Here, you will find all the questions of ISI Entrance Paper 2005 from the Indian Statistical Institute's B.Math Entrance. You will also get the solutions soon to all the previous year's problems. Problem 1 : For any \( k \in\mathbb{Z}^+ \) , prove that:-$$ \displaystyle{ 2(\sqrt{k+1}-\sqrt{k})<\frac{1}{\sqrt{k}}<\\2(\sqrt{k}-\sqrt{k-1})}$$Also compute integral part of \(\displaystyle{\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{10000}}}\). Problem 2 : Let […]
Try this problem from Test of Mathematics, TOMATO Objective problem number 44, useful for ISI B.Stat and B.Math. Problem: TOMATO Objective 44 Suppose that $\mathbf{ x_1 , \cdots , x_n}$ (n> 2) are real numbers such that x $\mathbf{x_i = -x_{n-i+1}}$ for $\mathbf{1\le i \le n}$ . Consider the sum $\mathbf{ S = \sum \sum […]
Here, you will find all the questions of ISI Entrance Paper 2010 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $\mathbf{a_1,a_2,\cdots, a_n }$ and $\mathbf{ b_1,b_2,\cdots, b_n }$ be two permutations of the numbers $\mathbf{1,2,\cdots, n }$. Show that $ {\sum_{i=1}^n […]
Here, you will find all the questions of ISI Entrance Paper 2009 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Two train lines intersect each other at a junction at an acute angle $ \mathbf{\theta}$. A train is passing along one of […]
Here, you will find all the questions of ISI Entrance Paper 2008 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Of all triangles with given perimeter, find the triangle with the maximum area. Justify your answer Problem 2: A $40$ feet high […]
Here, you will find all the questions of ISI Entrance Paper 2007 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Suppose \(a\) is a complex number such that \( { a^2+a+\frac{1}{a}+\frac{1}{a^2}+1=0 }\) If \(m\) is a positive integer, find the value of […]
Here, you will find all the questions of ISI Entrance Paper 2006 from Indian Statistical Institute's B. Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem1 : If the normal to the curve \(\displaystyle{ x^{\frac{2}{3}}+y^{\frac23}=a^{\frac23} }\) at some point makes an angle \(\displaystyle{\theta}\) with the \(X\)-axis, show that […]
This is a problem from I.S.I. M.Math Subjective Sample Paper 2013 based on Riemann Integrable Function. Try out this problem. Problem: Riemann Integrable function Let N>0 and let $latex \mathbf{ f:[0,1] to [0,1] }$ be denoted by f(x) = 1 if x=1/i for some integer $latex \mathbf{i\le N}$ and f(x) = 0 for all other […]
This is a problem from I.S.I. M.Math Subjective Sample Paper 2013 based on Maximal Ideal of a Polynomial Ring. Try this out. Problem: Maximal Ideal of a Polynomial Ring Let k be a field and k [x, y] denote the polynomial ring in the two variables x and y with coefficient from k . Prove that […]
Here, you will find all the questions of ISI Entrance Paper 2005 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let \( a,b \) and \( c \) be the sides of a right angled triangle. Let \( \displaystyle{\theta } \) be […]