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 […]
Here, you will find all the questions of ISI Entrance Paper 2012 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: 2012 Multiple-Choice Test Problem 1: A rod $A B$ of length 3 rests on a wall as […]
Given a triangle ABC, let P and Q be the points on the segments AB and AC, respectively such that AP = AQ. Let S and R be distinct points on segment BC such that S lies between B and R, ∠BPS = ∠PRS, and ∠CQR = ∠QSR. Prove that P, Q, R and S […]
Problem 1: Define a sequence as: Prove that this sequence has a finite limit as Also determine the limit. Problem 2: Let and be two sequences of numbers, and let be an integer greater than Define Prove that if the quadratic expressions do not have any real roots, then all the remaining polynomials also don’t […]
The best way to learn mathematics is to DO mathematics. In fact we can add something more to that. The best way to get inspired about mathematics is to 'experience' beautiful mathematics. In 2012 we are transforming our learning (and teaching) methods. Till today the basic style of our program comprised of: Inside Classroom a […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Odd and Even integers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Two and Three-digit numbers.
Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression and Integers. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2008 based on Trigonometry. You may use sequential hints to solve the problem.
Try this problem from the Singapore Mathematics Olympiad, SMO, 2010 based on the application of the Pythagoras Theorem. You may use sequential hints.
Try this beautiful problem from Probability in Dice from AMC-10A, 2009. You may use sequential hints to solve the problem.
Try this beautiful Problem from Singapore Mathematics Olympiad, 2012 based on Functional Equations. You may use sequential hints to solve the problem.
Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2018 based on Triangles. You may use sequential hints to solve the problem.
Try this beautiful problem from Pattern based on Triangle from AMC-10A, 2003. You may use sequential hints to solve the problem
Try this beautiful problem from Number theory based on divisibility from AMC-10A, 2003. You may use sequential hints to solve the problem.