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# Math test with answers Part 4

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**04.07.2013**

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# Description

BK2 higher mathematics test is often the number of questions 4 - 90.

Task 1

Question 1. Let A and B - set. What does the record A ... B, B ... A?

1. Set A is a proper subset of the set, which is a true subset of A

2. Sets A and B are endless

3. The sets A and B are finite

4. The sets A and B are not empty

5. The sets A and B are equal

Question 2. Let A be a non - empty set of all students at the school (A # ø), V \u200b\u200b- set of fifth grade students of this school, C - the set of seventh grade students of this school. Which records expresses a false statement? (Parentheses here, as in arithmetic expressions, set procedures).

1. B ... A

2. B ... C ... A

3. B \\ C ... A

4. (B∩A) \\ A = ø

5. A ... (B ... C)

Question 3. Which of the following statements is not always (not for any sets A, B, C) is true?

1. A∩B = B∩A

2. A È B = B È A

3. A \\ B = B \\ A

4. A Ç (BÈ C) = (AÇ B) È (A Ç C)

5. A È (BÇ C) = (AÈ B) Ç (A È C)

Question 4. Let NH - a lot of days of the week, and nI - a lot of days in January. What is the cardinality of the set NH

· NI?

1. 38

2. 217

3. 365

4. 31

5. 7

Question 5: Consider the set of the clock v = {(d1, d2, d3) │d1ÎN, d2ÎN, d3ÎN, 0 ≤ d1 ≤ 23, 0 ≤ d2 ≤ 59, 0 ≤ d3 ≤ 59} What can be asserted with respect to the element a set of n β v? (A ... n β V).

1. a Î R \\ N

2. aÎ N 2

3. a Î R 2

4. a ≤ 59

5. a ≤ 23

Task 2

Question 1. Consider the G line between A and B (GÍA'B). In which case a specific line called everywhere?

1. pr1 G = B

2. np2 G = B

3. pr1 G = A

4. pr2G = A

5. A = B

Question 2. Assume that there is a G-one correspondence between the sets A and B. What can be said about their powers?

1. │A│- │B│ <0

2. │A│ + │B│ = │G│

3. │A│ + │B│> │G│ + │G│

4. │A│-│B│ = 0

5. │G│-│B│> │A│

Question 3. What is the function is not a superposition of functions f1 (x1, x2) = x1

· X2, f2 (x1, x2) = x1

· X2 + x2, f3 (x1 + x2) 2?

1. f 1 (f 2 (x 3, x 4), f 3 (x1, x4))

2. f 1 (x 1, x 2) + f 2 (x 1, x 2)

3. f 3 (f 1 (x1, x 1), x 2)

4. (f 2 (x 1, x 2) + f 1 (x3, x 4)) 2

5. f 1 (x 1, x 2)

· X3

Question 4. Consider a binary relation R on the set M. What can be asserted on the R, if the ratio is transitive?

1. If a Î M, then there is a aRa

2. If a Î M, b Î M, aRa then if and only if bRa

3. The set M is not a member of this that I have during limited aRa

4. If the elements a, b, c of M performed aRb and aRc, it is not executed aRc

5. .R = R .., where - transitive closure R

Question 5. What property does not have a lax attitude about R?

1. Reflexivity

2. Transitivity

3. Antisymmetric

4. ... where - transitive closure R

5. Symmetry

Activity 3

Question 1. What is the signature of the Boolean algebra of sets?

1. {β (È), È, Ç, ¯}

2. {Ç, ¯, U}

3. U2 ® U

4. {+, -,

·}

5. {Ì, Í¯}

Question 2. What operation is not associative?

1. Combine sets

2. Divide numbers

3. The composition of maps

4. Multiply fractions

5. The intersection of sets

Question 3. Consider the algebra A = (M, j1, j2, j3), and algebra. In which case it can be argued chto│M│ + │N│?

1. If there is a homomorphism A to B

2. If there is a homomorphism B in A

3. If A and B are isomorphic

4. If the same arity operations and, and, and

5. If there is a mapping F: M ® N, satisfying for all i

# Additional information

Question 1. Which of the numbers is perfect?

1. 28

2. 36

3. 14

4. 18

5. 3

Question 2: Which of the values \u200b\u200bis a triangle?

1. 6

2. 10

3. 15

4. 21

5. 27

Question 3. What is the number of combinations of three to five C35?

1. 10

2. 20

3. 9

4. 11

5. 12

Question 4. Which of the formulas containing the number of combinations is not true?

1. C0n + C1n + C2n + ... + Cnn = 2n

2. ...

3. C36 = C35 + C26

4. C37 = C47

5. ...

Question 5: Suppose that we often throw a pair of dice (dice with numbers from 1 to 6 at the edges), and summarize the two fell for each throwing numbers. Which of the following amounts we will 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 Munter and Grotefend?

1. Selection of the most probable versions of translations for common words in cuneiform inscriptions

2. Selection of letters known language, similar letters cuneiform

3. Selection of the most loved of modern languages

4. Enter the cuneiform inscriptions in the computer

5. Formulation according to each letter cuneiform some positive integer

Question 2. How many different pairs can be composed of 4 letters? (How many different two-digit numbers can be formed using only the digits 1, 2, 3, 4?)

1. 4

2. 8

3. 16

4. 20

5. 2

Question 3. Which condition is satisfied all degenerate codes?

1. One word (a single object, such as an amino acid) is coded (may be represented or defined) are not one, but several combinations of characters (codons)

2. The terms of linearity

3. Conditions of correspondence between the source and encoded objects (states)

4. This code - nonoverlapping

5. These codes - overlapping

Question 4. Which statement does not match the DNA?

1. There exist codons which do not match any amino acid

2. This code - Line

3. This code - nondegenerate

4. This code - non-overlapping

5. This code - triplet

Question 5. What is the most important combinatorial problem was solved by February 17, 1869 Dmitri Ivanovich Mendeleev?

1. The task of going around Koenigsberg bridges

2. The task of drawing up the periodic table of chemical elements

3. The task of deciphering Mycenaean letter

4. Objectives on the simultaneous dropping out two sixes in throwing a pair of dice

5. The problem of optimal content of alcohol in alcoholic beverages

Task 6

Question 1: What is the condition (assumption) is characteristic of all combinatorial problems?

1. In combinatorial problems always referred to only finite sets

2. In combinatorial problems never used brute force options

3. In combinatorial problems always used the concept of infinity

4. Combinatorial problems always lead to differential equations

5. Combinatorial problems will never need to make an algorithm

Question 2. How quickly solve the problem of finding (the construction of) third-order magic square, without using a computer?

1. With the help of geometry Lobachevsky

2. Use the Euclidean geometry

3. Use of differentiation or integration

4. Use the sorting and analysis of all square matrices of size 3 on 3

5. Determine the amount of each of its rows, columns and diagonals, and accounting for all possible triples, giving this amount

etc.

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