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26th July 2014, 01:30 PM
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Join Date: Apr 2013
Re: TIFR MSc Mathematics Entrance Exam Question Paper

Here I am providing the list of few questions of Tata Institute of Fundamental Research MSc mathematics entrance exam question paper which you are looking for .

Let A be an n×n matrix with real entries such that Ak = 0 (0-matrix),
for some k ∈ N. Then
A. A has to be the 0 matrix
B. trace(A) could be non-zero
C. A is diagonalizable
D. 0 is the only eigenvalue of A.

There exists a map f : Z → Q such that f
A. is bijective and increasing
B. is onto and decreasing
C. is bijective and satisfies f(n) ≥ 0 if n ≤ 0
D. has uncountable image.

How many proper subgroups does the group Z ⊕ Z have?
A. 1
B. 2
C. 3
D. infinitely many.

X is a metric space. Y is a closed subset of X such that the distance
between any two points in Y is at most 1. Then
A. Y is compact
B. any continuous function from Y → R is bounded
C. Y is not an open subset of X
D. none of the above.










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