Mathematics part 3 test MPEI
Replenishment date: 05.10.2011
Content: 11005222110273.zip (28.25 KB)
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Description
Collection of assignments for the discipline "MATHEMATICS" (part 3)
Task 1
Question 1. Let A, B be sets. What does the entry mean?
1. The set A is a strict subset of the set B, which is the true subset of the set A
2. Sets A, B are infinite
3. Sets A, B are finite
4. Sets A, B are not empty
5. Sets A, B are equal
Question 2. Let A be a non-empty set of all students of the school, B - the set of fifth-grade students of this school, C - the set of seventh-grade students of this school. Which entry expresses a false statement? (The parentheses here, as in arithmetic expressions, indicate the order of actions).
1.
2.
3.
4.
5.
Question 3. Which of the statements is not always (not for any sets A, B, C) is true?
1.
2.
3.
4.
5.
Question 4. Let - many days of the week, and - many days in January. What is the cardinality of the set?
1 38
2 217
3 365
4 31
5 7
Question 5. Consider the set of clock readings What can be said about the element a of the set? ...
1.
2.
3.
4.
5.
Task 2
Question 1. Consider the correspondence G between the sets A and B. In what case is the correspondence called everywhere definite?
1.
2.
3.
4.
5.
Question 2. Suppose that there is a one-to-one correspondence G between the sets A and B. What can be said about their cardinalities?
1.
2.
3.
4.
5.
Question 3. What function is not a superposition of functions,,?
1.
2.
3.
4.
5.
Question 4. Consider a binary relation R on a set M. What can we say about R if this relation is transitive?
1. If, then
2. If,, then if and only if
3. The set M does not contain an element a such that
4. If for elements a, b, c of the set M and is satisfied, then
5., where is the transitive closure of R
Question 5. What property does the nonstrict order relation R have?
1. Reflexivity
2. Transitivity
3. Antisymmetry
4., where is the transitive closure of R
5. Symmetry
Task 3
Question 1. What is the signature of Boolean set algebra?
1.
2.
3.
4.
5.
Question 2. What operation is not associative?
1. Union of sets
2. Division of numbers
3. Composition of mappings
4. Multiplication of fractions
5. Intersection of sets
Question 3. Consider algebra and algebra. In what case can one assert that?
1. If there is a homomorphism A into B
2. If there is a homomorphism B into A
3. If A and B are isomorphic
4. If the arity of operations and, and, and
5. If there exists a mapping Γ: satisfying the condition for all and all, where is the arity of the operation and
Question 4. What operation is a required attribute of a semigroup?
1. Multiplication by 2
2. Extraction of the square root
3. Binary associative
4. Composition of mappings
5. Operation of identification
Question 5. What is a semigroup?
1. Abelian group
2. Cyclic group
3. Free semigroup
4. Monoid
5. Cyclic semigroup
Task 4
Question 1. Which number is perfect?
1 28
2 36
3 14
4 18
5 3
Question 2. Which number is not triangular?
1 6
2 10
3 15
4 21
5 27
Question 3. What is the number of combinations of five to three?
1 10
2 20
3 9
4 11
5 12
Question 4. Which of the formulas containing the number of combinations is not correct?
1.
2.
3.
4.
5.
Question 5. Suppose that we roll a pair of dice (dice with numbers from 1 to 6 on the edges) many times and add up the two numbers that dropped out with each throw. Which of the following amounts will we receive more often than others?
1 1
2 7
3 6
4 11
5 12
Task 5
Question 1. What was the first most important step in deciphering the cuneiform inscriptions made by Munter and Grotefend?
1. Selection of the most probable translation version for words often found in cuneiform inscriptions
2. Selection of letters from known languages, similar to cuneiform letters
3
Task 1
Question 1. Let A, B be sets. What does the entry mean?
1. The set A is a strict subset of the set B, which is the true subset of the set A
2. Sets A, B are infinite
3. Sets A, B are finite
4. Sets A, B are not empty
5. Sets A, B are equal
Question 2. Let A be a non-empty set of all students of the school, B - the set of fifth-grade students of this school, C - the set of seventh-grade students of this school. Which entry expresses a false statement? (The parentheses here, as in arithmetic expressions, indicate the order of actions).
1.
2.
3.
4.
5.
Question 3. Which of the statements is not always (not for any sets A, B, C) is true?
1.
2.
3.
4.
5.
Question 4. Let - many days of the week, and - many days in January. What is the cardinality of the set?
1 38
2 217
3 365
4 31
5 7
Question 5. Consider the set of clock readings What can be said about the element a of the set? ...
1.
2.
3.
4.
5.
Task 2
Question 1. Consider the correspondence G between the sets A and B. In what case is the correspondence called everywhere definite?
1.
2.
3.
4.
5.
Question 2. Suppose that there is a one-to-one correspondence G between the sets A and B. What can be said about their cardinalities?
1.
2.
3.
4.
5.
Question 3. What function is not a superposition of functions,,?
1.
2.
3.
4.
5.
Question 4. Consider a binary relation R on a set M. What can we say about R if this relation is transitive?
1. If, then
2. If,, then if and only if
3. The set M does not contain an element a such that
4. If for elements a, b, c of the set M and is satisfied, then
5., where is the transitive closure of R
Question 5. What property does the nonstrict order relation R have?
1. Reflexivity
2. Transitivity
3. Antisymmetry
4., where is the transitive closure of R
5. Symmetry
Task 3
Question 1. What is the signature of Boolean set algebra?
