 ## Average Determinant: TIFR GS 2017 Part A Problem 8.

Understand the problem True or False? Let (n geq 2) be a natural number. Let (S) be the set of all (n times n) real matrices whose entries are only (0,1) or (2). Then the average determinant of a matrix in (S) is greater than or equal to 1. Source of the problem TIFR... ## Connected Components: TIFR GS 2017 Part A Problem 7

Understand the problem True or False? Let (H_1, H_2, H_3,H_4 ) be four hyperplanes in ( R^3 ). The maximum possible number of connected components of ( R^3 – H_1 cup H_2 cup H_3 cap H_4 ) is 14. Source of the problem TIFR GS 2017 Entrance Examination Paper Topic... ## Differentiable and Bijective: TIFR GS 2017 Part A Problem 6.

Understand the problem True or False? If ( f: Bbb R to Bbb R ) is differentiable and bijective then (f^{-1} ) is also differentiable. Source of the problem TIFR GS 2017 Entrance Examination Paper Topic Real Analysis Difficulty Level Easy Suggested Book Introduction to... ## Controversial Function: TIFR GS 2017 Part A Problem 3

Understand the problem True or False? There exists a function ( f: Bbb R to Bbb R ) satisfying ( f(-1)=-1, f(1)=1 ) and (|f(x)-f(y)| leq |x-y|^{frac{3}{2}} forall x, y in Bbb R ) Source of the problem TIFR GS 2017 Entrance Examination paper Topic Real Analysis... ## L’Hospital’s Rule: TIFR GS 2017 Part A Problem 5.

Understand the problem True or False? Suppose (f(x) ) is a continuosy differentiable function on ( Bbb R ) such that ( lim_{x to infty} f(x)= 1 ) and ( lim_{x to infty} f'(x)=b). Then (b=1 ). Source of the problem TIFR GS 2017 Entrance Examination Paper Topic...