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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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Books and More sells books, music CDs and film DVDs. In December 2009, they earned 40% profit in music CDs and 25% profit in books. Music CDs contributed 35% towards their total sales in rupees. At the same time total sales in rupees from books is 50% more than that of music CDs.
[1] If Books and More have earned 20% profit overall, then in film DVDs they made
(1) 15.2% profit
(2) 10.0% profit
(3) 10.0% loss
(4) 16.3% loss
(5) 23.4% loss[2] If Books and More made 50% loss in film DVDs, then overall they made
(1) 12.3% profit
(2) 8. 7% profit
(3) 0.4% loss
(4) 6.25% loss
(5) 20% lossasked in XAT
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