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111年 - 111 教育部公費留學考試試題:離散數學#125727
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3. [15%] Which series is bigger,
? We have:
其他申論題
(1) Hfr 菌和F-菌的結合可以用來定位不同基因在細菌染色體上的序列,現在有一個 Hfr 菌,其基因型為 Arg⁺、His⁺、Mal⁺、Met⁺、Pyr⁺、Tyr⁺、Xyl⁺,想要知道這些基因在細菌染色體上的序列,則實驗所需使用的F-菌基因型應該為何?以上標「+」或「-」代表野生型或突變型的等位基因 (2分)
#534200
(2) 承上題,若設定結合5分鐘後中斷,結果發現只有 Pyr⁺ 的 F- 菌出現,並沒有發現其他基因的重組型,將結合時間改為30分鐘後中斷,結果在 Pyr⁺ 的 F- 菌中分別有 30% 是 Met⁺、90% 是 Xyl⁺、10% 是 Tyr⁺、60% 是 Arg⁺、70% 是 Mal⁺,但沒有發現 His⁺。依據此結果,這些基因 (Arg、His、Mal、Met、Pyr、Tyr、Xyl) 自傳送起點開始的序列為何? (2分)
#534201
1. [10%] How many subsets of size 5 from a set that contains n elements?
#534202
2. [10%] We flip a coin for 15 times and obtain a result of x times of coin facing up and y times of coin facing down. What is the most likely outcome of (x, y)? Apparently, we have x + y = 15. What is the probability to have such outcome (x, y)?
#534203
4. [15%] If both a + b and ab are even, then both a and b are even. Prove or disprove the statement.
#534205
5. [15%] Solve the recurrence equation given by:an+2 - 2an + an+1 = 0, a0 = 0, a1 = 1.
#534206
6. [15%] Which of the following graphs, K6 (complete graph with 6 vertices) or K7 (complete graph with 7 vertices) has closed Euler walk? Explain your answer as clear as possible. That is, in closed Euler walk, we allow each edge to be visited exactly once, and the initial vertex and ending vertex are the same. Can we modify the graph(s) to make it/them possible to contain a closed Euler walk?
#534207
Def 1.A tree consists of a root, and zero or more subtrees T1, T2, ..., Tk. Also, there is an edge from the root to the rootof each subtree.
#534208
Now someone modifies the definition and give the following alternative one:Def 2.A tree consists of a root, and one or more subtrees T1, T2,..., Tk. Also, there is an edge from the root to the root of each subtree.Can you describe what will happen if we choose the second one as the definition instead? What trees can be generated by the two definitions?
#534209
1. 在網際網路(Internet)中,何謂被動式攻擊(Passive Attack)?
#534210