收录一些赋能2题目

工具v2/文本文件/新题收录列表.txt

@@ -256,3 +256,24 @@
 20240131-150152
 004724,004726:004728,024298,004106,024299:024300,004736:004737
 
+20240131-150606
+024301:024305,017611,023955,024306:024308
+
+20240131-150939
+024309,024185,024310,012457,024214,015187,031718,024176,031139
+
+20240131-151033
+024311
+
+20240131-151408
+030964,030620,030758,024312:024313,031121,030858,024314,030645,031140
+
+20240131-152431
+024315:024317,023957,024318:024320,013396,024321:024322
+
+20240131-152939
+024323:024328,023939,024329:024331
+
+20240131-153325
+030615,030966,030760,024332:024334,031000,024335,030674,013417
+

题库0.3/Problems.json

@@ -20021,7 +20021,9 @@
             "20220624\t朱敏慧, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024301"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -145691,7 +145693,8 @@
             "003634",
             "010990",
             "011415",
-            "020312"
+            "020312",
+            "024326"
         ],
         "remark": "",
         "space": "",
@@ -147479,7 +147482,8 @@
             "004104",
             "004727",
             "010990",
-            "011415"
+            "011415",
+            "024326"
         ],
         "remark": "",
         "space": "",
@@ -217016,7 +217020,8 @@
         "same": [],
         "related": [
             "000580",
-            "004250"
+            "004250",
+            "024333"
         ],
         "remark": "",
         "space": "",
@@ -317499,7 +317504,8 @@
         ],
         "same": [],
         "related": [
-            "000716"
+            "000716",
+            "024301"
         ],
         "remark": "",
         "space": "",
@@ -320276,7 +320282,8 @@
         "related": [
             "004686",
             "004727",
-            "004747"
+            "004747",
+            "024326"
         ],
         "remark": "",
         "space": "",
@@ -343921,7 +343928,9 @@
             "20221209\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024309"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -348225,7 +348234,9 @@
             "20221212\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024325"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -355976,7 +355987,9 @@
             "20221220\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024315"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -424019,7 +424032,9 @@
             "20230414\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024301"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -439953,7 +439968,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024316"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -461006,7 +461023,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024331"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -477016,7 +477035,9 @@
             "20230602\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024323"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -535581,7 +535602,9 @@
             "20231103\t毛培菁"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024333"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -634362,7 +634385,8 @@
         "same": [],
         "related": [
             "009252",
-            "021036"
+            "021036",
+            "024334"
         ],
         "remark": "",
         "space": "",
@@ -658991,6 +659015,736 @@
         "space": "",
         "unrelated": []
     },
+    "024301": {
+        "id": "024301",
+        "content": "设全集 $U=\\{-1,0,1,2\\}$, 若集合 $A=\\{-1,0,2\\}$, 则 $\\overline{A}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "015164",
+            "011305",
+            "000536"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024302": {
+        "id": "024302",
+        "content": "若复数 $z=\\dfrac{2+\\mathrm{i}}{\\mathrm{i}}$ ($\\mathrm{i}$ 表示虚数单位), 则 $\\mathrm{Im}z=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024303": {
+        "id": "024303",
+        "content": "函数 $y=\\sqrt{x}-\\dfrac{1}{x}$ 的零点为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024304": {
+        "id": "024304",
+        "content": "曲线 $y^2=4 x$ 的顶点到其准线的距离为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024305": {
+        "id": "024305",
+        "content": "函数 $y=x^2$ 的驻点为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024306": {
