收录高三寒假作业15新题

工具v2/文本文件/新题收录列表.txt

@@ -43,3 +43,6 @@
 20240125-101303
 023723:023727,014571,023728:023729,019144,023730
 
+20240125-101736
+023731:023737
+

题库0.3/Problems.json

@@ -17156,7 +17156,9 @@
             "20220624\t朱敏慧, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023731"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -22536,7 +22538,9 @@
             "20220624\t朱敏慧, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023736"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -116265,7 +116269,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023732"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -217390,7 +217396,8 @@
         "same": [],
         "related": [
             "007589",
-            "007590"
+            "007590",
+            "023733"
         ],
         "remark": "",
         "space": "4em",
@@ -315357,7 +315364,9 @@
             "20220818\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023732"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -640920,6 +640929,155 @@
         "space": "",
         "unrelated": []
     },
+    "023731": {
+        "id": "023731",
+        "content": "$(2 x+\\sqrt{x})^5$ 的展开式中, $x^3$ 的系数是\\blank{50};(用数字作答).",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "000470"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023732": {
+        "id": "023732",
+        "content": "若二项式 $(a x+\\dfrac{\\sqrt{3}}{6})^6$ 的展开式的第二项的系数为 $-\\sqrt{3}$, 则实数 $a$ 的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "003735",
+            "011269"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023733": {
+        "id": "023733",
+        "content": "$(x^2+x+y)^5$ 的展开式中, $x^5 y^2$ 项的系数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "007587"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023734": {
+        "id": "023734",
+        "content": "$-1+3\\mathrm{C}_{11}^1-9\\mathrm{C}_{11}^2+27\\mathrm{C}_{11}^3-\\cdots-3^{10}\\mathrm{C}_{11}^{10}+3^{11}$ 除以 $5$ 的余数是\\bracket{20}.\n\\fourch{$1$}{$2$}{$3$}{$4$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023735": {
+        "id": "023735",
+        "content": "若 $(x+2)^9=a_0+a_1 x+a_2 x^2+\\cdots+a_9 x^9$,\n则 $(a_1+3 a_3+5 a_5+7 a_7+9 a_9)^2-(2 a_2+4 a_4+6 a_6+8 a_8)^2$ 的值为\\bracket{20}.\n\\fourch{$3^9$}{$3^{10}$}{$3^{11}$}{$3^{12}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023736": {
+        "id": "023736",
+        "content": "若 $(x+\\dfrac{1}{2 x})^n$($n \\geq 4$, $n \\in \\mathbf{N}$) 的二项展开式中前三项的系数依次成等差数列, 求 $n$ 的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "000600"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023737": {
+        "id": "023737",
+        "content": "已知 $(\\sqrt[3]{x}+x^2)^{2 n}$ 的展开式的二项式系数和比 $(3 x-1)^n$ 的展开式的二项式系数和大 $992$. 求在 $(2 x-\\dfrac{1}{x})^{2 n}$ 的展开式中, 系数的绝对值最大的项.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "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.",