Here, you will find all the questions of ISI Entrance Paper 2016 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems.
Problem 1:
In a sports tournament of players, each pair of players plays exactly one match against each other. There are no draws. Prove that the players can be arranged in an order
such that
defeats
Problem 2:
Consider the polynomial where
is odd and
is even. Prove that all roots of the polynomial cannot be rational.
Problem 3:
is a polynomial with real coefficients.
Prove that all roots of
cannot be real.
Problem 4:
Let be a square. Let
lie on the positive
-axis and
on the positive
-axis. Suppose the vertex
lies in the first quadrant and has co-ordinates
Then find the area of the square in terms of
and
.
Problem 5:
Prove that there exists a right angle triangle with rational sides and area if and only if
and
are squares of rational numbers and are in Arithmetic Progression
Here is an integer.
Problem 6:
Suppose in a triangle ,
,
,
are the three angles and
,
,
are the lengths of the sides opposite to the angles respectively. Then prove that if
then the triangle
is isoscelos.
Problem 7:
is a differentiable function such that
where
.Also
.Find the value of
Problem 8:
Suppose that is a sequence of real numbers satisfying
.
Here, you will find all the questions of ISI Entrance Paper 2016 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems.
Problem 1:
In a sports tournament of players, each pair of players plays exactly one match against each other. There are no draws. Prove that the players can be arranged in an order
such that
defeats
Problem 2:
Consider the polynomial where
is odd and
is even. Prove that all roots of the polynomial cannot be rational.
Problem 3:
is a polynomial with real coefficients.
Prove that all roots of
cannot be real.
Problem 4:
Let be a square. Let
lie on the positive
-axis and
on the positive
-axis. Suppose the vertex
lies in the first quadrant and has co-ordinates
Then find the area of the square in terms of
and
.
Problem 5:
Prove that there exists a right angle triangle with rational sides and area if and only if
and
are squares of rational numbers and are in Arithmetic Progression
Here is an integer.
Problem 6:
Suppose in a triangle ,
,
,
are the three angles and
,
,
are the lengths of the sides opposite to the angles respectively. Then prove that if
then the triangle
is isoscelos.
Problem 7:
is a differentiable function such that
where
.Also
.Find the value of
Problem 8:
Suppose that is a sequence of real numbers satisfying
.