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# ISI B.Stat, B.Math Paper 2016 Subjective| Problems & Solutions 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 .

1. Suppose , then prove that the sequence is increasing and hence show that .
2. Suppose , then prove that the sequence is decreasing and hence show that .

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 .

1. Suppose , then prove that the sequence is increasing and hence show that .
2. Suppose , then prove that the sequence is decreasing and hence show that .

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