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# 107 年 - [無官方正解]107 國立中山大學_碩士班招生考試_電機系(丙組)：離散數學#110222

1.Note: There are 20 questions in total. Each one is 5 points. Please choose one answer for each question. No extra points will be deducted for wrong answers. 1. In how many ways can the letters in AAANSYSU be linearly arranged?
(A) 40320；
(B) 13440
(C) 6720；
(D) 3360.

2.2. In how many ways can the letters in AAANSYSU be linearly arranged such that all the A's are adjacent?
(A) 720；
(B) 360；
(C) 240；
(D) 180.

3.3. In how many ways can the letters in AAANSYSU be linearly arranged such that N and U are adjacent?
(A) 840；
(B) 420；
(C) 210；
(D) 140.

4.

4. What is the probability that a random, linear arrangement of the letters in AAANSYSU starts and ends with the letter S?
(A) (B) (C) (D) .

5.

5. What is the coeffcient of x7y3 in the expansion of ?
(A) (B) (C) (D) 6.

6. What is the su of all the coefficients in the expansion of ?
(A) 256；
(B) 512；
(C) 1024；
(D) 2048.

7.

7. Let p, g be primitive statements for which p -＞ q is false. Which of the following is true?
(A) p g；
(B) -p V q；
(C) q →p；
(D) ㄱq → 8.

8. Let p, g be arbitrary statements. Which of the following is equivalent to p → q?
(A) p g；
(B) p Vㄱg；
(C) ㄱg → p；
(D) ㄱq→ 9.

9. Let p, g, and r be arbitrary statements. If p→ r is true and g is true, which of the following is also true?
(A) ㄱr→ g；
(B) r →q；
(C)ㄱr Vq；
(D) rVㄱg.

10.10. If a set S has 127 proper subsets, what is IS|?
(A) 128；
(B) 254；
(C) 256；
(D) 512.

11.11. How many subsets of {3, 4, 5,6, 7, 8,9, 10, 11, 12, 13}contain at least one even integer?
(A) 1981；
(B) 1982；
(C) 1983；
(D) 1984.

12.

12. What is the value of n, a positive integer, for which ?
(A) 17；
(B) 18；
(C) 19；
(D) 20.

13.

13. Let bs = 3 and = bn + 3n + 2 for n ≥ 1. What is ?
(A) 176；
(B) 156；
(C) 136；
(D) 116.

14.14. If we want to totally make sure at least two of n different pcople have birthdays that occur on the sare day of January, what is the minimum for n?
(A) 64；
(B) 32；
(C) 2；
(D) 31.

15.15. Let S = {Alan, John, Jone, Sam, Don, Mary, Tom, Bil}. How many subsets are there which contain both Sam and Tom?
(A) 16；
(B) 32；
(C) 48；
(D) 64.

16.

16. A company gets graphics cards from two sources. The first source provides 40% of the cards, and the second source provides 60% of the cards. Past experience has shown that of the cards from the first source are found to be defective, while of the cards from the second source are found to be defective. If a graphics cards is selected and found to be defective, what is the probability it was provided by the first source?
(A) (B) (C) (D) 17.17. The number of bacteria is I 00 initially, and the number doubles cvery four hours. How many bacteria are there after one day?
(A) 6400；
(B) 3200；
(C) 1600；
(D) 800.

18.

18. What is a for making the equation = 2 hold?
(A) 1000；
(B) 9；
(C) 300；
(D) 600.

19.19. Lct A, B, C be matices. Which of the following is true?
(A) IF AB and BA are computable, then AB = BA；
(B) If AB = AC, then B = C；
(C) IfA + B = A + C, then B = C；
(D) If A is square, then A is invertible.

20.

20. If = 13, what is the value of ?
(A) 312；
(B) 156；
(C) 104；
(D) 52.

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