# Cheenta Reading Room

Outstanding problems, discussion and more## Research Track – Cocompact action and isotropy subgroups

Suppose a group $latex \Gamma $ is acting properly and cocompactly on a metric space X, by isometries. (Understand: proper, cocompact, isometric action) Claim There are only finitely many conjugacy classes of the isotropy subgroups in $latex \Gamma $ Sketch Since the...

read more## I.S.I 2016 SUBJECTIVE PROBLEM – 1

Understand the problemSuppose that in a sports tournament featuring n players, each pairplays one game and there is always a winner and a loser (no draws).Show that the players can be arranged in an order P1, P2, . . . , Pn suchthat player Pi has beaten Pi+1 for all i...

read more## ISI 2019 : Problem #7

Understand the problem Let be a polynomial with integer coefficients. Define and for .If there exists a natural number such that , then prove that either or . I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2019. Subjective Problem...

read more## Working backward – C.M.I UG -2019

Understand the problem If there exists a calculator with 12 buttons, 10 being the buttons for the digits and A and B being two buttons being processes where if n is displayed on the calculator if A is pressed it increases the displayed number by 1 and if B is pressed...

read more## Solution in Real – C.M.I -U.G-2019

Understand the problem .Find all real numbers x for which C.M.I (Chennai mathematical institute ) U.G-2019 Algebra 8 out of 10.Start with hintsDo you really need a hint? Try it first!It is of the the form of . Do you observe ? where a=\(2^x\) b=\(3^x\)...

read more## I.S.I 2019 Subjective Problem -4

Understand the problem Let be a twice differentiable function such thatShow that there exist such that for all . I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2019. Subjective Problem no. 4 calculus 8.5 out of 10Problems In CALCULUS OF...

read more## Sum Of 1’S C.M.I UG-2019 Entrance

Understand the problem Find the sum 1+111+11111+1111111+.....1....111(2k+1) ones C.M.I UG-2019 entrance examAlgebra 3.5 out of 10 challenges and trills of pre college mathematics Start with hintsDo you really need a hint? Try it first!can you some how...

read more## C.M.I-2019 Geometry problem

Understand the problemlet O be a point inside a parallelogram ABCD such that \(\angle AOB+\angle COD =180\) prove that \(\angle OBC =\angle ODC\) C.M.I (Chennai mathematical institute UG-2019 entrance Geometry 5 out of 10challenges and thrills of pre college...

read more## Triangle in complex plane – ISI 2019 Obj P8

This problem from ISI Entrance 2019 is an interesting application of complex numbers in geometry. Try your hands on this!

read more## Four Points on a Circle, ISI Entrance 2017, Subjective Problem no 2

Understand the problem Consider a circle of radius 6 as given in the diagram below. Let \(B,C,D\) and \(E\) be points on the circle such that \(BD\) and \(CE\), when extended, intersect at \(A\). If \(AD\) and \(AE\) have length 5 and 4 respectively, and \(DBC\) is a...

read more