From fb832fd3a79feab52257e2d93310be7e1d06422d Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 10:18:02 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A15=E6=96=B0=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 168 ++++++++++++++++++++++++++++++- 2 files changed, 166 insertions(+), 5 deletions(-) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index d9f4fd02..c39d49be 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -43,3 +43,6 @@ 20240125-101303 023723:023727,014571,023728:023729,019144,023730 +20240125-101736 +023731:023737 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 6a6f201e..040a4d0a 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -17156,7 +17156,9 @@ "20220624\t朱敏慧, 王伟叶" ], "same": [], - "related": [], + "related": [ + "023731" + ], "remark": "", "space": "", "unrelated": [] @@ -22536,7 +22538,9 @@ "20220624\t朱敏慧, 王伟叶" ], "same": [], - "related": [], + "related": [ + "023736" + ], "remark": "", "space": "", "unrelated": [] @@ -116265,7 +116269,9 @@ "20220701\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023732" + ], "remark": "", "space": "", "unrelated": [] @@ -217390,7 +217396,8 @@ "same": [], "related": [ "007589", - "007590" + "007590", + "023733" ], "remark": "", "space": "4em", @@ -315357,7 +315364,9 @@ "20220818\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023732" + ], "remark": "", "space": "", "unrelated": [] @@ -640920,6 +640929,155 @@ "space": "", "unrelated": [] }, + "023731": { + "id": "023731", + "content": "$(2 x+\\sqrt{x})^5$ 的展开式中, $x^3$ 的系数是\\blank{50};(用数字作答).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "000470" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023732": { + "id": "023732", + "content": "若二项式 $(a x+\\dfrac{\\sqrt{3}}{6})^6$ 的展开式的第二项的系数为 $-\\sqrt{3}$, 则实数 $a$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "003735", + "011269" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023733": { + "id": "023733", + "content": "$(x^2+x+y)^5$ 的展开式中, $x^5 y^2$ 项的系数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "007587" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023734": { + "id": "023734", + "content": "$-1+3\\mathrm{C}_{11}^1-9\\mathrm{C}_{11}^2+27\\mathrm{C}_{11}^3-\\cdots-3^{10}\\mathrm{C}_{11}^{10}+3^{11}$ 除以 $5$ 的余数是\\bracket{20}.\n\\fourch{$1$}{$2$}{$3$}{$4$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023735": { + "id": "023735", + "content": "若 $(x+2)^9=a_0+a_1 x+a_2 x^2+\\cdots+a_9 x^9$,\n则 $(a_1+3 a_3+5 a_5+7 a_7+9 a_9)^2-(2 a_2+4 a_4+6 a_6+8 a_8)^2$ 的值为\\bracket{20}.\n\\fourch{$3^9$}{$3^{10}$}{$3^{11}$}{$3^{12}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023736": { + "id": "023736", + "content": "若 $(x+\\dfrac{1}{2 x})^n$($n \\geq 4$, $n \\in \\mathbf{N}$) 的二项展开式中前三项的系数依次成等差数列, 求 $n$ 的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "000600" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023737": { + "id": "023737", + "content": "已知 $(\\sqrt[3]{x}+x^2)^{2 n}$ 的展开式的二项式系数和比 $(3 x-1)^n$ 的展开式的二项式系数和大 $992$. 求在 $(2 x-\\dfrac{1}{x})^{2 n}$ 的展开式中, 系数的绝对值最大的项.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "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