Here, you will find all the questions of ISI Entrance Paper 2007 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $n$ be a positive integer . If $n$ has odd number of divisors ( other than $1$ and $n$ ) […]
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 […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Cones and circle.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2001 based on Incentre and Triangle.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime.
Try this beautiful problem from Geometry: Octahedron AMC-10A, 2006. You may use sequential hints to solve the problem
Try this beautiful problem from Probability in Coordinates from AMC-10A, 2003. You may use sequential hints to solve the problem.
Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2012 based on Triangle You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Triangle and Trigonometry.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2013 based on HCF. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad based on area of triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 based on Theory of Equations.