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, 1999 based on Function of Complex numbers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and Triangles.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on A Parallelogram and a Line.
Try this beautiful problem from the Pre-RMO, 2019 based on Triangle and Integer. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2019 based on Area of Triangle and Integer. You may use sequential hints to solve the problem.
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.
Let us learn about Stirling Numbers of First Kind. Watch video and try the problems related to Math Olympiad Combinatorics
Suppose $r\geq 2$ is an integer, and let $m_{1},n_{1},m_{2},n_{2} \cdots ,m_{r},n_{r}$ be $2r$ integers such that$$|m_{i}n_{j}−m_{j}n_{i}|=1$$for any two integers $i$ and $j$ satisfying $1\leq i <j <r$. Determine the maximum possible value of $r$. Solution: Let us consider the case for $r =2$. Then $|m_{1}n_{2} - m_{2}n_{1}| =1$.......(1) Let us take $m_{1} =1, n_{2} =1, m_{2} =0, n_{1} =0$. Then, clearly the condition holds for $r =2$. […]
This is a work in progress. Please come back soon for more updates. We are adding problems, solutions and discussions on INMO (Indian National Math Olympiad 2021) INMO 2021, Problem 1 Suppose $r \geq 2$ is an integer, and let $m_{1}, n_{1}, m_{2}, n_{2}, \cdots, m_{r}, n_{r}$ be $2 r$ integers such that $$|m_{i} n_{j}-m_{j} […]
Suppose we have a triangle $ABC$. Let us extend the sides $BA$ and $BC$. We will draw the incircle of this triangle. How to draw the incircle? Here is the construction. Draw any two angle bisectors, say of angle $A$ and angle $B$ Mark the intersection point $I$. Drop a perpendicular line from I to […]
This year Cheenta Statistics Department has done a survey on the scores in each of the sections along with the total score in IIT JAM MS. Here is the secret for you! We have normalized the score to understand in terms of percentage. There are three questions, we ask The general performance for the IIT […]
Here are the problems and their corresponding solutions from B.Math Hons Objective Admission Test 2008. Problem 1 : Let $a, b$ and $c$ be fixed positive real numbers. Let $u_{n}=\frac{n^{2} a}{b+n^{2} c}$ for $n \geq 1$. Then as $n$ increases, (A) $u_{n}$ increases;(B) $u_{n}$ decreases;(C) $u_{n}$ increases first and then decreases;(D) none of the above […]
Here are the problems and their corresponding solutions from B.Math Hons Objective Admission Test 2007. Problem 1 : The number of ways of going up $7$ steps if we take one or two steps at a time is (A) $19$ ;(B) $20$;(C) $21$ ;(D) $22$ . Problem 2 : Consider the surface defined by $x^{2}+2 […]
Here, you will find all the questions of ISI Entrance Paper 2011 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1 : Let $a \geq 0$ be a constant such that $\sin (\sqrt{x+a})=\sin (\sqrt{x})$ for all $x \geq 0 .$ What can […]
Here, you will find all the questions of ISI Entrance Paper 2010 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Prove that in each year, the $13$ th day of some month occurs on a Friday. Problem 2: In the accompanying […]
Here, you will find all the questions of ISI Entrance Paper 2009 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $x, y, z$ be non-zero real numbers. Suppose $\alpha, \beta, \gamma$ are complex numbers such that $|\alpha|=|\beta|=|\gamma|=1 .$ If $x+y+z=0=\alpha […]