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40. Which of the following statement about coefficient of determination $R^2$ is incorrect? (A) As the number of explanatory variables increases, \( R^2 \) may increase. (B) It provides the percentage of explained variance in the response variable using the regression model. (C) Its value must fall in 0 and 1. (D) The correlation of coefficient must equal to \( R^2 \). (E) When \( R^2 = 1 \), the response variable has an exact linear relationship with the explanatory variable in the simple regression model.

39. Which of the following statement is when the one-way ANOVA provides relatively more evidence that $H_0: \mu_1 = \mu_2 = \cdots = \mu_g$ is rejected? (A) The smaller the between-groups variation. (B) The smaller the within-groups variation. (C) The larger the between-groups variation. (D) The larger the within-group variation. (E) None of the above.

38. Suppose that a 99% confidence interval for the difference $p_1 - p_2$ between the proportions of men and women in Taiwan who are alcoholics equals (0.02, 0.09). (A) We are \( 99\% \) confident that the proportion of alcoholics is between 0.02 and 0.09. (B) We are \( 99\% \) confident that the proportion of men in Taiwan who are alcoholics is between 0.02 and 0.09 larger than the proportion of women in Taiwan who are. (C) We can conclude that the population proportions may be equal. (D) We are \( 99\% \) confident that a minority of Taiwan residents are alcoholics. (E) Since the confidence interval does not contain 0, it is impossible that \( p_1 = p_2 \)

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43. 下列反應的主要產物為何?(A)(B)(C)(D)

18. A polar molecule may be modeled approximately as a positive charge ? at x = a and a negative charge −q at x = −a. If we calculate the electric field on the y-axis, what is an approximate expression valid at large distance ( |y| ≫ a )? Note that k is the Coulomb constant, and and are the unit vectors. (A)(B) (C) (D) (E)

19. In the figure, ?1, ?2, and ?3 are charges on a two-dimensional plane. We take . If the force on q1 points in the −x-direction, what is the magnitude of ?3? (A) Q (B) (C) (D) (E)

42. 某客服系統開發團隊希望聊天機器人的回覆風格更貼近人類偏好,因此在模型訓練後期導入人類回饋強化學習(Reinforcement Learning from Human Feedback, RLHF)技術。關於 RLHF 核心作法,下列敘述何者最正確? (A)蒐集人類對不同模型回覆的偏好評比,建立獎勵模型作為模型優化的依據; (B)蒐集更大量的公開網路文字重新進行預訓練,以提升模型回答的專業度; (C)調整系統提示(System Prompt),引導模型採用指定的回覆風格; (D)蒐集高品質問答範例,直接進行監督式微調(Supervised Fine-Tuning, SFT)

43. 某企業導入大型語言模型處理超長合約文件(數萬字),發現輸入越長,運算時間與資源消耗增加得越快,遠超過文件長度增加的比例。下列何者最能解釋此現象發生的主要原因? (A)長文本包含較多生僻字,系統偵測到新詞時會自動暫停並即時重建底層詞彙表; (B)模型為了確保長文本的生成品質,會隨輸入長度自動動態增加模型的參數數量; (C)自注意力機制在處理文本時,時間複雜度會隨輸入長度呈二次方(平方)快速上升; (D)隨著合約內容變長,模型內部會自動切換為檢索增強生成(RAG)架構,以提升長文本處理效率