109年 - [非官方正解]108 國立中山大學_碩士班招生考試_電機系(丙組)：離散數學#110538

科目：中山◆電機◆離散數學 | 年份：109年 | 選擇題數：19 | 申論題數：0

試卷資訊

所屬科目：中山◆電機◆離散數學

選擇題 (19)

1. How many positive integer solutions to the equation 4x + 7y = 117? (A) 1； (B) 2； (C) 3； (D)4
2. How many subsets of [3,4,5,6, 7,8,9, 10,11, 12, 13) contain 3, 9, and 13? (A) 1024； (B) 256； (C) 512； (D) 762.
複選題
3. Suppose we have two functions fand g, withf(1)=3,f(2)=1,f(3)=4,f(4)=6, g(1)=5,g(2)=3,g(3) =4,g(4)=1,g(5) =3,and g(6) = 2. Which is the correct mapping of the composite function g o f? (A) go f(1) = 5； (B) go f(2) = 3； (C) go f(3) = 1； (D) g o f(4) = 6.
4. Let LOVENSYSU be a string of 9 characters. How many different permutations of these characters such that the two S's are not adjacent? (A) 141120； (B) 362880； (C) 181440； (D) 40320.
5. Let A, B, and C are three sets. Which is incorrect about the difference set? (A) (A-B)-C = A -(BUC)；(B)(A-B) -C = (A-C) - B；(C) (A-B) -C= A-(BnC)； (D) (A- B)-C=(A-C)-(B-C).
6. Suppose A is a set with 21 elements. How many subsets of A can be obtained such that each subset has 11 or more elements? (A) 131072； (B) 262144； (C) 524288； (D) 1048576.
7. Let f(x) = 2x3 - 70x - 9 and g(x) = 3x2 - 10x - 2. A composite function g o f o g(x) is formed. What is the value of g o f o g(4)? (A) -5； (B) -2； (C) 2；(D) 5.
8. In how many ways can the letters in ANSYSUAA be linearly arranged such that Y and U are not adjacent? (A) 1260； (B) 2520； (C) 5040； (D) 1400.

9. Let p, g, and r be primitive statements for which (p → g) - r is false. Which of the following is false? (A) (B) (C) (D) is true.
10. Let X = (1,2,3, 4] and Y = fa,b). How many onto functions can be defined from X to Y? (A) 8； (B) 11； (C) 14； (D) 17.

11. Let f(n) = (2i + 9) for positive integer n and n 2 ≥5. Which of the following is false? (A) The constant term of f(n) is negative； (B) f(n) is a polynomial of order 2； (C) f(40) = 2044； (D) f(55) = 3519.

12. Which value is closest to the solution to log1o(3x2) - =1?(A)-5.237； (B)-4.482； (C) 4.983；(D) 6.329.

13. What is the sum of all the coefficients in the expansion of ? (A) 1256； (B) -512； (C)-2048；(D)-1024.
複選題

14. Let H(x) be a function of u:

Which of the following are true for the expanded form of H(x)? (A) The constant term is
； (B) There are 9 different terms； (C) The coefficient of the term with is negative； (D)
The coefficient of the term with x3 is .
複選題

15. Suppose we want to generate randomly 8 bits, with O or 1 in cach bit. Let E1, be the event of bit O being 1, Ez be the event of bit 7 being 0, and Es be the event of both bits 3 and 4 being 1. Which of the following are true? (A) The probability P(E1| E2)= ； (B) The probability P(E1| E2) = ； (C) The probability P(E1| E2, E3)= ；(D) The probability PE2| E1, E3)=
複選題

16. Assume that there is a recurrent relation + 3, with A0 = 1. Which of the following are true? (A) = 732694； (B) == 16381； (C) A8 = 7381； (D) is a multiple of 3.
複選題
17. Suppose the frequency of occurrence for C is 1, for O is 2, for U is 3, for N is 4, for T is 5, for E is 6, and for R is 7. We create a Huffman tree and find Huffman codes for them. Which of the following are true? (A) The code for T is 101； (B) The code for U is shorter than the code for T； (C) The shortest code is one bit long； (D) The longest code is 4 bits long.
複選題

18. It is known that 12 + 22 + ... .+n2=n(n+1)(2n+1)/6.Let H(n)=(1+3)2 +(2+ 3)2+. + (n + 3)2. Which of the following are true about H(n)? (A) The constant term is not 0； (B) The coefficient of the term with n is ； (C) The coefficient of the term with n2 is ；(D) H(50) is greater than 50000.
複選題

19. Let P, Q, and R be propositions. Which of the following are tautologies? (A) P V Q V R； (B)(P→Q)≡(-Q→-P)；(C)(D)

申論題 (0)