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 is a complex number such that
If
is a positive integer, find the value of
Discussion
Problem 2:
Use calculus to find the behaviour of the function and sketch the graph of the function for
. Show clearly the locations of the maxima, minima and points of inflection in your graph.
Problem 3:
Let be a continuous function and, for any real number
, let
denote the greatest integer less than or equal to
. Show that for any
,
Problem 4:
Show that it is not possible to have a triangle with sides , and
whose medians have length
and
.
Problem 5:
Show that for all values of
.
Problem 6:
Let where
is an odd integer. Let
be a function defined on
taking values in
such that
 (a) for all
(b) for all
Show that
Problem 7:
Consider a prism with triangular base. The total area of the three faces containing a particular vertex is
. Show that the maximum possible volume of the prism is
and find the height of this largest prism.
Problem 8:
The following figure shows a grid divided into
subgrids of size
. This grid has
cells,
in each subgrid.
Now consider an grid divided into
subgrids of size
. Find the number of ways in which you can select
cells from this grid such that there is exactly one cell coming from each subgrid, one from each row and one from each column.
Problem 9:
Let
be a set satisfying the following properties:
2. there are two elements and
in
such that for any
,
 3. if are two elements of
, then for all
Show that if , then for some
Problem 10:
Let be a set of positive integers satisfying the following properties:
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 is a complex number such that
If
is a positive integer, find the value of
Discussion
Problem 2:
Use calculus to find the behaviour of the function and sketch the graph of the function for
. Show clearly the locations of the maxima, minima and points of inflection in your graph.
Problem 3:
Let be a continuous function and, for any real number
, let
denote the greatest integer less than or equal to
. Show that for any
,
Problem 4:
Show that it is not possible to have a triangle with sides , and
whose medians have length
and
.
Problem 5:
Show that for all values of
.
Problem 6:
Let where
is an odd integer. Let
be a function defined on
taking values in
such that
 (a) for all
(b) for all
Show that
Problem 7:
Consider a prism with triangular base. The total area of the three faces containing a particular vertex is
. Show that the maximum possible volume of the prism is
and find the height of this largest prism.
Problem 8:
The following figure shows a grid divided into
subgrids of size
. This grid has
cells,
in each subgrid.
Now consider an grid divided into
subgrids of size
. Find the number of ways in which you can select
cells from this grid such that there is exactly one cell coming from each subgrid, one from each row and one from each column.
Problem 9:
Let
be a set satisfying the following properties:
2. there are two elements and
in
such that for any
,
 3. if are two elements of
, then for all
Show that if , then for some
Problem 10:
Let be a set of positive integers satisfying the following properties:
How to solve the 3rd problem?