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Explore the Back-StoryHere, you will find all the questions of ISI Entrance Paper 2005 from Indian Statistical Institute's B.Math Entrance. You will also get the solutions soon of all the previous year problems.

**Problem 1 :**

For any , prove that:-

Also compute integral part of .

**Problem 2 : **

Let and for all . Define : Compute

**Problem 3 :**

Let be a quadrilateral such that the sum of a pair of opposite sides equals the sum of other pair of opposite sides . Prove that the circles inscribed in triangles and are tangent to each other.

**Problem 4 :**

For a set S we denote its cardinality by |S|. Let be non-negative integers. Let (respectively ) be the set of all k-tuples of integers such that for all i and is even (respectively odd). Show that .

**Problem 5 :**

Find the point in the closed unit disc at which the function f(x,y)=x+y attains its maximum .

**Problem 6 :**

Let Show that, for , the polynomial p(t) has exactly one root in the interval

**Problem 7 :**

Let M be a point in the triangle ABC such that

Show that the locus of all such points is a straight line.

**Problem 8 : **

In how many ways can one fill an matrix with and so that the product of the entries in each row and each column equals ?

Here, you will find all the questions of ISI Entrance Paper 2005 from Indian Statistical Institute's B.Math Entrance. You will also get the solutions soon of all the previous year problems.

**Problem 1 :**

For any , prove that:-

Also compute integral part of .

**Problem 2 : **

Let and for all . Define : Compute

**Problem 3 :**

Let be a quadrilateral such that the sum of a pair of opposite sides equals the sum of other pair of opposite sides . Prove that the circles inscribed in triangles and are tangent to each other.

**Problem 4 :**

For a set S we denote its cardinality by |S|. Let be non-negative integers. Let (respectively ) be the set of all k-tuples of integers such that for all i and is even (respectively odd). Show that .

**Problem 5 :**

Find the point in the closed unit disc at which the function f(x,y)=x+y attains its maximum .

**Problem 6 :**

Let Show that, for , the polynomial p(t) has exactly one root in the interval

**Problem 7 :**

Let M be a point in the triangle ABC such that

Show that the locus of all such points is a straight line.

**Problem 8 : **

In how many ways can one fill an matrix with and so that the product of the entries in each row and each column equals ?

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