Education and Career Forum

The paper contains forty questions carrying 20 marks each. The first half is on mathematics and the second half on statistics. The examinees have to answer any ten questions in about 300 words each. The maximum marks are 200. Some of the questions in the papers are: prove that every compact subset of a metric space is bounded, show that every compact subset of a Hausdorff space is closed, show that the closed and bounded subset of a metric space need not be compact, give an example of a metric space in which every closed and bounded subset is compact, find the Galois group of the polynomial x2 +1 over the field of real numbers, assuming H to be a separable Hilbert space, show that any orthonormal set in H is almost countable, draw a connected graph of 7 vertices in which every non-zero distance is 1, 2 or 3, find the sum of divisors of a natural number n in terms of its prime factors, find all the possible Jordan canonical forms of a matrix whose characteristic polynomial is (t-2)2(t-5)5. The paper is quite scoring and you can score good marks if you concentrate well on your studies.