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\[\Large \underbrace{3^{3^{3^{3^{\cdot^{\cdot^{\cdot^{3}}}}}}} }_{2012 \text{ times}} \pmod {100} = \, ? \]

In Guerickeâ€™s experiment to show the effect of atmospheric pressure, two copper hemispheres were tightly fitted to each other to form a hollow sphere and the air from the ...

\(AD\), \(BE\) and \(CF\) are concurrent lines drawn from the vertices of \(\triangle ABC\) to points \(D\), \(E\) and \(F\) on the opposite sides. If \(AD\) is the altitude of ...

If \(x^4+2x^3+ax^2+bx+9\) is a perfect square polynomial, where \(a\) and \(b\) are real numbers, then what is the values of \(a+b?\)

If \(72^{x}48^{y}=6^{xy}\) for non-zero rational numbers \(x,y\), then find \(x+y\).

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