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OABC is a square where O is the origin and AB = 1. Consider the set of points S = {(xi, yi )} in the square such that xi + yi ≤ 1. Let P (x1 , y1 ) and Q (x2 , y2 ) be two such points. Two operations addition (+) and multiplication (.) on S are defined as
P + Q = (x1 + x2 – x1 x2, y1 y2)
P.Q = (x1 x2 , y1 + y2 – y1 y2 )[1] For a very large number n, Pn + Qn is
(1) close to (0, 0)
(2) close to (1,0)
(3) close to (0, 1)
(4) any point in the region x + y < 1
(5) None of the above[2] For a very large number n, nP + nQ is
(1) close to (0, 0)
(2) close to (1,0)
(3) close to (0, 1)
(4) Any point in the region x + y < 1
(5) None of the aboveasked in XAT
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