Answer key to TIFR 2013 entrance
Let's understand one-one function and differentiability with the help of a problem. Try it yourself before reading the solution. Let f be real valued, differentiable on (a, b) and $ f'(x) \ne 0 $ for all $ x \in (a, b) $. Then f is 1-1. True Discussion: Suppose f is not 1-1. Then there […]
Lets understand direct product of two subgroups with the help of a problem. This problem is useful for College Mathematics.
Let's understand Fixed Point of continuous bounded function with the help of a problem. This problem is useful for College Mathematics.
Given any integer $n \ge 2 $ , we can always find an integer m such that each of the n-1 consecutive integers m + 2, m + 3,..., m + n are composite. True Discussion: Take m=n!. Then the consecutive integers n! + 2 , n! + 3 , ... n! + n are […]
Let's discuss a problem based on Least Value of a Sum of Complex Numbers. Try to solve it yourself before reading the solution. Problem: Least Value of a Sum of Complex Numbers If $ z_1 , z_2 , z_3 , z_4 \in \mathbb{C} $ satisfy $ z_1 + z_2 + z_3 + z_4 = 0 […]
A lamp is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 ft/sec from the lamp to the nearest point on the wall. When he is midway between the lamp and the wall, the rate of change in the length of his shadow is (in ft/ sec)?
View the other sections of this test. Algebra || Geometry Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at helpdesk@cheenta.com View the other sections of this test. Algebra || Geometry Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at […]
Section 3: Geometry View the other sections of this test. Algebra || Analysis Try an online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at helpdesk@cheenta.com Find the reflection of the point (2, 1) with respect to the line x=y in the xy-plane. Find the area of the circle in […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2019 based on Equations and Complex numbers.
Try this beautiful problem from American Invitational Mathematics Examination, AIME, 2009 based on Probability of tossing a coin.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2009 based on Equations with a number of variables.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2010 based on Probability of divisors.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 from Geometry based on Area of Equilateral Triangle.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2015 based on Probability. You may use sequential hints.
Try this beautiful problem from the Pre-RMO, 2019 based on Two Arrangements. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2012 based on Arrangement of Digits. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Complex Numbers and prime.
Try this beautiful problem from American Invitational Mathematics Examination I, AIME I, 2009 based on geometric sequence. Use 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 […]