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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...

## 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...

## 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...

## 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...

## 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=$$3^x$$...

## 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...

## 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...

## 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...

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...