Understand the problem Let be a twice differentiable function such thatShow that there exist such that for all . Source of the problem I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2019. Subjective Problem no. 4 Topic calculus Difficulty...

Understand the problem Find the sum 1+111+11111+1111111+…..1….111(2k+1) ones Source of the problem C.M.I UG-2019 entrance exam Topic Algebra Difficulty Level 3.5 out of 10 Suggested Book challenges and trills of pre college mathematics ...

Understand the problem let O be a point inside a parallelogram ABCD such that (angle AOB+angle COD =180) prove that (angle OBC =angle ODC) Source of the problem C.M.I (Chennai mathematical institute UG-2019 entrance Topic Geometry Difficulty Level 5 out of 10...

Understand the problem For each natural number k, choose a complex number (z_k) , with( | z_k | = 1 ), and denote ( a_k ) by the area of the triangle formed by (z_k , i cdot z_k , z_k + i cdot z_k ) . Then which of the following is true for the series below: $$...

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 right angle,...

Understand the problem Let (g : mathbb{N} to mathbb{N} ) with ( g(n) ) being the product of digits of (n). (a) Prove that ( g(n)le n) for all ( n in mathbb{N} ) . (b) Find all (n in mathbb{N} ) , for which ( n^2-12n+36=g(n) ). Source of the problem...