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 […]
CHENNAI MATHEMATICAL INSTITUTE B.SC. MATH ENTRANCE 2012ANSWER FIVE 6 MARK QUESTIONS AND SEVEN OUT 10 MARK QUESTIONS.6 mark questions Find the number of real solutions of $latex x = 99 \sin (\pi ) x $ Find $latex {\displaystyle\lim_{xto\infty}\dfrac{x^{100} \ln(x)}{e^x \tan^{-1}(\frac{\pi}{3} + \sin x)}}$ (part A)Suppose there are k students and n identical chocolates. The chocolates […]
Q7. Consider two circles with radii a, and b and centers at (b, 0), (a, 0) respectively with b<a. Let the crescent shaped region M has a third circle which at any position is tangential to both the inner circle and the outer circle. Find the locus of center c of the third circle as it […]
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 the Pre-RMO, 2019 based on Trigonometry Problem. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2010 based on functional equation. You may use sequential hints.
Try this beautiful problem from Algebra based on quadratic equation from PRMO 2016. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2009 based on Triangles and sides.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Rectangles and sides.
Try this beautiful problem from algebra, based on Arithmetic Progression from AMC-10B, 2004. You may use sequential hints to solve the problem
Try this beautiful problem from PRMO, 2016 based on Triangle You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Area of triangle from AMC-10A, 2009, Problem-10. You may use sequential hints to solve the problem.