For a very large number n, $P^{n}+ Q^{n}$ is… | XAT 2010 Question Paper

XAT 2010Verbal Ability & RCMiscellaneousHARD+1 / −0.25

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OABC is a square where O is the origin and AB = 1. Consider the set of points $s = {(x_{i},y_{i})}$ in the square such that $x_{i}+y_{i}$ ≤1. Let $P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2})$ be two such points. Two operations addition (+) and multiplication (.) on S are defined as
$P + Q = (x_{1}+x_{2} - x_{1}x_{2},y_{1}y_{2})$
$P.Q = (x_{1}x_{2},y_{1}+y_{2} - y_{1}y_{2})$

For a very large number n, $P^{n}+ Q^{n}$ is

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