TIFR 2013 Paper - Problem and Solutions

This post consists of Problems and solutions from TIFR 2013 Paper. Try to solve them and then read their solutions.

TIFR 2013 Paper

• PART A (Linear and Abstract Algebra)
  • Problem 1
  • Problem 2 - Automorphism of the Additive Group of Rationals
  • Problem 3 - Existence of Real Root
  • Problem 4 - Existence of Complex Root
  • Problem 5 - Non trivial Proper subgroups of additive group of real numbers
  • Problem 6 -
  • Problem 7
  • Problem 8
  • Problem 9 - Multiplicative Group
  • Problem 10 - Center of group and normal subgroup of order 2
• Part B (Analysis)
  • Problem 11
  • Problem 12
  • Problem 13
  • Problem 14 - Uniform Continuity of $latex sin (x^3 ) $
  • Problem 15
  • Problem 16
  • Problem 17
  • Problem 18
  • Problem 19 - Differentiability and Uniform Continuity
  • Problem 20
• Part C (Topology)
  • Problem 21
  • Problem 22
  • Problem 23
  • Problem 24
  • Problem 25
  • Problem 26
  • Problem 27
  • Problem 28
  • Problem 29
  • Problem 30
• Part D (Miscellaneous)
  • Problem 31 - Inequality of square root function
  • Problem 32
  • Problem 33
  • Problem 34
  • Problem 35
  • Problem 36
  • Problem 37
  • Problem 38
  • Problem 39
  • Problem 40