7.
Sum = [n(n+1)/2]^2
= [7(7+1)/2]^2
= (7*8/2)^2
= (7*4)^2
= (28)^2
= 784.

Tricks:-9.

Agar nth numbers me even and odd numbers ek sath hai aur agar even and odd numbers ki sankhya nikalna hai to.
Number of even numbers = (n-1)/2.
Numbers of odd numbers = (n+1)/2

Example:- Find the number of even and odd numbers of the following
1, 2, 3, 4,.........., 123.

Soln. Here n = 123.
Even no. = (n-1)/2 = (123 - 1)/2 = 61.
Odd no. = (n+1)/2 = (123+1)/2 = 62.

Dosto uppar diye gaye inn short maths tricks ko dhayan se read kare aur agar samajne me koi problem hote hai to comment jarur kare.

Try your self.

Dosto Edhar maine apki liye uppar diye gaye tricks se related some multiple choice questions diye hai, inn question ki solution kare aur agar solution nikalne me koi problem hota hai to comment jarur kare.

1. Find the sum of first 25 natural numbers
 a)432, b) 315, c) 325, d) 335.

2. Find the sum of the square of first 35 natural numbers.
a.)14910, b) 15510, c) 14510, d) 16510.

3. Find the sum of the cubes of first 15 natural numbers.
a.) 15400, b) 14400, c) 16800, d) 13300.

4. Find the sum of the first 37 odd numbers.

5. Find the sum of first 84 even numbers.

I hope number system short tricks with examples in hindi post aapko acha laga hoga, agar ha to number system shortcut method tricks post ko apne dosto ki sath share kare. Thank you....