7. (3%) Which of the following statements is false?
(A)
(B)
(C)
(D)

8. (3%) How many bit strings are there containing exactly five 0s and fourteen Is if every0 must be immediately followed by two ls? (A) 112 (B) 124 (C) 126 (D) 132

9. (3%) Find the number of ways in which nine identical blocks can be given to four children A, B, C, D, where child A gets at most two blocks. (A) 100 (B) 136 (C) 142 (D) 164

10. (3%) How many ways are there to put five temporary employees into four identical offices? (A) 48 (B) 51 (C) 56 (D) 60

11. (3%) Let x= a+ bk be the solution of the system of congrucnces x = 7 (mod 9), x≡ 4 (mod 12),and x≡16 (mod 21), where a and b are the smallest positive integer, k e Z. Which is the correct value of (2a+b) mod 11? (A)9 (B) 7 (C) 4 (D) 6 

12. (3%) Let A be a set with n clements. Which of the followings is the number of binary relations on A which are symmetric and antisymmetric, and not irreflexive? (A)2n(B) 2n -1 (C)(D)

13. (3%) Let A be a set with n elements. Which of the followings is the number of binary relations on A which are reflexive and not symmetric? (A) (B)(C)(D)

14. (3%) Suppose that someone starts a chain letter. Each person who receives the letter is asked to send it to four other people. Let k be the number of people who have seen the letter, including the first person. Suppose no one receives more than one letter and the chain letter ends after there have been 100 people who read it but did not send it out. which is the correct value of k mod 11? (A) 0 (B) 3 (C) 4 (D) 8

15. (3%) Let G be a connected bipartite planar simple graph with 12 vertices, and let e be the maximum value of the number of edges in G. Which of the followings is the value of e mod 11? (A) 3 (B) 7 (C) 9 (D) 10

16. (3%) Consider the following string aaabbcddddddeeeeeffgggggghhhhiii. Suppose we at least require k bits to encode the string. Which of the followings is the value of k mod 11? (A)1(B) 6 (C) 5(D) 10

17. (3%) Suppose the solution of the recurrence relation with a0= -2, a1 = 0, and a2 =5, is an = . Which of the following is the value of(a + b+ c+d0+d1 +d2) mod 11? (A) 9 (B) 8 (C) 7 (D) 6

110年 - 110 國立政治大學_碩士班暨碩士在職專班招生考試_資訊科學系:計算機數學#108089