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1)Let p be an odd prime and n a positive integer. In the coordinate plane, eight distinct points with integer coordinates lie on a circle with diameter of length p^n. Prove that there exists a triangle with vertices at three of the given points such that the squares of its side lengths are  integers  divisible by p^n+1


2)Show that 1+2+3+........+n divides 1^k+2^k+...........+n^k, for and odd positive integer k and for nay natural number n


3)Denote by a, b, c the lengths of the sides of a triangle. Prove that
a^2(b + c − a) + b^2(c + a − b) + c^2(a + b − c) ≤ 3abc.

4)Prove that the 8th power of any integer is of the form 17k or 17k+1 or 17k-1 where k is an integer #Maths #Number Theory

5) From ten distinct two-digit numbers, one can always choose two-disjoint nonempty subsets, so that their elemets have the same sum #Maths #IMO 1972

"Dare To Try"

10 challenging problem for bright students its aimed for students preparing for Olympiad or Indian Statistical institute

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CBSE Maths Paper for XI

Download maths paper for XI ( CBSE ). Chapters included in this paper are Sets,Realations and Function, Trigonometry and Principle of Mathematical Induction.

Airthmetic Progression

Another free problem sheet on A.P for ISC,CBSE, HS and other state board. Click here  Dont think that the picture is irrelevant . It has got a connection with Fibonnaci Series!!

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Problems for WBJEE,ISC,CBSE and other boards on Trigonometry

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Problem sheet on Inverse Trigonometric Function for ISC,HS,WBJEE,AIEEE,IIT and other state boards and competetive exams

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