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I would do the second question first. Now, we are to find if x and y are positive. Let us assume that x and y are integers. According to (1) 2x - 2y = 1 if x= 1 y= 1/2, if x= 3/2 y= 1, if x= 2 y= 3/2, if x= -1 y= -3/2, if x= -1/2 y= -1 and so on... the statement is not self sufficient to conclude. Second statement, x/y> 1 if x=1 y= 1/2, and when x= -1/2 y=-1, then only we get x/y > 1. Still we don't come to a conclusion. Now even if we combine the 2 statements, we would not be ale to decide the sign of x and y. Therefore, I go for 'E'.
The first question. 'k' lies between 1 and 10 inclusive. Since (-1)^k+1, therefore for every even value the term would be odd and for even odd value the term would be even. The terms that we get are 1/2, -1/4, 1/8, -1/16...-1/1024. by subtracting the successive terms we get all positive terms 1/4, 1/16, 1/64... 1/1024. now we add these terms, so if answer would be greater than 1/4 but, since the terms being added to 1/4 are very small, the answer would lie between 1/2 and 1/4, so I go for 'D'.
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