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  #2  
18th August 2014, 02:33 PM
Super Moderator
 
Join Date: Apr 2013
Re: Chennai Mathematical Institute Entrance Exam Sample Papers

You are asking for the BSc Programmes at CMI Entrance Examination sample papers. This is as follows:


1. For sets A and B, let f : A ! B and g : B ! A be functions such that f(g(x)) = x for
each x. For each statement below, write whether it is TRUE or FALSE.
a) The function f must be one-to-one.
Answer:
b) The function f must be onto.
Answer:
c) The function g must be one-to-one.
Answer:
d) The function g must be onto.
Answer:







Here I am also uploading a file that contains the CMI Entrance Examination sample papers for BSc Programmes. You can download it from here.
  #3  
16th May 2015, 11:19 AM
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Re: Chennai Mathematical Institute Entrance Exam Sample Papers

I am looking for sample question papers of Entrance Exam for admission in B.Sc at Chennai Mathematical Institute. So will you provide me Question Paper of B.Sc Entrance Exam of Chennai Mathematical Institute?
  #4  
16th May 2015, 11:28 AM
Super Moderator
 
Join Date: Apr 2013
Re: Chennai Mathematical Institute Entrance Exam Sample Papers

Here you want to get question papers of B.Sc Entrance Exam conducted by Chennai Mathematical Institute, so here is following question paper:

Chennai Mathematical Institute B.Sc Entrance Exam Paper

1. For sets A and B, let f : A → B and g : B → A be functions such that f(g(x)) = x for
each x. For each statement below, write whether it is TRUE or FALSE.
a) The function f must be one-to-one.
Answer:

b) The function f must be onto.
Answer:

c) The function g must be one-to-one.
Answer:

d) The function g must be onto.
Answer:


. Let S be a circle with center O. Suppose A, B are points on the circumference of S with ∠AOB = 120◦
. For triangle AOB, let C be its circumcenter and D its orthocenter (i.e.,
the point of intersection of the three lines containing the altitudes). For each statement below, write whether it is TRUE or FALSE.

a) The triangle AOC is equilateral.
Answer:

b) The triangle ABD is equilateral.
Answer:

c) The point C lies on the circle S.
Answer:

d) The point D lies on the circle S.
Answer:

Part A. (10 problems _ 5 points = 50 points.) Attempt all questions in this part
before going to part B. Carefully read the details of marking scheme given
below. Note that wrong answers will get negative marks!
In each problem you have to _ll in 4 blanks as directed. Points will be given based only on
the _lled answer, so you need not explain your answer. Each correct answer gets 1 point
and having all 4 answers correct will get 1 extra point for a total of 5 points per problem.
But each wrong/illegible/unclear answer will get minus 1 point. Negative points from any
problem will be counted in your total score, so it is better not to guess! If you are unsure
about a part, you may leave it blank without any penalty. If you write something and then
want it not to count, cross it out and clearly write \no attempt" next to the relevant part.
1. For sets A and B, let f : A ! B and g : B ! A be functions such that f(g(x)) = x for
each x. For each statement below, write whether it is TRUE or FALSE.
a) The function f must be one-to-one.
Answer:
b) The function f must be onto.
Answer:
c) The function g must be one-to-one.
Answer:
d) The function g must be onto.
Answer:

2. Let f : R ! R be a function, where R is the set of real numbers. For each statement
below, write whether it is TRUE or FALSE.
a) If jf(x) _ f(y)j _ 39jx _ yj for all x; y then f must be continuous everywhere.
Answer:
b) If jf(x) _ f(y)j _ 39jx _ yj for all x; y then f must be di_erentiable everywhere.
Answer:
c) If jf(x) _ f(y)j _ 39jx _ yj2 for all x; y then f must be di_erentiable everywhere.
Answer:
d) If jf(x) _ f(y)j _ 39jx _ yj2 for all x; y then f must be constant.
Answer:

3. Let S be a circle with center O. Suppose A;B are points on the circumference of S with
\AOB = 120_. For triangle AOB, let C be its circumcenter and D its orthocenter (i.e.,
the point of intersection of the three lines containing the altitudes). For each statement
below, write whether it is TRUE or FALSE.
a) The triangle AOC is equilateral.
Answer:
b) The triangle ABD is equilateral.
Answer:
c) The point C lies on the circle S.
Answer:
d) The point D lies on the circle S.
Answer:

4. A polynomial f(x) with real coe_cients is said to be a sum of squares if we can write
f(x) = p1(x)2 +_ _ _+pk(x)2, where p1(x); : : : ; pk(x) are polynomials with real coe_cients.
For each statement below, write whether it is TRUE or FALSE.
a) If a polynomial f(x) is a sum of squares, then the coe_cient of every odd power of x in
f(x) must be 0.
Answer:
b) If f(x) = x2 + px + q has a non-real root, then f(x) is a sum of squares.
Answer:
c) If f(x) = x3 + px2 + qx + r has a non-real root, then f(x) is a sum of squares.
Answer:
d) If a polynomial f(x) > 0 for all real values of x, then f(x) is a sum of squares.
Answer:

5. There are 8 boys and 7 girls in a group. For each of the tasks speci_ed below, write an
expression for the number of ways of doing it. Do NOT try to simplify your answers.
a) Sitting in a row so that all boys sit contiguously and all girls sit contiguously, i.e., no
girl sits between any two boys and no boy sits between any two girls
Answer:
b) Sitting in a row so that between any two boys there is a girl and between any two girls
there is a boy
Answer:
c) Choosing a team of six people from the group
Answer:
d) Choosing a team of six people consisting of unequal number of boys and girls
Answer:

rest of the question here i am attaching pdf file


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