BETTER MATHEMATICAL SOLUTION 4 U

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ঘনফল-এর সূত্র সংক্রান্ত প্রশ্নবলী-

$a+b=1$ এবং $a^3+b^3+3ab=k$ হলে, $k$ এর মান কত? উত্তর : ‍‍$a+b=1$ $\Rightarrow (a+b)^3=1$ $\Rightarrow a^3+b^3+3ab(a+b)=1$...
পূরক কোণের ত্রিকোণমিতিক অনুপাত

Q1. $A$ ও $B$ দুটি পরস্পর পূরক কোণ। দেখাও যে, $\sin{A}+\sin{B}=1+2\sin{A}\cos{B}$ সমাধান : যেহেতু $ A $ ও $ B $ দুটি পরস...
General Formula for Converting Repeating Decimals to Fractions

Suppose that the decimal number is $x=a.d_1d_2\cdots d_m \overline{d_{m+1}\cdots d_{m+p}d_{m+p}}$, where the $d_k$ are digits, $a$...
শতকরা [Percentage]

প্র শ্ন :- চালের দাম $r%$ বাড়লে এক পরিবার চালের ব্যবহারের পরিমান কত কমালে মোট খরচ অপরিবর্তিত থাকবে ? সমাধান : মনেকরি অাগে $100$ টা...
Calculus Formulas

$D$ denotes $\frac{d}{dx}$ $D c=0$ $D x=1$ $D \frac{1}{x}=-\frac{1}{x^2}$ $D x^n=nx^{n-1}$ $D \sqrt{x}=\frac{1}{2\s...
CSIR-UGC NET Question Paper for Mathematical Sciences

CSIR-UGC NET Math. Sciences QP, June 2012.pdf
Proof for the Ramanujan's formula ?

$x+n+a=\sqrt{ax+(n+a)^2+x \sqrt{a(x+n)+(n+a)^2 +(x+n) \sqrt\cdots}}$ Proof : $F(x)=\sqrt{ax+(n+a)^2+x \sqrt{a(x+n)+(n+a)^2 +(x+n) \sqrt...
Some Algebraic Formulae

$(a+b)^2=a^2+2ab+b^2 $ $ (a+b)^2=(a-b)^2+4ab $ $ (a-b)^2=a^2-2ab+b^2 $ $ (a-b)^2=(a+b)^2-4ab $ $ a^2+b^2...
Nested Radical of Ramanujan

Evaluate : $\sqrt{1+2 \sqrt{1+3 \sqrt{1+\cdots\infty}}}$ Solution : Note that $(x+1)^2=1+x(x+2)$ , now taking the principal square r...
General Proof of Divisibility Tests

Here is a basic fact: Suppose you have a positive integer $n$ which, when you write its digits look liks : $a_m a_{m-1}\cdots a_2 a...

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BETTER MATHEMATICAL SOLUTION 4 U

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