Understand the problem True or false: There exists a continuous function (f: Bbb R to Bbb R) such that (f(Bbb Q) subseteq {Bbb R}setminus {Bbb Q}) and (f({Bbb R}setminus {Bbb Q}) subseteq {Bbb Q}) Source of the problem TIFR 2019 GS Part B, Problem 1 Topic Real...

Understand the problem A stick of length (1) is broken into two pieces by cutting at a randomly chosen point. What is the expected length of the smaller piece? (1 /8) (1 /4) (1 /e) (1 /pi) Source of the problem TIFR 2019 GS Part A, Problem 20 Topic Statistics...

Understand the problem Consider maps (C^{infty} to C^{infty}) s.t (f mapsto f+ frac{df}{dx}). We have to check whether this map is injective or surjective. Start with hints Source of the problem TIFR 2019 GS Part A, Problem 19 Topic Functions on differential equation...

Understand the problem Consider the different ways to colour a cube with given colours such that each face will be given a single colour and all the six colours will be used. Define two such colourings to be equivalent if one will get from another just by rotation....

Understand the problem Let be the subset s.t Consider the following statements: X is compact. X is connected. X is path-connected. How many of the statements is/are true: 0 1 2 3 Source of the problem TIFR 2019 GS Part A, Problem 17 Topic Topology Difficulty Level...