Solved Problems on Tangent and Normal mainly for IIT,WBJEE and AIEEE. Click here to download For more problems visit http://kolkatamaths.yolasite.com/xi-xii.php
Showing posts with label free maths materials. Show all posts
Showing posts with label free maths materials. Show all posts
Thursday, August 11, 2011
Saturday, December 4, 2010
Saturday, November 13, 2010
Something Different!
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
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
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