Here, you will find all the questions of ISI Entrance Paper 2014 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 class there are student. We define
as the number of friends of
student and
as the number of students who has at least i friends. Prove that
Problem 2:
be a triangle. Take a point
on or inside the triangle. Let
. Show that
Solution
Problem 3:
Let (where
. it is given that the functions cuts the
axis at least
distinct points. Then show that it either cuts the
axis at
distinct point or
distinct point and at any one of these three points we have a maxima or minima.
Solution
Problem 4:
Let and
be twice differentiable non decreasing functions defined on an interval
such that for each
,
and
and also that
is a linear in
on
. Then show that
.
Problem 5:
Prove that sum of any consecutive integers cannot be perfect square. Give an example where sum of
consecutive integers is a perfect square.
Solution
Problem 6:
. Then what is the maximum length of a line segment enclosed in this area.
Problem 7:
Let be a non decreasing function defined on the domain
. Then show that if
Problem 8:
lotus leaf's are arranged in a circle. A frog jumps from a particular leaf by the following rule: It always moves clockwise. From staring point it skips
leaf and jumps to the next. Then it skips
leaves and jumps to the following. That is in the
jump it skips
leaves and
jump it skips
leaves and so on. In this manner it keeps moving round and round the circle of leaves. It may go to one leaf more than once. If it reaches each leaf at least once then n (the number of leaves) cannot be odd.
Solution
Here, you will find all the questions of ISI Entrance Paper 2014 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 class there are student. We define
as the number of friends of
student and
as the number of students who has at least i friends. Prove that
Problem 2:
be a triangle. Take a point
on or inside the triangle. Let
. Show that
Solution
Problem 3:
Let (where
. it is given that the functions cuts the
axis at least
distinct points. Then show that it either cuts the
axis at
distinct point or
distinct point and at any one of these three points we have a maxima or minima.
Solution
Problem 4:
Let and
be twice differentiable non decreasing functions defined on an interval
such that for each
,
and
and also that
is a linear in
on
. Then show that
.
Problem 5:
Prove that sum of any consecutive integers cannot be perfect square. Give an example where sum of
consecutive integers is a perfect square.
Solution
Problem 6:
. Then what is the maximum length of a line segment enclosed in this area.
Problem 7:
Let be a non decreasing function defined on the domain
. Then show that if
Problem 8:
lotus leaf's are arranged in a circle. A frog jumps from a particular leaf by the following rule: It always moves clockwise. From staring point it skips
leaf and jumps to the next. Then it skips
leaves and jumps to the following. That is in the
jump it skips
leaves and
jump it skips
leaves and so on. In this manner it keeps moving round and round the circle of leaves. It may go to one leaf more than once. If it reaches each leaf at least once then n (the number of leaves) cannot be odd.
Solution
In the 1st problem, the summation of Ai will be over 1 to 100
In the 2nd one, it is to be shown that f(A) ≤ max {f(P),f(Q),f(R)}
In the 4th one, it is given that f(x)g(x) is a linear function
Thanks for the clarification.
Problem 4th is f(x), g(x) are non-decreasing functions. Wouldn't work without that?
Was it given? 'Non - decreasing' part?
Sir, i solved only 4 problems correctly,may i have a chance for ISI??(75% in objective)
This problems are number 4,5,6,7
It is possible.5+ is better.
Yeah, the question specifically stated f and g are non-decreasing.
sir pls give inside out of isi b.stats interview... i will be highly obliged.... thanks .
I don't think I have understood the first question correctly .
. Also
because all students have more than
friends. Note ,
because all students have at least 1 friend.
. This counter example hence proves the given equation false . But we are required to prove it true . I think I have made a mistake in understanding the question .
Consider a situation where each student has only one friend. This is possible if we see 100 students as 50 pairs where in each pair, each student is friend of the other.
In that case
Therefore
In the first question ci is no. of students having strictly greater than i friends. Or the summation of ci should run from 1 to 99. As such the problem is wrong.
Yes, I agree, I tried to use induction to solve the problem, and it returns me an ambiguity. The solution will be correct, only if, as you have stated, ci summn. runs from 1 to 99
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What is the answer to the 6th question?
Let u be Kcos(A) and v be Ksin(A), where mod(K) is less than 1. By solving the Q, we obtain an equation of the type x^2+ (2)y^2- 2xy = K^2, this is the equation of an ellipse,,,
Sir,minimum how many questions should i attempt in the objective and the subjective paper so as to get selected for the interview?
22/30 and 4/6 should suffice
For the undergraduate course?I'm never able to solve more than 12 in the objective paper
Yes for B Stat Bmath entrance
I didn't expect ISI questions to be this easy
sir the frog and leaf problem. ....can it be solved without using modulo? ?
Possible... But it would be modular arithmetic in disguise
Plz give the solution of the first problem.