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 […]
Compute I = $latex (\int_e^{e^4}\sqrt{\log(x)}dx)$ if it is given that $latex (\int _1^2 e^{t^2} dt = \alpha )$ I = $latex ([x \sqrt{\log(x)}]_e^{e^4} - \int_e^{e^4} x \frac{1}{2 \sqrt{log(x)}} \frac {1}{x} dx )$ = $latex ([e^4 \sqrt {\log_e e^4} - e \sqrt {\log _e e}] - \frac{1}{2} \int_e^{e^4}\frac{1}{\sqrt{log(x)}} dx )$ = $latex (2 e^4 - e […]
P148. Show that there is no real constant c > 0 such that $latex (\cos\sqrt{x+c}=\cos\sqrt{x})$ for all real numbers $latex (x\ge 0)$.Solution: If the given equation holds for some constant c>0 then, f(x) = $latex (\cos\sqrt{x}-\cos\sqrt{x+c}=0)$ for all $latex (x\ge 0)$$latex (\Rightarrow 2\sin\frac{\sqrt{x+c}+\sqrt{x}}{2}\sin\frac{\sqrt{x+c}-\sqrt{x}}{2}=0)$Putting x=0, we note$latex (\Rightarrow\sin^2\frac{\sqrt{c}}{2}=0)$As $latex (c\not=0)$$latex (\sqrt{c}=2n\pi)$$latex (\Rightarrow c=4n^2\pi^2)$We put n=1 and […]
P164. Show that the area of the bounded region enclosed between the curves $latex (y^3=x^2)$ and $latex (y=2-x^2)$, is $latex (2\frac{2}{15})$. Solution: Note that $latex (y=x^{\frac{2}{3}})$ is an even function (green line). P165. Find the area of the region in the xy plane, bounded by the graphs of $latex (y=x^2)$, x+y = 2 and $latex […]
That is a good start. And a demanding one. All good starts are demanded by birthright. They ask you to do more in the subsequent days. This article is mainly targeted at class 12 pass-outs who are targeting I.S.I. 2012 (or those 12th graders who are able to devote some serious time to mathematics). Target […]
Indian Statistical Institute (I.S.I.), Chennai Mathematical Institute (C.M.I.) and Institute of Mathematics and Application (I.M.A.) can be regarded as three Indian institutions that provided world class mathematics course at undergraduate level. The B.Stat Course at I.S.I. is also world famous. The courses at C.M.I. and I.M.A. have computer science as second major. Each of these […]
Try this beautiful problem from Geometry:Area of Trapezium.AMC-10A, 2018. You may use sequential hints to solve the problem
Try this beautiful problem from Geometry: Triangle from AMC-10B, 2011, Problem-9. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2009 based on Centroid of Triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2019 based on Rectangle and Squares. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2018 based on Centroids and Area. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2007 based on Sequence and Integers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2001 based on Patterns and Integers.
Try this beautiful problem from the Pre-RMO, 2017 based on GCD and Primes. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Planes and distance.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1985 based on GCD and Sequence.