A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 - a, find the possible values of a.

The 3rd term of an A.P is 4x - 2y and the 9th term is 10x - 8y. Find the common difference.

Find the inverse of p under the binary operation * defined by p*q = p + q - pq, where p and q are real numbers and zero is the identity

Evaluate (\(\frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{16} + ...) -1\)

if (x - 1), (x + 1) and (x - 2) are factors of the polynomial ax\(^3\) + bx\(^2\) + cx - 1, find a, b, c in that order.