Quadratic Equation

Solved Problems on Quadratic Equation for CBSE and ICSE (IX and X). Click here to download for more problems click here

Solved Problems on Definite Integrals

Few difficult problems on Definite Integrals which I have solved partially. Click here to download These problems are important for understanding the application of the properties of the definite integrals which are commonly asked in boards and exams like IIT, AIEEE, WBJEE and other exams of same nature.

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

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.