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Find the coefficient of \(x^{70}\) in the expansion of \[(x-1)(x^2-2)(x^3-3)....(x^{11}-11)(x^{12}-12)\]

\[\huge x^{1729}+x^{-1729}\]

Find the value of the above expression if \(x + \frac 1 x = 1 \)

Given that \(a,b,c\) are positive reals such that the maximum value of \(N\) which satisfies the inequality

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In \(\triangle ABC,\) \(AB=6 \) , \(BC = 4\) and \( AC=8.\) A segment parallel to \( \overline{BC}\) and tangent to the incircle of \(\triangle ABC\) intersects \(\overline{AB}\) at \(M\) and ...

\[\large \sum_{n=1}^{2014} \bigg [ (-1)^{n}\times \lfloor \sqrt{n} \rfloor \bigg ] = \, ? \]

\[\] Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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