Here, you will find all the questions of ISI Entrance Paper 2011 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $x_1, x_2, \cdots , x_n $ be positive reals with $x_1+x_2+\cdots+x_n=1 $. Then show that $ \sum_{i=1}^n \frac{x_i}{2-x_i} \ge \frac{n}{2n-1} $ […]
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It is possible to input Latex in facebook to input math equations. Latex in Facebook Down side is, only viewers using chrome and latex extension installed can view the equations. Other browsers can only see latex code. Anyways, it is better than not having latex at all. Steps: Go to Google Chrome Click on Settings […]
Day 1 - 03 January 2014 1 Let be two positive sequences defined by and for all . Prove that they are converges and find their limits. 2 Given the polynomial where is a positive integer. Prove that can't be written as a product of non-constant polynomials with integer coefficients. 3 Given a regular […]
Problem 1In a triangle $A B C,$ let $D$ be a point on the segment $B C$ such that $A B+B D=A C+C D .$ Suppose that the points $B, C$ and the centroids of triangles $A B D$ and $A C D$ lie on a circle. Prove that $A B=A C .$Solution […]
This is a problem from Test of Mathematics, TOMATO problem 6. It is useful for ISI and CMI Entrance Exam. Problem : TOMATO Problem 6 Let $latex x_1 , x_2, ..... , x_{100} $ be positive integers such that $latex x_i + x_{i+1} = k $ for all $latex i $ where $latex k $ […]
This is a problem from Test of Mathematics, TOMATO Problem 106. It is useful for ISI and CMI Entrance Exam. Try out the problem. Problem: TOMATO Objective 106 The term that is independent of x in the expansion of $[\frac{3x^2}{2}-\frac{1}{3x}]^9 $ a) ${{9} \choose {6}}(\frac{1}{3})^3(\frac{3}{2})^6 $ b) ${{9} \choose {5}}(\frac{3}{2})^5(-\frac{1}{3})^4 $ c) ${{9} \choose {3}}(\frac{1}{6})^3 […]
We observe a renewed interest in Math and Basic Science in India after decades of engineering mania. This is a welcome change. The top tier students, in increasing numbers, are opting for such courses. In this article we present some of the institutes which offer world class education in basic science after school.
This is a problem from Test of Mathematics, TOMATO Objective 8, useful for ISI and CMI Entrance. Try out this problem. (by Rahul Roy) Problem: Two trains of equal length L,travelling at speeds v1 and v2 miles per hour in opposite directions,take t seconds to cross each other .then L in feet is: Solution: Total […]
Objective Questions: Problem 1: Let $A=\left(\begin{array}{rrr}1 & 1 & 1 \\ 3 & -1 & 1 \\ 1 & 5 & 3\end{array}\right)$ and $V$ be the vector space of all $X \in \mathbb{R}^{3}$ such that $A X=0$. Then ${dim}(V)$ is(A) 0(B) 1(C) 2(D) 3 Problem 2. The value of $n$ for which the divergence of […]