+        "id": "024306",
+        "content": "已知由样本数据 $(x_i, y_i)$($i=1,2,3, \\cdots, 10$) 组成的一个样本, 得到回归直线方程为 $\\hat{y}=2 x-0.4$, 且 $\\overline{x}=2$, 其中发现两个歧义点 $(-2,1)$ 和 $(2,-1)$ 偏差过大, 去除这两点后, 得到新的回归直线的斜率为 $3$, 则新的回归直线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024307": {
+        "id": "024307",
+        "content": "设 $a$、$b$ 均为非零实数且 $a>b$, 则下列结论中正确的是\\bracket{20}.\n\\fourch{$a^{-2}>b^{-2}$}{$a^{-1}>b^{-1}$}{$a^2>b^2$}{$a^3>b^3$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "032030"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024308": {
+        "id": "024308",
+        "content": "设 $7<m<16$, 则双曲线 $\\dfrac{x^2}{16-m}+\\dfrac{y^2}{7-m}=1$ 的焦点坐标是\\bracket{20}.\n\\fourch{$( \\pm 4,0)$}{$( \\pm 3,0)$}{$(0, \\pm 5)$}{$(0, \\pm 4)$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024309": {
+        "id": "024309",
+        "content": "已知集合 $A=(-2,3)$, $B=[-1,4]$, 则集合 $A \\cap B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "030618",
+            "012267"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024310": {
+        "id": "024310",
+        "content": "已知函数 $f(x)=2 x^2+x$, 则 $f'(2)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024311": {
+        "id": "024311",
+        "content": "已知 $a, b \\in \\mathbf{R}$, 则``$a>0$ 且 $b>0$''是``$a+b>\\sqrt{a b}$''的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{既不充分也不必要条件}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024312": {
+        "id": "024312",
+        "content": "已知直线 $y=k x$ 是曲线 $y=\\ln x$ 的一条切线, 则 $k$ 的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024313": {
+        "id": "024313",
+        "content": "函数 $f(x)=\\mathrm{e}^x-x+1$ 在区间 $[-1,1]$ 上的最大值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024314": {
+        "id": "024314",
+        "content": "$A$、$B$、$C$ 三位好友进行乒乓球擂台赛, $A$、$B$ 先进行一局决胜负, 负者下, 由 $C$ 挑战胜者, 继续进行一局决胜负, 负者下, 胜者接受第三人的挑战, 依次举行. 假设三人水平接近, 任意两人的对决胜负都是五五开, 已知三人共比赛了 3 局, 则三人各胜一局的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024315": {
+        "id": "024315",
+        "content": "设集合 $A=(1,3)$, $B=(2,4)$, 则 $A \\cap B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "012676"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024316": {
+        "id": "024316",
+        "content": "曲线 $y=x^3$ 在点 $(1,1)$ 处的切线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "015817"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024317": {
+        "id": "024317",
+        "content": "已知各项为正的等差数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 若 $a_5+a_7-a_6{}^2=0$, 则 $S_{11}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024318": {
+        "id": "024318",
+        "content": "已知某社区的家庭年收入的频率分布如下表所示, 可以估计该社区内家庭的平均年收入为\\blank{50}万元.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline 家庭年收入(万元) &{$[4,5)$}&{$[5,6)$}&{$[6,7)$}&{$[7,8)$}&{$[8,9)$}&{$[9,10)$}\\\\\n\\hline 频率 $f$ & $0.2$ & $0.2$ & $0.2$ & $0.26$ & $0.07$ & $0.07$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024319": {
+        "id": "024319",
+        "content": "经过点 $(2,4)$ 的抛物线 $y=a x^2$ 焦点坐标是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024320": {
+        "id": "024320",
+        "content": "用 $0$、$1$ 两个数字编码, 码长为 $4$ 的二进制四位数 (首位可以是 $0$), 从所有码中任选一码, 则事件 $A$ :``码中至少有两个 1''发生的概率是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024321": {
+        "id": "024321",
+        "content": "如图, $PA \\perp$ 平面 $ABCD, ABCD$ 为矩形, 连接 $AC$、$BD$、$PB$、$PC$、$PD$, 下面各组向量中, 数量积不一定为零的是\\bracket{20} .\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,2) node [left] {$B$} coordinate (B);\n\\draw (3,0,2) node [right] {$C$} coordinate (C);\n\\draw (3,0,0) node [right] {$D$} coordinate (D);\n\\draw (0,2,0) node [left] {$P$} coordinate (P);\n\\draw (P) -- (B) -- (C) -- (D) -- (P) (P) -- (C);\n\\draw [dashed] (A) -- (P) (A) -- (B) (A) -- (D) (A)--(C)(B)--(D);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\overrightarrow{PC}$ 与 $\\overrightarrow{BD}$}{$\\overrightarrow{PB}$ 与 $\\overrightarrow{DA}$}{$\\overrightarrow{PD}$ 与 $\\overrightarrow{AB}$}{$\\overrightarrow{PA}$ 与 $\\overrightarrow{CD}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024322": {
+        "id": "024322",
+        "content": "下列选项中, $y$ 可表示为 $x$ 的函数是\\bracket{20}.\n\\fourch{$3^{|y|}-x^2=0$}{$x=y^{\\frac{2}{3}}$}{$x=\\sin y$}{$\\ln y=x^2$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024323": {
