Important Simplification (सरलीकरण) Tricks Hindi & English For SBI PO
Important Simplification (सरलीकरण) Tricks Hindi & English For SBI PO
Simplification(सरलीकरण) सभी कॉम्पीटिशन में Quantitative Aptitude यानि Math का सबसे महत्वपूर्ण टॉपिक होता है क्योकि Quantitative aptitude question सेक्शन में आपसे बहुत से पूछे जाते है उन्ही में से एक है सरलीकरण (Simplification) इस टॉपिक से हमे एग्जाम में डिफरेंट टाइप के प्रशन पूछे जाते है और सरलीकरण (Simplification) जिस भी उम्मीदवार को अच्छी तरह से आती है उसको बहुत से टॉपिक में हेल्प मिलती है क्योकि सरलीकरण (Simplification) से calculation बहुत तेज हो जाती है
और Quantitative Aptitude के प्रश्नों की सबसे अच्छी बात यह है की अगर इस विषय की ठीक से तैयारी की जाये तो हम इसमें 100% अंक प्राप्त कर सकते है और इसमें नंबर बहुत कम कटते है लेकिन Simplification(सरलीकरण) को स्ट्रोंग करने का सबसे अच्छा तरीका ज्यादा से ज्यादा प्रैक्टिस और अच्छी ट्रिक्स के साथ प्रैक्टिस करे Simplification(सरलीकरण) की प्रैक्टिस करते समय कुछ बाते और कुछ ट्रिक्स ध्यान में रखनी पड़ती है जो आज हम आपके साथ शेयर करेंगे और एक बात ध्यान में जरुर रखे की Simplification में बहुत से फार्मूला इंग्लिश में होते है तो ज्यादा ट्रिक्स को इंग्लिश भाषा में इस्तेमाल करे
Important Simplification Tricks
Simplification BODMAS Rule
One of the primary techniques to solve simplification problems is BODMAS rule which is explained below.
B = Bracket
Order = (Powers, square roots, etc.)
D = Division
M = Multiplication
A = Addition
S = Subtraction
Simplification problems are solved by using the BODMAS technique. As per the BODMAS technique/rule we must first solve the numbers that have been given in the brackets, next to this, orders and powers are solved followed by Division, Multiplication, Addition and Subtraction.
Let us solve an example –
Example 1
18 + 22 / 11 * (18 / 3) 2 – 5
= 18 + 22 / 11 * 6 *2 – 5 (First solve the Brackets)
= 18 + 22 / 11 * 36 – 5 (then solve Exponents)
= 18 + 2 * 36 -5 (further attempt Division and Multiplication, left to right)
= 18 + 72 – 5 (finally Add and Subtract, Left to right)
= 90 – 5
= 85
BASIC FORMULAE
- (a+b)2=a2+b2+2ab
- (a−b)2=a2+b2−2ab
- (a +b)2− (a−b) 2=4ab
- (a+b)2+ (a−b) 2=2(a2+b2)
- (a2–b2)= (a+b) (a−b)
- (a+b+c)2=a2+b2+c2+2(ab+bc+ca)
- (a3+b3) = (a+b) (a2−ab+b2)
- (a3–b3) = (a−b) (a2+ab+b2)
- (a3+b3+c3−3abc)= (a+b+c) (a2+b2+c2−ab−bc−ca)
- If a+b+c=0, then a3+b3+c3=3abc.
TYPES OF NUMBERS
- Natural Numbers:
Counting numbers 1, 2, 3, 4, 5 … are called natural numbers
- Whole Numbers:
All counting numbers together with zero form the set of whole numbers.
Thus,
(I) 0 is the only whole number which is not a natural number.
(II) Every natural number is a whole number.
- Integers:
All natural numbers, 0 and negatives of counting numbers i.e.,…,−3,−2,−1,0,1,2,3,….. together form the set of integers.
(i) Positive Integers: 1, 2, 3, 4….. is the set of all positive integers.
(ii) Negative Integers: −1, −2, −3… is the set of all negative integers.
(iii) Non-Positive and Non-Negative Integers: 0 is neither positive nor negative.
So, 0,1,2,3,…. represents the set of non-negative integers, while 0,−1,−2,−3,….. represents the set of non-positive integers.
- Even Numbers:
A number divisible by 2 is called an even number, ex. 2, 4, 6, 8, etc.
- Odd Numbers:
A number not divisible by 2 is called an odd number. e.g. 1, 3, 5, 7, 9, 11 etc.
- Prime Numbers:
A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.
- Composite Numbers:
Numbers greater than 1 which are not prime, are known as composite numbers, e.g., 4,6,8,9,10,12.
Note:
- 1 is neither prime nor composite.
- 2 is the only even number which is prime.
- There are 25 prime numbers between 1 and 100.
REMAINDER AND QUOTIENT:
“The remainder is r when p is divided by k” means p=kq+r the integer q is called the quotient.
EVEN ,ODD NUMBERS
A number n is even if the remainder is zero when n is divided by 2: n=2z+ 0 or n=2z.
A number n is odd if the remainder is one when n is divided by 2: n=2z+1.
- even X even = even
- odd X odd = odd
- even X odd = even
- even + even = even
- odd + odd = even
- even + odd = odd
Some important tricks
-
- 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
- (12 + 22 + 32 + ….. + n2) = n ( n + 1 ) (2n + 1) / 6
- (13 + 23 + 33 + ….. + n3) = (n(n + 1)/ 2)2
- Sum of first n odd numbers = n2
- Sum of first n even numbers = n (n + 1)
तो कोई भी उम्मीदवार जो कोई कॉम्पीटिशन एग्जाम की तेयारी कर रहा है वह इन ट्रिक्स का इस्तेमाल कर सकता है और कोई सवाल या सुझाव है तो कमेंट करे
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