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# ISI B.Math 2005 Subjective Paper| Problems & Solutions 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 ?

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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