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\hspace{-16}\bf{\mathbb{F}}$ind a function $\bf{f:\mathbb{R}\rightarrow \mathbb{R}}$ that satisfy\\\\\\ $\bf{2f(x)+f(-x)=\left\{\begin{matrix} \bf{-x^3-3}\;\;\;,\;x\leq 1\\\\ \bf{7-x^3}\;\;\;,\;x> 1 \end{matrix}\right.}$ ...
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Given: f(x) =ax2+bx+c g(x)= px2+qx+r such that f(1)=g(1), f(2)=g(2) and f(3)-g(3) = 2 . Find f(4)-g(4). The q is easy but i want a shorter method... ...
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\hspace{-16}\bf{\int_{0}^{\frac{\pi}{4}}\ln \left(\frac{1+\sin^2 2x}{\sin^4 x+\cos^4 x}\right)dx} ...
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\hspace{-16}\bf{\int_{-1}^{1}\frac{2x^{1004}+x^{3014}+x^{2008}.\sin(x)^{2007}}{1+x^{2010}}dx} ...
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\hspace{-16}$If $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}}$ are the roots of the equation $\bf{4x^4-ax^3+bx^2-cx+5=0}$\\\\\\ Where $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}>0}$ and satisfy $\bf{\frac{r_1}{2} + \frac{r_2}{4} + \frac{r_3} ...
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\hspace{-16}$If $\bf{f(x,y)=\frac{\sin(x)-\sin (y)}{x-y},}$ Where $\bf{x\neq y}$\\\\\\ Then $\bf{\lfloor f(x,y)\rfloor =}$\\\\\\ Where $\bf{\lfloor x \rfloor = }$ Floor function ...
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\hspace{-16}$If $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}}$ are the roots of the equation $\bf{4x^4-ax^3+bx^2-cx+5=0}$\\\\\\ Where $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}>0}$ and satisfy $\bf{\frac{r_1}{2} + \frac{r_2}{4} + \frac{r_3} ...
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\hspace{-16}$find value of $\bf{x}$ in \\\\\\ $\bf{\left|\left|\left|\left|\left|x^2-x-1\right|-2\right|-3\right|-4\right|-5\right|=x^2+x-30} ...
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\hspace{-16}$If $\bf{a,b,c\in\mathbb{R}}$ and $\bf{f(x)}$ is a Quadratic Polynomial such that\\\\ $\bf{\begin{Bmatrix} \bf{f(a)=bc} \\\\ \bf{f(b)=ca} \\\\ \bf{f(c)=ab} \end{Bmatrix}}$\\\\\\ Then $\bf{f(a+b+c)=}$ I am Getting ...
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\hspace{-16}\bf{\int\frac{x^2.\cos^{-1}\big(x\sqrt{x}\big)}{\big(1-x^3\big)^2}dx} ...
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\hspace{-16}$If $\bf{f:\mathbb{Z}\rightarrow \mathbb{Z}}$ and $\bf{m + f\big(m + f(n + f(m))\big) = n + f(m)}$\\\\ and $\bf{f(6)=6}$.\;Then $\bf{f(2012)=}$ ...
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\hspace{-16}$If $\bf{x^3-3x+1=0}$ has a $\bf{\mathbb{R}}$oots $\bf{a\;\;,b\;\;,c}$ Respectively.\\\\ Then $\bf{a^8+b^8+c^8=}$ ...
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Well ,the title is obvious. Any thing to share. Personally, I feel that this year's paper was DIFFICULT than the Previous years one. The questions which were doable were lenghtly (not all I mean) and some were really outsmart ...
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Well ,the title is obvious. Any thing to share. Personally, I feel that this year's paper was DIFFICULT than the Previous years one. The questions which were doable were lenghtly (not all I mean) and some were really outsmart ...
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Well ,the title is obvious. Any thing to share. Personally, I feel that this year's paper was DIFFICULT than the Previous years one. The questions which were doable were lenghtly (not all I mean) and some were really outsmart ...
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Well ,the title is obvious. Any thing to share. Personally, I feel that this year's paper was DIFFICULT than the Previous years one. The questions which were doable were lenghtly (not all I mean) and some were really outsmart ...
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Well ,the title is obvious. Any thing to share. Personally, I feel that this year's paper was DIFFICULT than the Previous years one. The questions which were doable were lenghtly (not all I mean) and some were really outsmart ...
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∫[ ( x2 + 1 ) / ( x4 + 1) ] dx ...
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Well ,the title is obvious. Any thing to share. Personally, I feel that this year's paper was DIFFICULT than the Previous years one. The questions which were doable were lenghtly (not all I mean) and some were really outsmart ...
