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CSIR UGC NET 2008 : MATHEMATICAL SCIENCES - PAPER I

19 pages, 75 questions, 23 questions with responses, 26 total responses,

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MATHEMATICAL SCIENCES PAPER-I (PART-B) 41. Let {xn} be a sequence of non-zero real numbers. Then If xn a, then a = sup xn. xn +1 If < 1 n , then xn 0. xn If xn < n n , then {xn}diverges. If n xn n, then {xn} diverges. 1. 2. 3. 4. 42. Let {xn} and {yn} be two sequences of real numbers such that xn yn xn+2, n = 1, 2, 3, L 1. {yn}is an bounded sequence. 2. {xn} is an increasing sequence. 3. {xn} and {yn} converge together. 4. {yn} is an increasing sequence. 43. Let f:[0, 1] (0, ) be a continuous function. Suppose f(0) = 1 and f(1) = 7. Then 1. f is uniformly continuous and is not onto. 2. f is increasing and f([0, 1]) = [1, 7]. 3. f is not uniformly continuous. 4. f is not bounded. 44. Let f: [a, b] [c, d] be a monotone and bijective function. then f is continuous, but f 1 need not be. f and f 1 are both continuous. If b a > d c, then f is a decreasing function. f is not uniformly continuous. 1. 2. 3. 4. 45. Let xn be a series of real numbers. Which of the following is true? n =1 1. If x n is divergent, then {xn} does not converge to 0. 1 2. If x n is convergent, then 3. If x n n is absolutely convergent. 1 1 x 2 is convergent, then xn 0 , as n . 1 4. If xn 0, then x n 1 is convergent.

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Additional Info : CSIR UGC (National Eligibility Test) NET New Exam Scheme December 2008 Model Question Paper - Mathematical Sciences Paper II Joint CSIR UGC NET Exam Question Papers
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