+        "id": "024323",
+        "content": "已知集合 $A=\\{x|| x-1 |<1\\}$, $B=\\{1,2,3\\}$, 则 $A \\cap B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "017465"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024324": {
+        "id": "024324",
+        "content": "若复数 $z$ 满足 $z \\cdot(1+\\mathrm{i})=2$ ($\\mathrm{i}$ 为虚数单位), 则 $z=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024325": {
+        "id": "024325",
+        "content": "已知 $k$ 为实数, 向量 $\\overrightarrow{a}=(4,-2)$, $\\overrightarrow{b}=(k, 2)$, 若 $\\overrightarrow{a}\\perp \\overrightarrow{b}$, 则 $k=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "012420",
+            "030928"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024326": {
+        "id": "024326",
+        "content": "在 $(x+2)^6$ 的二项展开式中, 含 $x^3$ 项的系数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "004686",
+            "004747",
+            "011415"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024327": {
+        "id": "024327",
+        "content": "如图所示, 在平行六面体 $ABCD-A_1B_1C_1D_1$ 中, $A_1C_1 \\cap B_1D_1=F$, 若 $\\overrightarrow{AF}=x \\overrightarrow{AB}+y \\overrightarrow{AD}+z \\overrightarrow{AA_1}$,则 $x+y+z=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n--++ (0.2,1.5) node [above right] {$C_1$} coordinate (C1)\n--++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n\\draw (A) ++ (2.2,1.5) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-2,0)  (D1) -- (B1);\n\\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0.2,1.5);\n\\draw (A1)--(C1);\n\\draw ($(A1)!0.5!(C1)$) node [above] {$F$} coordinate (F);\n\\draw [dashed, ->] (A)--(F);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024328": {
+        "id": "024328",
+        "content": "曲线 $y=\\sin 3 x$ 在点 $P(\\dfrac{\\pi}{3}, 0)$ 处切线的斜率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024329": {
+        "id": "024329",
+        "content": "已知随机变量 $X$ 服从的分布为 $\\begin{pmatrix}0 & 1 \\\\ \\dfrac{1}{3}& \\dfrac{2}{3}\\end{pmatrix}$, 则随机变量 $X$ 的方差 $D[X]=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024330": {
+        "id": "024330",
+        "content": "经过点 $(1,1)$, 且法向量为 $(2,-1)$ 的直线方程是\\bracket{20}.\n\\fourch{$2 x-y-1=0$}{$2 x+y-3=0$}{$x-2 y+1=0$}{$x+2 y-3=0$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024331": {
+        "id": "024331",
+        "content": "设 $\\alpha$、$\\beta$ 表示两个不同的平面, $l$ 表示一条直线, 且 $l \\subset \\alpha$, 则 $l \\parallel  \\beta$ 是 $\\alpha \\parallel  \\beta$ 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": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "016761"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024332": {
+        "id": "024332",
+        "content": "已知函数 $f(x)=\\ln (1-x)$, 则其导函数 $f'(x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024333": {
+        "id": "024333",
+        "content": "在 $(x+\\dfrac{1}{x})^5$ 的展开式中, 含 $x^3$ 项的系数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "007552",
+            "019973",
+            "031873"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024334": {
+        "id": "024334",
+        "content": "从 $1,2,3,4,5$ 这五个数字中任意选取两个不同的数字组成一个两位数, 则这个两位数是偶数的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "023256"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024335": {
+        "id": "024335",
+        "content": "若随机变量 $X$ 服从二项分布 $B(4, \\dfrac{2}{3})$, 则 $E[X]=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240131\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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
@@ -679105,7 +679859,9 @@
             "20230106\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024309"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -686170,7 +686926,9 @@
             "20230108\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024325"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -709933,7 +710691,9 @@
             "20230730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024333"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -713617,7 +714377,9 @@
             "20231223\t王伟叶, 毛培菁"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024307"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []