From 8ecb16b4b3d78c30039fe53001da72bdb9c5cd1e Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sat, 6 Jan 2024 21:45:57 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A52025=E5=B1=8A=E5=91=A8?= =?UTF-8?q?=E6=9C=AB=E5=8D=B710=E8=A1=A5=E5=85=85=E9=A2=98=E7=9B=AE?= =?UTF-8?q?=E5=B9=B6=E5=BB=BA=E7=AB=8Brelated?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 414 +++++++++++++++++++++++++++++++++++++++++- 1 file changed, 408 insertions(+), 6 deletions(-) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index c0900807..758f7c7c 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -218528,7 +218528,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023251" + ], "remark": "", "space": "4em", "unrelated": [] @@ -301542,7 +301544,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023250" + ], "remark": "", "space": "4em", "unrelated": [] @@ -419540,7 +419544,9 @@ "20230414\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023242" + ], "remark": "", "space": "", "unrelated": [] @@ -459894,7 +459900,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023250" + ], "remark": "", "space": "4em", "unrelated": [] @@ -460180,7 +460188,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023250" + ], "remark": "", "space": "4em", "unrelated": [] @@ -604917,7 +604927,9 @@ "20231218\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023253" + ], "remark": "", "space": "4em", "unrelated": [] @@ -622142,6 +622154,396 @@ "space": "4em", "unrelated": [] }, + "023237": { + "id": "023237", + "content": "(1) $\\mathrm{C}_{10}^3+\\mathrm{C}_{10}^4+\\mathrm{C}_{11}^5+\\mathrm{C}_{12}^6=$\\blank{50};\\\\\n(2) 已知 $\\mathrm{C}_{14}^r+\\mathrm{C}_{14}^{r+1}=\\mathrm{C}_{15}^6$, $r=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023238": { + "id": "023238", + "content": "解方程 $p_{10}^n-p_9^n=126 n! $ , 则 $n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023239": { + "id": "023239", + "content": "解方程 $\\begin{cases}\\mathrm{C}_x^y=\\mathrm{C}_x^{2 y}\\\\3\\mathrm{C}_x^{y+1}=11\\mathrm{C}_x^{y-1}\\end{cases}$, 则 $x=$\\blank{50}, $y=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023240": { + "id": "023240", + "content": "从集合 $A=\\{1,2,3,5,7,9\\}$ 中任取两个不同的数分别作为对数的底数和真数, 则所有这样的对数值的集合中的元素的个数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023241": { + "id": "023241", + "content": "正方体的每一条对角线与正方体的棱可以组成异面直线的对数最多是\\blank{50}对.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023242": { + "id": "023242", + "content": "3 个医生和 6 个护士分配到 3 个学校为学生体检, 每个学校被分配 1 个医生和 2 个护士, 不同的分配方法有\\blank{50}种.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [ + "015170" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023243": { + "id": "023243", + "content": "8 人分两排坐, 每排 4 人, 甲必须坐前排, 乙丙必须坐后排且不相邻, 共有\\blank{50}种排法.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023244": { + "id": "023244", + "content": "一份考卷有 10 道考题, 分为 $A, B$ 两组, 每组 5 道, 要求考生选答 6 道, 但每组最多选 4 道, 有\\blank{50}种选法.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023245": { + "id": "023245", + "content": "数列 $\\{b_n\\}$ 中, $b_1=1$, $b_2=5$ 且 $b_{n+2}=b_{n+1}-b_n(n \\in \\mathbf{N})$, $b_{2002}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023246": { + "id": "023246", + "content": "数列 $\\{a_n\\}$ 中, 若 $a_1=1$, $a_{n+1}=a_n+2^n-2^{n-1}$, 则 $\\{a_n\\}$ 的通项 $a_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023247": { + "id": "023247", + "content": "数列 $\\{a_n\\}$ 前 $n$ 项和为 $S_n$, 并且 $S_n=2 a_n-1$($n \\in \\mathbf{N}$, $n\\ge 1$), 则 $\\{a_n\\}$ 的通项 $a_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023248": { + "id": "023248", + "content": "在数列 $\\{a_n\\}$ 中, $a_1=1$, $a_{n+1}=\\dfrac{1}{3}a_n-4$, 则通项 $a_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023249": { + "id": "023249", + "content": "若 $\\{a_n\\}$ 是以 $-60$ 为首项, $3$ 为公差的等差数列, 则数列 $\\{|a_n|\\}$ 的前 $30$ 项和为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023250": { + "id": "023250", + "content": "$200$ 件产品中有 $5$ 件是次品, 现从中任意抽取 $4$ 件, 按下列条件, 各有多少种不同的抽法?\\\\\n(1) 都不是次品;\\\\\n(2) 至少有一件次品;\\\\\n(3) 不都是次品;\\\\\n(4) 至多有两件次品.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [ + "016957", + "016944", + "010859" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023251": { + "id": "023251", + "content": "某车间有 9 名工人, 其中有 2 人既能当车工又能当钳工, 有 3 人只能当车工, 4 分只能当钳工,现要 3 名车工, 3 名钳工, 有多少种不同抽法?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [ + "007675" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023252": { + "id": "023252", + "content": "求下列数列的通项公式:\\\\\n(1) $a_1=1$, $a_{n+1}=\\dfrac{2 a_n}{a_n+2}$;\\\\\n(2) $a_1=1$, $a_{n+1}=3 a_n+2$;\\\\\n(3) $a_1=1$, $a_{n+1}=a_n+2^n$;\\\\\n(4) $a_1=2$, $a_{n+1}=\\dfrac{1+a_n}{1-a_n}$;\\\\\n(5) $a_1=1$, $a_{n+1}=2 a_n+2^{n+1}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023253": { + "id": "023253", + "content": "已知数列的通项公式为 $a_n=-n^2+7 n+8$.\\\\\n(1) $\\dfrac{45}{4}$ 是否是数列中的项?\\\\\n(2) 求数列 $\\{a_n\\}$ 的最大项的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [ + "022568" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023254": { + "id": "023254", + "content": "已知数列 $\\{a_n\\}$ 的通项公式为 $a_n=3 n+1$, 取出其中的第 $2$ 项、第 $4$ 项、第 $8$ 项、 $\\cdots$、 第 $2^n$ 项依次构成一个新的数列 $\\{b_n\\}$.\n(1) 问 $b_4$ 是数列 $\\{a_n\\}$ 的第几项?\\\\\n(2) 求数列 $\\{b_n\\}$ 的通项公式.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023255": { + "id": "023255", + "content": "已知数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 且满足 $a_n+2S_n \\cdot S_{n-1}=0(n \\geq 2)$, $a_1=\\dfrac{1}{2}$.\\\\\n(1) 求证: $\\{\\dfrac{1}{S_n}\\}$ 是等差数列;\\\\\n(2) 求 $a_n$ 的表达式.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0