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Explore the Back-StoryHere, you will find all the questions of ISI Entrance Paper 2017 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems.

**Problem 1 :**

Let the sequence be defined by

where . Show that for all n is a rational number which can be written with an odd denominator.

...........................

...........................

**Problem 2 : **

Consider a circle of radius as given in the diagram below. Let and be points on the circle such that and , when extended, intersect at . If and have length and respectively, and is a right angle, then show that the length of is

...........................

...........................

**Problem 3 : **

Suppose is a function given by

- Find

2. Evaluate

...........................**Discussion**

...........................

**Problem 4 : **

Let be the square formed by the four vertices , and . Let the region be the set of points inside which are closer to the center than to any of the four sides. Find the area to the region .

...........................**Discussion**

...........................

**Problem 5 : **

Let with being the product of the digits of .

- Prove that for all

2. Find all for which

**Problem 6 : **

Let be primes with such that and are perfect squares. Find all possible values of .

**Problem 7 : **

Let . For a permutation of the elements of , let denote the first element of . Find the number of all such permutations so that for all

- if then appears before in

2. if then appears before in

**Problem 8 : **

Let and be positive integers.

- Let be a polynomial with real coefficients. Show that the function is strictly positive for all real satisfying .

2. Let be a non-zero polynomial with real coefficients. Let be the smallest number such that . Prove that the graph of cuts the -axis at the origin (i.e. changes sign at ) and only if is an odd integer.

Here, you will find all the questions of ISI Entrance Paper 2017 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems.

**Problem 1 :**

Let the sequence be defined by

where . Show that for all n is a rational number which can be written with an odd denominator.

...........................

...........................

**Problem 2 : **

Consider a circle of radius as given in the diagram below. Let and be points on the circle such that and , when extended, intersect at . If and have length and respectively, and is a right angle, then show that the length of is

...........................

...........................

**Problem 3 : **

Suppose is a function given by

- Find

2. Evaluate

...........................**Discussion**

...........................

**Problem 4 : **

Let be the square formed by the four vertices , and . Let the region be the set of points inside which are closer to the center than to any of the four sides. Find the area to the region .

...........................**Discussion**

...........................

**Problem 5 : **

Let with being the product of the digits of .

- Prove that for all

2. Find all for which

**Problem 6 : **

Let be primes with such that and are perfect squares. Find all possible values of .

**Problem 7 : **

Let . For a permutation of the elements of , let denote the first element of . Find the number of all such permutations so that for all

- if then appears before in

2. if then appears before in

**Problem 8 : **

Let and be positive integers.

- Let be a polynomial with real coefficients. Show that the function is strictly positive for all real satisfying .

2. Let be a non-zero polynomial with real coefficients. Let be the smallest number such that . Prove that the graph of cuts the -axis at the origin (i.e. changes sign at ) and only if is an odd integer.

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If i have made a slight calculation error by writing f'1 =-500e and the follow up question as well when the answer doesnt have e, how much will be deducted?

That depends on the process that you have used to solve the problem.

If your process is correct then they will more or less deduct 1-2 marks at max.

Thanks a lot!

7. (n-1)! (n+1)C3

[…] Back to the Question Paper […]

[…] Back to the question paper […]

complete solution of isi b math 2017 objective and subjective paper. And result date