CSIR NET MATHEMATICAL SCIENCE JUNE 2012 QUESTION & ANSWER CSIR NET MATHEMATICAL SCIENCE JUNE 2012 QUESTION & ANSWER, CSIR NET MATHS JUNE 2012 QUESTION & ANSWER, CSIR NET MATHEMATICS JUNE 2012 QUESTION & ANSWER (Memory Based)

Part C

1. If f is an entire function and Im f > 0 then
   1) Re f is constant   2) f is constant    3) f = 0     4) f' is a non-zero constant
2.  Let C be an n x n matrix. Let V be a vector space spanned by {I, C, C^2, ... C^2n}. Then dim V is
   1) n^2     2) 2n       3) at most n^2             4) at most 2n
3. Let N be a 3x3 non-zero matrix with the property that N^2 = 0. Then
   1) N is not similar to a diagonal matrix    2) N is  similar to a diagonal matrix 
   3) N has one non-zero eigen vector    4) N has three linearly independent  eigen vectors
   
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