diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index bc05d8e6..9618d964 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -616831,6 +616831,86 @@ "space": "", "unrelated": [] }, + "023011": { + "id": "023011", + "content": "不等式 $2^{x^2-5}>\\dfrac{1}{2}$ 的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240104\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023012": { + "id": "023012", + "content": "在 $(1+2 x)^5$ 的二项展开式中, $x^2$ 的系数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240104\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023013": { + "id": "023013", + "content": "设 $a, b \\in \\mathbf{R}$, 则``$a>b$''是``$(\\dfrac{a+b}{2})^2>a b$''的\\bracket{20}条件.\n\\fourch{充分而不必要}{必要而不充分}{充要}{既不充分又不必要}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240104\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023014": { + "id": "023014", + "content": "已知函数 $f(x)=2 \\sin \\dfrac{\\pi}{2}x$. 若对任意实数 $x$, 都有 $f(x_1) \\leq f(x) \\leq f(x_2)$,则 $|x_2-x_1|$ 的最小值是\\bracket{20}.\n\\fourch{$\\pi$}{$2 \\pi$}{$2$}{$4$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240104\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "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