录入2026届高三基础赋能卷5A部分题目

题库0.3/Problems.json

@@ -15320,7 +15320,8 @@
         ],
         "same": [],
         "related": [
-            "011723"
+            "011723",
+            "019946"
         ],
         "remark": "",
         "space": "",
@@ -520585,6 +520586,90 @@
         "space": "",
         "unrelated": []
     },
+    "019945": {
+        "id": "019945",
+        "content": "已知集合 $A=\\{1,3\\}$, $B=\\{3,5\\}$, 则 $A \\cup B=$\\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": [
+            "030598"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019946": {
+        "id": "019946",
+        "content": "在 $(\\dfrac{3}{x^2}+\\sqrt{x})^n$ ($n$ 为正整数) 的二项展开式中, 所有项的系数之和为 $1024$, 则 $n=$\\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": [
+            "000462"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019947": {
+        "id": "019947",
+        "content": "已知常数 $a \\in \\mathbf{R}$, 在 $(x-a)^{10}$ 的二项展开式中, $x^7$ 的系数是 $15$, 则 $a=$\\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": []
+    },
+    "019948": {
+        "id": "019948",
+        "content": "已知 $l$ 是平面 $\\alpha$ 给定的一条斜线, 动直线 $m$ 在平面 $\\alpha$ 上, 则\\bracket{20}.\n\\twoch{存在唯一的直线 $m$, 使得 $l \\perp m$}{存在无穷多条直线 $m$, 使得 $l \\perp m$}{存在唯一的直线 $m$, 使得 $l \\parallel  m$}{存在无穷多条直线 $m$, 使得 $l \\parallel  m$}",
+        "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.",
@@ -613401,7 +613486,9 @@
             "20230106\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "019945"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []