Difference between revisions of "MIE 2015"
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Revision as of 09:18, 11 January 2018
Contents
Day 1
Problem 1
Given any three sets , and . The set is equal to the set:
(a)
(b)
(c)
(d)
(e)
Problem 2
The polynomial has real roots , and . Thus the value of the sum of is:
(a)
(b)
(c)
(d)
(e)
Problem 3
Let and be positive integers such that . Find the remainder of the division of by .
(a)
(b)
(c)
(d)
(e)
Problem 4
Compute
Imgcis
(a)
(b)
(c)
(d)
(e)
Note: Img(w) is the imaginary part of w.
Problem 5
Let . It's known that and have a root in common. Therefore, we can say that for every value of and :
(a)
(b)
(c)
(d)
(e)
Problem 6
Let be a geometric progression and , and be a arithmetic progression, both in these order, so we can say that , and :
(a) are the sides of a obtusangle triangle.
(b) are the sides of a acutangle triangle that's not equilateral.
(c) are the sides of a equilateral triangle.
(d) are the sides of a right triangle.
(e) can't be the sides of a triangle.
Problem 7
Compute
(a)
(b)
(c)
(d)
(e)
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