Problem: Let f: R --> R be defined by $latex f(x) = sin (x^3) $. Then f is continuous but not uniformly continuous. Discussion: True It is sufficient to show that there exists an $latex epsilon > 0 $ such that for all $latex \delta > 0 $ there exist $latex x_1 , x_2 \in […]
This post contains a problem from TIFR 2013 Math paper D based on Inequality of square root function. The inequality $ \sqrt {n+1} - \sqrt n < \frac {1}{\sqrt n } $ is false for all in n such that $ 101 \le n \le 2000 $ False Discussion: $ \sqrt {n+1} - \sqrt n […]
Any automorphism of the group Q under addition is of the form x → qx for some q ∈ Q. True Discussion: Suppose f is an automorphism of the group Q. Let f(1) = m (of course 'm' will be different for different automorphisms). Now $f(x+y) = f(x) + f(y)$ implies $f(x) = mx$ where m […]
Problem 1 . A shop sells two kind of products A and B. One day a salesman sold both A and B at the same price, $2100$ to a customer. Suppose A makes a profit of 20% and B makes a loss of 20%. Then the deal(A) make a profit of $70$; (B) make a […]
What motivates research in Non-Linear Partial Differential Equation? Swarnendu Sil, presently a Ph.D. student in Ecole polytechnique de federale de lausannee (one of the leading universities of the world located in Switzerland), delivered a talk (through video conference) on this topic this Sunday in the reunion of Cheenta. The seminar began with an analysis of […]
1. For how many values of N (positive integer) N(N-101) is a square of a positive integer? Solution: (We will not consider the cases where N = 0 or N = 101) $N(N-101) = m^2$ => $N^2 - 101N - m^2 = 0$ Roots of this quadratic in N is => $\frac{101 \pm\ sqrt { […]
Here, you will find all the questions of ISI Entrance Paper 2013 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. B.Stat. (Hons.) & B.Math. (Hons.) Admission Test: 2013 Multiple-Choice Test Problem 1: Let $i=\sqrt{-1}$ and $S=\{i+i^{2}+\cdots+i^{n}: n \geq 1\}$. The number of distinct real […]
Given: AB is the diameter of a circle with center O. C be any point on the circle. OC. is joined. Let Q be the midpoint of OC. AQ produced meet the circle at E. CD be perpendicular to diameter AB. ED and CB are joined. R.T.P. : CM = MB Construction: AC and BD […]
Try this beautiful problem from the Pre-RMO, 2019 based on Triangles and Internal bisectors. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra based on Linear equations from AMC-8, 2007. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2012 based on digit. You may use sequential hints to solve the problem.
Try this beautiful problem from AMC-8, 2013, (Problem-20) based on area of semi circle.You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Radius of semicircle from AMC-8, 2013, Problem-23. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra based on Perfect cubes from AMC-8, 2018, Problem -25. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra based on integer from PRMO 8, 2018. You may use sequential hints to solve the problem.
Try this beautiful problem from Integer from TOMATO useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.
Learn the concept of the Counting Principle and make algorithms to count complex things in a simpler way with the help of Combinatorics problem.
Try this beautiful problem from Geometry: Area of the Regular Hexagon - AMC-8, 2012 - Problem 23. You may use sequential hints to solve the problem.