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
?