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录入24届赋能补充题至6B

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wangweiye7840 2024-01-05 09:19:30 +08:00
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题库0.3/Problems.json
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@ -617151,6 +617151,126 @@
"space": "",
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},
"023027": {
"id": "023027",
"content": "二项式 $(x+\\dfrac{1}{x})^6$ 的展开式中, 常数项为\\blank{50}(结果用数值表示).",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "24届赋能补充题目",
"edit": [
"20240105\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
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},
"023028": {
"id": "023028",
"content": "已知向量 $\\overrightarrow{a}=(3, m)$, $\\overrightarrow{b}=(-1,2)$, 若向量 $\\overrightarrow{a}\\parallel \\overrightarrow{b}$, 则实数 $m=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "24届赋能补充题目",
"edit": [
"20240105\t毛培菁"
],
"same": [],
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"remark": "",
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"023029": {
"id": "023029",
"content": "已知角 $\\alpha \\in(\\dfrac{\\pi}{2}, \\pi)$, 且 $\\tan \\alpha=-2$, 则 $\\sin (\\pi-\\alpha)=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "24届赋能补充题目",
"edit": [
"20240105\t毛培菁"
],
"same": [],
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"remark": "",
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"023030": {
"id": "023030",
"content": "已知函数 $f(x)=\\log _a x$ 和 $g(x)=k(x-2)$ 的图像如图所示, 则不等式 $\\dfrac{f(x)}{g(x)}\\geq 0$ 的解集是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.25:3, samples = 100] plot (\\x,{ln(\\x)/ln(2)});\n\\draw (1,-2) node [below] {$f(x)=\\log_a x$};\n\\end{tikzpicture}\n\\hspace*{5em}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (-1,2) -- (3,{-2/3});\n\\draw (1,-2) node [below] {$g(x)=k(x-2)$};\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "24届赋能补充题目",
"edit": [
"20240105\t毛培菁"
],
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"remark": "",
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"023031": {
"id": "023031",
"content": "已知 $x \\in \\mathbf{R}$, 则``$x \\geq 0$''是``$x>3$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "24届赋能补充题目",
"edit": [
"20240105\t毛培菁"
],
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"023032": {
"id": "023032",
"content": "某象棋俱乐部有队员 5 人, 其中女队员 2 人. 现随机选派 2 人参加一个象棋比赛,则选出的 2 人中恰有 1 人是女队员的概率为\\bracket{20}.\n\\fourch{$\\dfrac{3}{10}$}{$\\dfrac{3}{5}$}{$\\dfrac{2}{5}$}{$\\dfrac{2}{3}$}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "24届赋能补充题目",
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"20240105\t毛培菁"
],
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"remark": "",
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"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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",