Mathematics 2 Final 12. Deneme Sınavı
Toplam 16 Soru1.Soru
Which of the following is the maximin strategy for Player I, if the matrix game is given as
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1st column |
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3rd row |
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1st row |
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2nd column |
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2nd row |
minimum {-2,3,4}=-2, minimum {2,-1,0}=-1, minimum {3,-2,5}=-2, maximum {-2,-1,-2}=-1. This number -1 corresponds the 2nd row.
2.Soru
What is the solution of the initial value problem
with the initial value y(1)=1?
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The integrating factor is
So we multiply both side of the given equation by and we obtain
3.Soru
For the matrix game
which of the following is the sum of the lower and upper values?
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4 |
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6 |
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2 |
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3 |
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1 |
Maximum
minimum
Correct answer is D
4.Soru
Which of the following is true for zero sum matrix games?
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Every game has an equilibrium pair. |
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The lower value is greater than or equal to the upper value. |
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Player I chooses a column, Player II chooses a row. |
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Player I minimizes, Player II maximizes the matrix elements |
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Player I chooses a row, Player II chooses a column. |
In a game firs player chooses a row and second player chooses a column. Except E all the answers are false. The answer is E.
5.Soru
What is the upper value of the matrix game given by
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-5 |
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-3 |
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0 |
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1 |
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3 |
When ve consider the given matrix, we find
minimum {3, 6, 5, 2, 0}=0. Hence the answer is C.
6.Soru
What is the weight of the graph shown below?
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190 |
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171 |
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153 |
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136 |
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120 |
A weighted graph is a graph G, in which each edge e has been assigned a nonnegative real number w (e), called the weight of e. The weight of a graph is simply defined to be the sum of the weights of its edges. The weight of graph shown above is 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18= 171.The correct answer is B.
7.Soru
Given the matrix game
which of the following is equilibrium pair?
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(1st row, 3rd column) |
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(1st row, 2nd column) |
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(2nd row, 1st column) |
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(2nd row, 2nd column) |
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(2nd row, 3rd column) |
For each row write the lowest element to the right, and for each column write the greatest element below the matrix
maximum {2,1} = 2, minimum {4, 2, 7} = 2. There exists an equilibrium pair (1st row, 2nd column). The number 2, which lies in the intersection of 1st row and 2nd column, is the lowest in the 1st row, is the greatest in the 2nd column.
8.Soru
Which element of the matrix
gives the equilibrium pair?
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2 |
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3 |
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5 |
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7 |
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8 |
The number 7 is the lowest in 1st row and the greatest in 1st column. (1st row, 1st column) is the equilibrium pair.
9.Soru
Which of the following is the maximin strategy for Player I, if matrix game is given as
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1st row |
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2nd row |
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3rd row |
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1st column |
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2nd column |
Minimum {-1,2,3} = -1, minimum {0,-2,2} = -2, minimum {1,-3, 5} = -3, minimum {3, 2, 4} = 2. The maximum of the numbers -1, -2 and -3 is -1. The corresponding row is the first row. Hence the answer is A.
10.Soru
What can m and n be so that the lines
intersect at the point
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The point of intersection lies on both of the lines. Using this information one can write
From the first equation we see that
and from the second equation we get
So the correct answer is C.
11.Soru
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Therefore the correct answer is the B option.
12.Soru
Find the maximum value of
on the constraint set given below.
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249 |
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259 |
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269 |
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279 |
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289 |
The maximum of over the constraint set will occur at
13.Soru
What is the lower value of the game given by the matrix
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-3 |
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-2 |
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0 |
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-1 |
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4 |
Correct answer is D
14.Soru
Given the system of linear inequalities
Which of the following points belongs to the constraint set?
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(1,2) |
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(-3,2) |
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(2,1) |
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(1,3) |
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(4,3) |
The point (4,3) satisfies the system of inequalities
Correct answer is E
15.Soru
Consider the matrix game
Which of the following is the lower value of this game?
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-2 |
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-3 |
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-1 |
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0 |
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1 |
Maximum
Correct answer is C.
16.Soru
Given the matrix game
which of the following is the equilibrium pair?
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(1st row, 2nd column) |
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(2nd row, 1st column) |
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(2nd row, 2nd column) |
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(3rd row, 1st column) |
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(4th row, 2nd column) |
If in the game matrix, there exists an element which is smallest in its row and greatest in its column then this row-column pair is an equilibrium pair. For each row write the lowest element to the right, and for each column write the greatest element below the matrix:
Now, observe that max {-7, -4, -2, -1} = -1 and min {-1, 0, 2} = -1. Therefore, (1st row, 2nd column) is an equilibrium pair. The correct answer is A.