This is an objective problem 151 from TOMATO based on Consecutive composites, useful for Indian Statistical Institute Entrance Exam. Let $n = 51! + 1$. Then the number of primes among $n+1, n+2, ... , n+50$ is (A) $0$; (B) $1$; (C) $2$; (D) more than $2$; Discussion: $51!$ is divisible by $2, 3,... 51$. […]
If three prime numbers, all greater than $3$, are in A.P. , then their common difference (A) must be divisible by $2$ but not necessarily by $3$; (B) must be divisible by $3$ but not necessarily by $2$; (C) must be divisible by both $2$ and $3$; (D) need not be divisible by any of […]
Let N be a positive integer not equal to 1. Then note that none of the numbers 2, 3, ... , N is a divisor of (N! -1). From this we can conclude that: (A) (N! - 1) is a prime number; (B) at least one of the numbers N+1 , N+2 , ...., N! […]
The number $1000! = 1.2.3...1000$ ends exactly with (A) $249$ zeroes; (B) $250$ zeroes; (C) $240$ zeroes; (D) $200$ zeroes; Discussion: To find the number of zeroes at the end of n! we just need to figure out the number of 5's occurring in prime factorization of it. Why? Because there are much more 2's […]
This post consists of Problems and solutions from TIFR 2013 Paper. Try to solve them and then read their solutions. TIFR 2013 Paper PART A (Linear and Abstract Algebra) Problem 1 Problem 2 - Automorphism of the Additive Group of Rationals Problem 3 - Existence of Real Root Problem 4 - Existence of Complex Root […]
This is an (ever-growing and ever-changing) list of books, useful for school and college mathematics students. If you are working toward Math Olympiad, I.S.I., C.M.I. entrance programs or intense college mathematics, these books may prove to be your best friend. If you are taking a Cheenta Advanced Math Program, chances are that you will referred […]
Let's discuss this objective problem number 14 from ISI BStat BMath. Try to solve the problem and then read their solution. Problem 14 f(x) = tan(sinx) (x > 0) To understand the graph of a function, easiest and the most proper method is to apply techniques from calculus. We will quickly compute, derivative and second […]
This post contains the six Indian National Maths Olympiad, INMO 2015 problems. Try to solve these problems. Let ABC be a right-angled triangle with $ \angle{B}=90^{\circ} $. Let BD is the altitude from B on AC. Let P, Q and Ibe the incenters of triangles ABD, CBD, and ABC respectively. Show that circumcenter of triangle […]
Let's understand the factor method of Diophantine equations step-by-step. Aso, try the question related to it. Diophantine Equations Consider an equation for which we seek only integer solutions. There is no standard technique of solving such a problem, though there are some common heuristics that you may apply. A simple example is $ x^2 - […]
Try this beautiful problem from Geometry:Tetrahedron box from AMC-10A, 2011. You may use sequential hints to solve the problem
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Largest Area of Triangle.
Try this beautiful problem from Algebra:Roots of cubic equation from AMC-10A, 2010. You may use sequential hints to solve the problem
Try this beautiful Geometry Problem on Equilateral Triangle from AMC-10A, 2010.You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry:cubical box from AMC-10A, 2010. You may use sequential hints to solve the problem
Try this beautiful problem from the Pre-RMO, 2017 based on GP and 2-digit number. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Altitudes of triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from PRMO, 2018 based on Geometry. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Quadratic Equation. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Hexagon from AMC-10A, 2010. You may use sequential hints to solve the problem.