Wednesday, 31 August 2016

संख्या: Maths Number System Short Tricks In Hindi ट्रिक्स इन हिंदी

Number System ट्रिक्स इन हिंदी 

If you want to learn short tricks of number system in Hindi as well as English language for solving in very short time. These tricks is also very useful for those candidates who want to crack many competitive exams of national and state level. In this article we also share some definitions, most important and frequently asked questions in previous year examinations. 

Introduction:

Natural number (प्राकृतिक संख्या) :- 

                                    The numbers in which counting is done, is known as Nature numbers.
For example: 1 2 3 4 5 ..............etc are natural numbers.

Whole number (पूर्ण संख्या) :- 

                                    In natural numbers if 0 is added to it then it will known as Whole numbers
For example: 0 1 2 3 4 5................etc are whose numbers.


Even number (सम संख्याएं) :- 

                                    The numbers which is divisible by 2 is called Even numbers.
For example: 2 4 6 8................etc are even numbers.



Odd number (विषम संख्या) :- 

                                    The numbers which is not divisible by 2 is called Odd numbers.
For example: 3 5 7 9................etc are odd numbers.

Prime number (अभाज्य सँख्या) :- 

                                    The numbers grater then 1, which is only divisible by it self or by 1 is known is Prime numbers.
For example:2 3 5 7................etc are prime numbers.





Composite number (समग्र संख्या) :- 

                                    The numbers grater then 1, which is also divisible by other numbers is known is Prime numbers.
For example:4 6 8 9 10................etc


Co-prime number  :- 

                                 Two numbers whose H.C.F is 1 is known as co-prime numbers.
For example:4 and 9


Prime triplet number  :- 

                                 Three numbers whose H.C.F is 1 is known as prime triplet numbers.
For example:8 9 and 25

Most Important questions (asked in Exams)

Ex. 1
The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number.
दो संख्याओ का योग 184 है। यदि पहली संख्या का 1/3 दूसरी संख्या के 1/7 से 8 ज्यादा है। छोटा नंबर ज्ञात करो।
Sol.
Let the numbers be x and (184 — x). Then,
x/3 - (184-x)/7 = 8
7x-3(184-x) = 168
lOx = 720 x = 72.
So, the numbers are 72 and 112. Hence, smaller number = 72.
Ex. 2.
The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers.
दो नुंबरों का अंतर 11 है तथा दोनो नंबर्स के 1/5 का योग 9 है। नंबर्स ज्ञात करो
Sol.
Let the numbers be x and y. Then.
x—y=11 ...(i)
and (X+y)x 1/5=9
x+y=45
Adding (i) and (ii), we get : 2x = 56 or x = 28. Putting x = 28 in (i), we get: y = 17.
Hence, the numbers are 28 and 17.
Ex. 3
If the sum of two numbers is 42 and their product is 437, then find the absolute difference between the numbers.
दो संखायो का योग 42 है तथा उनका गुना 437 है। दोनों का अंतर ज्ञात करो।
Sol.
Let the numbers be x and y. Then, x+ y = 42 and xy = 437.
x—y = {(x÷y)^2 - 4xy}^1/2 = {(42)^2 - 4x437}^1/2 = 4.
Required difference = 4.
Ex 4 
The average of four consecutive even numbers is 27. Find the largest of these
4 एक के बाद एक सम संखायो का औसत 27 है। बड़ा नंबर ज्ञात करो।
Sol.
Let the four consecutive even numbers be x, x + 2, x + 4 and x + 6.
Then, sum of these numbers = (27 x 4) = 108.
So,x+ (x+2)+(x+4)+(x+ 6)= 108 or 4x= 96 or x=24.
Largest number = (x + 6) = 30
Ex. 5.
The sum of the squares of three consecutive odd numbers is 2531. Find the numbers.
3 एक के बाद एक विषम्न संखयाओ के वर्गो का योग 2531 है। नंबर ज्ञात करो।
Sol
Let the numbers be x x + 2 and x + 4.
Then, x^2 + (x + 2)^2 + (x + 4)^2 = 2531
3x^2 + 12x — 2511 = 0
x^2 + 4x—837=0
(x—27)(x+31)=0
x=7.
Hence, the required numbers are 27, 29 and 31.
Ex. 6
Of two numbers, 4 times the smaller one is less than 3 times the larger one by 5. If the sum of the numbers is larger than 6 times their difference by 6, find the two
numbers.
दोनुंबेर्स मे से चोटी संख्या बड़ी से 3 गुना ठठा बड़ी संख्या चोटी से 4 गुना तथा 5 ज्यादा है। यदि उनका योग टहठा उनके अंतर का अन्तर  6 है। दोनों नंबर्स ज्ञात करो।
Sol
. Let the numbers be x and y, such that x> y.
Then, 3x — 4y = 5 ...(i)
and (x + y) — (x — y) = 6
= — 5x + 7y = 6 ...(ii)
Solving (i) and (ii), we get : x = 59 and y = 43.
Hence, the required numbers are 59 and 43.

Rational number :- 

                               The number formed by dividing one number with other number (insted of 0) then the new form of number is formed this type of number is known as rational number.
For example: p/q (where q is not equal 0) is a rational number.



Irrational number :- 

                               That real number which is not a rational number is known as Irrational number.
For example: 2^(1/2) , 2^(1/2) , (1/2)^(1/2) , (5/3)^(1/2) (where q is not equal 0) is a rational number.



Positive and Negative integers :- 

                               Whole numbers 1 2 3 4 5 ............ is called positive integers. they are also written as +1 +2 +3 +4 +5 ............
                              -1 -2 -3 -4 -5........... are called negative integers.


Real numbers :- 

                           Rational numbers and irrational numbers are in common known as real numbers.

Imaginary numbers :- 

                           The numbers which is not real is called imaginary numbers.
For example: -3^(1/2) , -7^(1/2) , -18^(1/2)   etc




Solved questions








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