diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 852fab2c..5f160460 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -13642,7 +13642,8 @@ ], "related": [ "001721", - "004470" + "004470", + "019974" ], "remark": "", "space": "", @@ -110907,7 +110908,8 @@ "002961", "004125", "011091", - "011475" + "011475", + "019971" ], "remark": "", "space": "", @@ -124438,7 +124440,8 @@ "same": [], "related": [ "003421", - "004534" + "004534", + "019976" ], "remark": "", "space": "", @@ -314981,7 +314984,8 @@ "004469", "011091", "011475", - "011604" + "011604", + "019971" ], "remark": "", "space": "", @@ -521158,6 +521162,173 @@ "space": "", "unrelated": [] }, + "019971": { + "id": "019971", + "content": "不等式 $\\dfrac{x}{x-1}>2$ 的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [ + "003675", + "011559" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "019972": { + "id": "019972", + "content": "设全集 $U=\\mathbf{R}$, 若 $A=\\{-2,-1,0,1,2\\}$, $B=\\{x | y=\\log _3(1-x)\\}$, 则 $A \\cap \\overline{B}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019973": { + "id": "019973", + "content": "在 $(x-\\dfrac{2}{x})^5$ 的展开式中 $x$ 的系数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019974": { + "id": "019974", + "content": "若一个球的表面积为 $4 \\pi$, 则它的体积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [ + "000419" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "019975": { + "id": "019975", + "content": "函数 $f(x)=x+\\dfrac{8}{x}$, $x \\in[2,8)$ 的值域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019976": { + "id": "019976", + "content": "双曲线 $\\dfrac{x^2}{4}-\\dfrac{y^2}{3}=1$ 的焦点到其渐近线的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [ + "004169" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "019977": { + "id": "019977", + "content": "已知 $x \\in \\mathbf{R}$, 则``$|x-\\dfrac{1}{3}|<\\dfrac{2}{3}$''是``$x<1$''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": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019978": { + "id": "019978", + "content": "关于三个不同平面 $\\alpha, \\beta, \\gamma$ 与直线 $l$, 下列命题中的假命题是\\bracket{20}.\n\\onech{若 $\\alpha \\perp \\beta$, 则 $\\alpha$ 内一定存在直线平行于 $\\beta$}{若 $\\alpha$ 与 $\\beta$ 不垂直, 则 $\\alpha$ 内一定不存在直线垂直于 $\\beta$}{若 $\\alpha \\perp \\gamma$, $\\beta \\perp \\gamma$, $\\alpha \\cap \\beta=l$, 则 $l \\perp \\gamma$}{若 $\\alpha \\perp \\beta$, 则 $\\alpha$ 内所有直线垂直于 $\\beta$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",