Here, you will find all the questions of ISI Entrance Paper 2006 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Bishops on a chessboard move along the diagonals ( that is, on lines parallel to the two main diagonals). Prove that […]
Here, you will find all the questions of ISI Entrance Paper 2005 from the Indian Statistical Institute's B.Math Entrance. You will also get the solutions soon to all the previous year's problems. Problem 1 : For any \( k \in\mathbb{Z}^+ \) , prove that:-$$ \displaystyle{ 2(\sqrt{k+1}-\sqrt{k})<\frac{1}{\sqrt{k}}<\\2(\sqrt{k}-\sqrt{k-1})}$$Also compute integral part of \(\displaystyle{\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{10000}}}\). Problem 2 : Let […]
Try this problem from Test of Mathematics, TOMATO Objective problem number 44, useful for ISI B.Stat and B.Math. Problem: TOMATO Objective 44 Suppose that $\mathbf{ x_1 , \cdots , x_n}$ (n> 2) are real numbers such that x $\mathbf{x_i = -x_{n-i+1}}$ for $\mathbf{1\le i \le n}$ . Consider the sum $\mathbf{ S = \sum \sum […]
Here, you will find all the questions of ISI Entrance Paper 2010 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $\mathbf{a_1,a_2,\cdots, a_n }$ and $\mathbf{ b_1,b_2,\cdots, b_n }$ be two permutations of the numbers $\mathbf{1,2,\cdots, n }$. Show that $ {\sum_{i=1}^n […]
Here, you will find all the questions of ISI Entrance Paper 2009 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Two train lines intersect each other at a junction at an acute angle $ \mathbf{\theta}$. A train is passing along one of […]
Here, you will find all the questions of ISI Entrance Paper 2008 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Of all triangles with given perimeter, find the triangle with the maximum area. Justify your answer Problem 2: A $40$ feet high […]
Here, you will find all the questions of ISI Entrance Paper 2007 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Suppose \(a\) is a complex number such that \( { a^2+a+\frac{1}{a}+\frac{1}{a^2}+1=0 }\) If \(m\) is a positive integer, find the value of […]
Here, you will find all the questions of ISI Entrance Paper 2006 from Indian Statistical Institute's B. Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem1 : If the normal to the curve \(\displaystyle{ x^{\frac{2}{3}}+y^{\frac23}=a^{\frac23} }\) at some point makes an angle \(\displaystyle{\theta}\) with the \(X\)-axis, show that […]
Here, you will find all the questions of ISI Entrance Paper 2005 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let \( a,b \) and \( c \) be the sides of a right angled triangle. Let \( \displaystyle{\theta } \) be […]
Here, you will find all the questions of ISI Entrance Paper 2011 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $x_1, x_2, \cdots , x_n $ be positive reals with $x_1+x_2+\cdots+x_n=1 $. Then show that $ \sum_{i=1}^n \frac{x_i}{2-x_i} \ge \frac{n}{2n-1} $ […]
Try this beautiful problem from Geometry: Triangle from AMC-10B, 2011, Problem-9. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2019 based on Rectangle and Squares. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2018 based on Centroids and Area. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2007 based on Sequence and Integers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2001 based on Patterns and Integers.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2009 based on Centroid of Triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on GCD and Primes. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Planes and distance.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1985 based on GCD and Sequence.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Logic and speed.