TIFR Math Question Paper

Hey ! myself Pooja and I am pursuing B.sc in IT from Tata Institute of Fundamental Research (TIFR) so kindly provide the Maths question paper for the Bsc IT students ??? if possible than avail the questions papers in Pdf format????

Can you provide me the previous year GS (Graduate School Admissions Entrance) -2018 (Mathematics) Question Paper of TIFR (Tata Institute of Fundamental Research)?

[pooja]

The previous year GS (Graduate School Admissions Entrance) -2018 (Mathematics) Question Paper of TIFR (Tata Institute of Fundamental Research) is as follows:

Part A
Answer whether the following statements are True or False. Mark your answer on the machine checkable answer sheet that is provided.

Let A be a countable subset of R which is well-ordered with respect to the usual ordering on R (where well-ordered means that every nonempty subset has a minimum element in it). Then A has an order preserving bijection with a subset of N.

Let G, H be finite groups. Then any subgroup of G H is equal to A B for some subgroups A<G and B<H.

Let V be the subspace of the real vector space of real valued functions on R, spanned by cost and sin t. Let D : V V be the linear map sending f(t) V to df(t)/dt. Then D has a real eigenvalue.

A countable group can have only countably many distinct subgroups.

Let f(x) and g(x) be uniformly continuous functions from R to R. Then their pointwise product f(x)g(x) is uniformly continuous.

Part B
Answer the following multiple choice questions, by appropriately marking your answer on the machine checkable answer sheet that is provided

The set of real numbers in the open interval (0, 1) which have more than one decimal expansion is
(a) empty.
(b) non-empty but finite.
(c) countably infinite.
(d) uncountable.

The number of rings of order 4, up to isomorphism, is:
(a) 1
(b) 2
(c) 3
(d) 4


TIFR GS Math Question Paper