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Let \(\alpha\), \(\beta\) and \(\gamma\) be the real roots of the cubic equation \(x^3-7x^2+ax+50=0\), and their absolute values be the roots of another cubic ...

\[\large{\dfrac{7n-12}{2^n} + \dfrac{2n -14}{3^n} + \dfrac{24n}{6^n} = 1}\]

Find the sum of all integers \(n\), such that the above equation satisfies.

In front of you are two coins. They are identical in appearance, but one is fair (when flipped, it comes up Heads 50% of the time), while the other comes ...

A letter is known to have come from CHENNAI, JAIPUR, NAINITAL, MUMBAI. Your mother receives the letter and she randomly tells you two consecutive alphabets. If she tells you AI ...

Find sum of all value(s) of \(n\) such that if the first digit in decimal representation of \(2^n\) is removed , the remaining digits can be represented as some ...

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