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Find the area of the shaded region.

Details and Assumptions

We have an isosceles triangle with lengths 10, 10, 12.

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 \(x + \frac 1 x = 1 \)

How many ordered tuples of natural numbers \((a,b,c)\) satisfy \[\frac{1}{a}+\frac{1}{ab}+\frac{1}{abc}=1?\]

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

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