1.
2.
3.
4.
5.
Question 2. What operation is not associative?
1. Union of sets
2. Division of numbers
3. Composition of mappings
4. Multiplication of fractions
5. Intersection of sets
Question 3. Consider algebra and algebra. In what case can one assert that?
1. If there is a homomorphism A into B
2. If there is a homomorphism B into A
3. If A and B are isomorphic
4. If the arity of operations and, and, and
5. If there exists a mapping Γ: satisfying the condition for all and all, where is the arity of the operation and
Question 4. What operation is a required attribute of a semigroup?
1. Multiplication by 2
2. Extraction of the square root
3. Binary associative
4. Composition of mappings
5. Operation of identification
Question 5. What is a semigroup?
1. Abelian group
2. Cyclic group
3. Free semigroup
4. Monoid
5. Cyclic semigroup
Task 4
Question 1. Which number is perfect?
1 28
2 36
3 14
4 18
5 3
Question 2. Which number is not triangular?
1 6
2 10
3 15
4 21
5 27
Question 3. What is the number of combinations of five to three?
1 10
2 20
3 9
4 11
5 12
Question 4. Which of the formulas containing the number of combinations is not correct?
1.
2.
3.
4.
5.
Question 5. Suppose that we roll a pair of dice (dice with numbers from 1 to 6 on the edges) many times and add up the two numbers that dropped out with each throw. Which of the following amounts will we receive more often than others?
1 1
2 7
3 6
4 11
5 12
Task 5
Question 1. What was the first most important step in deciphering the cuneiform inscriptions made by Munter and Grotefend?
1. Selection of the most probable translation version for words often found in cuneiform inscriptions
2. Selection of letters from known languages, similar to cuneiform letters
3
Additional Information
Task 11Question 1. Indicate the mathematical model for the problem:
The confectionery factory for the production of three types of caramel A, B and C uses three types of main raw materials: sugar sand, molasses and fruit puree. The consumption rates of each type of raw material for the production of 1 ton of caramel of this type are given in the table. It also indicates the total amount of raw materials of each type that can be used by the factory, as well as the profit from the sale of 1 ton of caramel of this type.
Type of raw materials Consumption rates of raw materials (t) per 1 ton of caramel Total amount of raw materials (t)
A B C
Granulated sugar 0.8 0.5 0.6 800
Molasses 0.4 0.4 0.3 600
Fruit puree - 0.1 0.1 120
Profit from the sale of 1 ton of products (rubles) 108 112 126
Find a plan for the production of caramel, providing the maximum profit from its implementation.
1. Find the minimum of the function under the conditions:
2. Find the maximum of the function under the conditions:
3. Find the minimum of the function under the conditions:
4. Find the maximum of the function under the conditions:
5. Find the maximum of the function under the conditions:
Question 2. Indicate the mathematical model for the problem:
When fattening animals, each animal must receive at least 60 units of nutrient A, at least 50 units of substance B and at least 12 units of substance C daily. These nutrients contain three types of feed. The content of nutrient units in 1 kg of each type of feed is shown in the following table:
Nutrients Number of nutrient units in 1 kg of feed of the species
I II III
A 1 3 4
B 2 4 2
C 1 4 3
Make up a daily ration that ensures the receipt of the required amount of nutrients with minimal cash costs, if the price of 1 kg of feed of type I is 9 kopecks, feed of type II is 12 kopecks and feed of type III is 10 kopecks.
1. Find the maximum of the function under the conditions:
2. Find the minimum of the function under the conditions:
3. Find the minimum of the function under the conditions:
4. Find the maximum of the function under the conditions:
5. Find the minimum of the function under the conditions:
Question 3. Indicate the mathematical model for the problem:
At three points of departure, homogeneous cargo is concentrated in quantities of 420, 380, 400 tons. This cargo must be transported to three points of destination in quantities, respectively, equal to 260, 520, 420 tons. The cost of transportation of 1 ton of cargo from each point of departure to each point the assignments are known and are set by the matrix (in conventional units):
Where
Find a transportation plan that ensures the removal of the cargo available at the points of departure and the delivery of the necessary cargo to the points of destination at the lowest total cost of transportation.
1. Find the minimum of the function
under conditions:
2. Find the minimum of the function under the conditions:
3. Find the minimum of the function under the conditions:
4. Find the minimum of the function under the conditions:
5. Find the minimum of the function under the conditions:
Question 4. Indicate the non-equivalent form for the task:
1.
2.
3.
4.
5.
Question 5. Specify the standard form for the task
1.
2.
3.
4.
5.
Task 12
Question 1. Which of the figures shows the correct geometric interpretation of the solution to the linear programming problem that provides the maximum objective function F.
Question 2. Which of the figures shows the correct geometric interpretation of the solution of the linear programming problem, which ensures the minimum of the objective function F.
Question 3. Indicate an equivalent form of writing the problem that allows geometric interpretation of solutions in the form of a polygon:
1.
2.
3.
4.
5.
Question 4. Using a geometric interpretation, find the solution to the problem:
1.when
2.when
3.when
4.when
5.when
Question 5. Using a geometric interpretation, find the solution to the problem:
1.when
2.when
3.when
4.when
5.when
Task 13
Question 1. Specify the maximum value of the objective function for the task:
1.
2.
3.
4.
5.
Question 2. Indicate the solution to the problem: