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You are looking for the Indian Statistical Institute M.Stat Question Paper. Here I am uploading a file that contains the Indian Statistical Institute M.Stat Question Paper. You can download this from here. Here I am also providing you some question from the file. These are as follows: 1. x2 + x + 1 is a factor of (x + 1)n − xn − 1, whenever (A) n is odd (B) n is odd and a multiple of 3 (C) n is an even multiple of 3 (D) n is odd and not a multiple of 3. 2. The equation x6 − 5x4 + 16x2 − 72x + 9 = 0 has (A) exactly two distinct real roots (B) exactly three distinct real roots (C) exactly four distinct real roots (D) six distinct real roots. 3. In a rectangle ABCD, the co-ordinates of A and B are (1, 2) and (3, 6) respectively and some diameter of the circle circumscribing ABCD has the equation 2x − y + 4 = 0. Then the area of the rectangle ABCD is (A) 16 (B) 2p10 (C) 2p5 (D) 20. 4. If the tangent at the point P with co-ordinates (h, k) on the curve y2 = 2x3 is perpendicular to the straight line 4x = 3y, then (A) (h, k) = (0, 0) (B) (h, k) = (1/8,−1/16) (C) (h, k) = (0, 0) or (h, k) = (1/8,−1/16) (D) no such point (h, k) exists. 5. Consider a family of straight lines ax + by − 49 = 0, where a2 + b2 = 1. Then the curve which touches each of these straight lines at a single point is ![]() ![]() ![]() ![]() ![]() ![]()
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