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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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1. [10%] How many subsets of size 5 from a set that contains n elements?
其他申論題
(5) 藜麥和玉米都被稱為穀類作物,它們主要有哪些構造是不同的?
#534198
1. 腎絲球過濾率(glomerular filtration rate,簡稱 GFR)(單位為 mL/min)可用以 判別腎臟疾病,每天正常的腎絲球濾過量約為 180 L(正負 15%內均算正常),試計算出正常的 GFR 範圍。(注意:採無條件進位,取到個位數)(2分)GFR 範圍:_________
#534199
(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
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
3. [15%] Which series is bigger, ? We have:
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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
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