diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 758f7c7c..116c5944 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -122034,7 +122034,9 @@ "20220701\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023261" + ], "remark": "", "space": "4em", "unrelated": [] @@ -259068,7 +259070,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023256" + ], "remark": "", "space": "4em", "unrelated": [] @@ -323358,7 +323362,9 @@ "20220819\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023264" + ], "remark": "", "space": "", "unrelated": [] @@ -560881,7 +560887,9 @@ "20230101\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023256" + ], "remark": "", "space": "4em", "unrelated": [] @@ -622544,6 +622552,213 @@ "space": "4em", "unrelated": [] }, + "023256": { + "id": "023256", + "content": "$1,2,3,4,5$ 这五个数字中任取不重复的 $3$ 个数字组成一个三位数, 则组成的三位数是奇数的概率是\\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": [ + "009252", + "021036" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023257": { + "id": "023257", + "content": "某班有 $50$ 名学生, 其中 $15$ 人选修 $A$ 课程, 另外 $35$ 人选修 $B$ 课程. 从班级中任选两名学生, 他们是选修不同课程的学生的概率是\\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": [] + }, + "023258": { + "id": "023258", + "content": "两部不同的长篇小说各由第一、二、三、四卷组成, 每卷 $1$ 本, 共 $8$ 本. 将它们任意地排成一排, 左边 $4$ 本恰好都属于同一部小说的概率是\\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": [] + }, + "023259": { + "id": "023259", + "content": "在一个口袋中装有 $5$ 个白球和 $3$ 个黑球, 这些球除颜色外完全相同, 从中摸出 $3$ 个球,至少摸到 $2$ 个黑球的概率等于\\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": [] + }, + "023260": { + "id": "023260", + "content": "用 $0 \\sim 9$ 这十个数字组成没有重复数字的五位数, 任取一个五位数, 奇数位上都是偶数的概率是\\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": [] + }, + "023261": { + "id": "023261", + "content": "甲、乙等五名奥运志愿者被随机地分到 A, B, C, D 四个不同的岗位服务, 每个岗位至少有一名志愿者, 则甲、乙两人不在同一个岗位服务的概率是\\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": [ + "003998" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023262": { + "id": "023262", + "content": "等差数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 已知 $S_{10}=0$, $S_{15}=25$, 则 $n S_n$ 的最小值为\\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": [] + }, + "023263": { + "id": "023263", + "content": "在正项等比数列 $\\{a_n\\}$ 中, $a_5=\\dfrac{1}{2}$, $a_6+a_7=3$, 则满足 $a_1+a_2+\\cdots+a_n>a_1 a_2 \\cdots a_n$ 的最大正整数 $n$ 的值为\\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": [] + }, + "023264": { + "id": "023264", + "content": "一个盒子里放有分别写着编号为 $0$、$1$、$2$、$3$ 的四张卡片, 从中任意取两张, 求卡片上的两个编号之积为偶数的概率.", + "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": [ + "011654" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023265": { + "id": "023265", + "content": "给定数列 $a_1, a_2, \\cdots, a_n$, 对 $i=1,2, \\cdots, n-1$, 该数列前 $i$ 项 $a_1, a_2, \\cdots, a_i$ 中的最大值记为 $A_i$, 后 $n-i$ 项 $a_{i+1}, a_{i+2}, \\cdots, a_n$ 的最小值记为 $B_i$, 设 $d_i=A_i-B_i$.\\\\\n(1) 设数列 $\\{a_n\\}$ 为 $3,4,7,1$ . 写出 $d_1, d_2, d_3$ 的值;\\\\\n(2) 设 $a_1, a_2, \\cdots, a_n$($n \\geq 4$) 是公比大于 $1$ 的等比数列,且 $a_1>0$ . 证明: $d_1, d_2, \\cdots, d_{n-1}$是等比数列;\n(3) 设 $d_1, d_2, \\cdots, d_{n-1}$ 是公差大于 $0$ 的等差数列, 且 $d_1>0$, 证明: $a_1, a_2, \\cdots, a_{n-1}$是等差数列.", + "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