theorems

Parin Sir > theorems

May

Examples 1 to 10 of Fundamental(Numbers)

(1) Evaluate : 25 – | – 8 | – | 7 | + | – 31 |.

Soln. 25 – | – 8 | – | 7 | + | – 31 | = 25 – 8 – 7 + 31 = 41

(2) Find the value of i¹⁸.

Soln. i¹⁸ = …

Posted in: Fundamental(Numbers) Examples,

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May

Progressions

■Sequence : A succession of numbers formed and arranged in a definite order according to certain definite rule, is called a sequence.

The number occurring at the n-th place of a sequence is called its n-th term.

■P…

Posted in: Progressions,

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28

May

Properties of Irrationals and Surds
▪ The set P of all irrationals is not closed for addition, since the sum of two irrationals need not be irrational.

e.g. ( 5 + $\sqrt{3}$

Posted in: Properties of Irrationals and Surds,

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27

May

Operations On Rational Numbers
Properties of Addition on Q :

▪ Q is closed for addition.

▪ Addition on Q is commutative as well as associative.

▪ 0

Posted in: Operations On Rational Numbers,

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27

May

Operations on integers
Properties of Addition & Subtraction on I :

▪ I is closed for addition.

i.e. a $\in$

Posted in: Operations on integers,

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27

May

Operation Of Real Numbers
Properties of addition on   R   :

Closure Property :   The sum of two real numbers is always a real number. We say that R is closed for addition. …

Posted in: Operation Of Real Numbers,

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27

May

Multiplication By Short Cut-Methods
Multiplication of a Number By 99, 999, 9999 etc. :   Place as many zeros to the right of the multiplicand as is the number of nines and from the number so formed, subtract the multiplicand to get the answer.

e.g. Multiplyi…

Posted in: Multiplication By Short Cut-Methods,

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27

May

Tests for Divisibility
Divisible by   2ⁿ : If last n digits of a number is divisible by 2ⁿ, the whole number is divisible by 2ⁿ.

Divisible by 2   :   A number is divis…

Posted in: Tests for Divisibility,

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27

May

BODMAS ( Process for Basic Arithmetic Operation )
When we have to perform a series of mathematical operations, there is a rule regarding the order in which we should perform these operations. This rule is called BODMAS.

B = Bracket

Posted in: Process for Basic Arithmetic Operation,

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27

May

convert a Recurring Decimal into Vulgar Fraction
…

Posted in: convert a Recurring Decimal into Vulgar Fraction,

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