{"id":31203,"date":"2021-03-28T13:00:42","date_gmt":"2021-03-28T13:00:42","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=31203"},"modified":"2025-01-12T13:28:01","modified_gmt":"2025-01-12T13:28:01","slug":"%e0%a4%a5%e0%a4%b0%e0%a5%8d%e0%a4%ae%e0%a5%8b%e0%a4%a1%e0%a4%be%e0%a4%af%e0%a4%a8%e0%a4%be%e0%a4%ae%e0%a4%bf%e0%a4%95%e0%a5%8d%e0%a4%b8-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%95%e0%a5%89%e0%a4%ae%e0%a5%8d","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%a5%e0%a4%b0%e0%a5%8d%e0%a4%ae%e0%a5%8b%e0%a4%a1%e0%a4%be%e0%a4%af%e0%a4%a8%e0%a4%be%e0%a4%ae%e0%a4%bf%e0%a4%95%e0%a5%8d%e0%a4%b8-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%95%e0%a5%89%e0%a4%ae%e0%a5%8d\/","title":{"rendered":"\u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902"},"content":{"rendered":"<style>\n<p>\tp, ul, ol {\n\t\ttext-align: justify;\n\t}<\/p>\n<p>\th1, h2 {\n\t\ttext-align: center;\n\t}<\/p>\n<\/style>\n<h1>\u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902<\/h1>\n<p style=\"text-align:center;\"><em>\u090f\u0915 \u0910\u0938\u0940 \u092d\u094c\u0924\u093f\u0915 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u091c\u093f\u0938\u092e\u0947\u0902 \u0932\u093e\u0916\u094b\u0902 \u0924\u0924\u094d\u0935 \u0939\u094b\u0902, \u0909\u0938\u0947 \u0915\u093f\u0924\u0928\u0947 \u0924\u0930\u0940\u0915\u094b\u0902 \u0938\u0947 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948? \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u093e \u0909\u0924\u094d\u0924\u0930 \u0926\u0947\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0917\u0923\u093f\u0924 \u0915\u0947 \u0909\u092a\u092f\u094b\u0917 \u0915\u094b \u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0926\u0947\u0916\u0947\u0902\u0917\u0947\u0964 \u0907\u0938\u092e\u0947\u0902 \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0915\u0947 \u0935\u093f\u0924\u0930\u0923 \u0938\u0947 \u0932\u0947\u0915\u0930 \u092c\u0921\u093c\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0935\u093f\u0928\u094d\u092f\u093e\u0938\u094b\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0964 \u0939\u092e \u092c\u0921\u093c\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0938\u0902\u092d\u093e\u0932\u0928\u0947 \u0914\u0930 \u0915\u0920\u093f\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938, \u0932\u0949\u0917\u0930\u093f\u0926\u092e\u094d\u0938 \u0914\u0930 \u0938\u094d\u091f\u0930\u094d\u0932\u093f\u0902\u0917 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e \u091c\u0948\u0938\u0940 \u0909\u092a\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/strong><br \/>\n\u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u0924\u0915 \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:<\/p>\n<ol>\n<li><strong>\u0938\u092e\u091d\u0928\u093e<\/strong> \u0915\u093f \u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u092d\u094c\u0924\u093f\u0915 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u0915\u094b \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0948\u0938\u0947 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e<\/strong> \u0915\u093f \u0906\u0923\u0935\u093f\u0915 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0935\u093f\u0928\u094d\u092f\u093e\u0938\u094b\u0902 \u0915\u094b \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0930\u0942\u092a \u0938\u0947 \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964<\/li>\n<li><strong>\u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u093e<\/strong> \u0915\u093f \u0938\u094d\u091f\u0930\u094d\u0932\u093f\u0902\u0917 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u091c\u091f\u093f\u0932 \u0935\u093f\u0928\u094d\u092f\u093e\u0938\u094b\u0902 \u0915\u0940 \u092a\u0930\u093f\u092e\u093e\u0923 \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u0948\u0938\u0947 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><u>\u0935\u093f\u0937\u092f-\u0938\u0942\u091a\u0940:<\/u><br \/>\n<a href=\"#1\"><strong>\u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u092c\u0921\u093c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902<\/strong><\/a><br \/>\n<a href=\"#3\">\u0906\u0930\u094d\u0921\u0930 \u0911\u092b \u092e\u0948\u0917\u094d\u0928\u0940\u091f\u094d\u092f\u0942\u0921 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0947 \u0932\u093f\u090f \u0932\u0949\u0917\u0930\u093f\u0926\u092e \u0914\u0930 \u0938\u094d\u091f\u0930\u094d\u0932\u093f\u0902\u0917 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917<\/a><br \/>\n<a href=\"#4\"><em>\u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0935\u093f\u0915\u093e\u0938<\/em><\/a><br \/>\n<a href=\"#5\"><em>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0935\u093f\u0915\u093e\u0938<\/em><\/a><br \/>\n<a href=\"#6\"><strong>\u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0914\u0930 \u092a\u0930\u093f\u092e\u093e\u0923 \u0917\u0923\u0928\u093e \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923<\/strong><\/a><br \/>\n<a href=\"#7\">\u0915\u0947\u0938 1: \u092c\u0921\u093c\u0947 \u092b\u0948\u0915\u094d\u091f\u094b\u0930\u093f\u092f\u0932\u094d\u0938<\/a><br \/>\n<a href=\"#8\">\u0915\u0947\u0938 2: \u092c\u0921\u093c\u0947 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938<\/a>\n<\/p>\n<p>\u0915\u0941\u091b \u092d\u094c\u0924\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u090f\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0935\u093e\u0932 \u092f\u0939 \u0939\u094b\u0924\u093e \u0939\u0948: \u0915\u093f\u0938\u0940 \u0926\u093f\u090f \u0917\u090f \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b \u0915\u093f\u0924\u0928\u0947 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0924\u0930\u0940\u0915\u094b\u0902 \u0938\u0947 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948? \u092f\u0947 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902 \u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0906\u092e \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f \u092f\u0947 \u0936\u0941\u0930\u0942 \u092e\u0947\u0902 \u0938\u0930\u0932 \u0932\u0917 \u0938\u0915\u0924\u0940 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u092c\u0921\u093c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0924\u0947 \u0938\u092e\u092f \u091c\u091f\u093f\u0932 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948\u0902, \u091c\u0948\u0938\u0947 \u0915\u093f <strong><a href=\"http:\/\/toposuranos.com\/material\/mol-y-masa-molar\/\" rel=\"noopener\" target=\"_blank\">\u090f\u0935\u094b\u0917\u093e\u0921\u094d\u0930\u094b \u0938\u0902\u0916\u094d\u092f\u093e<\/a><\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">N_A<\/span>, \u091c\u094b \u092f\u0939 \u0926\u093f\u0916\u093e\u0924\u0940 \u0939\u0948 \u0915\u093f \u0907\u0924\u0928\u0940 \u092c\u0921\u093c\u0940 \u092e\u093e\u0924\u094d\u0930\u093e \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0928\u093e \u0915\u093f\u0924\u0928\u093e \u091a\u0941\u0928\u094c\u0924\u0940\u092a\u0942\u0930\u094d\u0923 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/K7_De9wux4A?si=q93_T8xh15EdfJ6B\" title=\"YouTube \u0935\u0940\u0921\u093f\u092f\u094b \u092a\u094d\u0932\u0947\u092f\u0930\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0936\u093e\u092e\u093f\u0932 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u091c\u091f\u093f\u0932\u0924\u093e \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0909\u0926\u093e\u0939\u0930\u0923 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902:<\/p>\n<h4>\u0909\u0926\u093e\u0939\u0930\u0923: \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0915\u0947 \u0935\u093f\u0924\u0930\u0923 \u092a\u0930 \u0938\u0902\u092f\u094b\u091c\u0928<\/h4>\n<p>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u090f\u0915 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 10 \u092a\u0930\u092e\u093e\u0923\u0941\u0913\u0902 \u0938\u0947 \u092c\u0928\u0940 \u0939\u0948\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u0930\u092e\u093e\u0923\u0941 \u0915\u0947\u0935\u0932 1 \u092f\u093e 0 \u090a\u0930\u094d\u091c\u093e \u0907\u0915\u093e\u0907\u092f\u094b\u0902, \u091c\u093f\u0928\u094d\u0939\u0947\u0902 <strong>\u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902, \u0915\u094b \u0938\u0902\u0917\u094d\u0930\u0939\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 (a) 10 \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0914\u0930 (b) 5 \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0939\u094b\u0902, \u0924\u094b \u0907\u0928 \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0915\u094b \u0915\u093f\u0924\u0928\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0924\u0930\u0940\u0915\u094b\u0902 \u0938\u0947 \u0935\u093f\u0924\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948?<\/p>\n<h5>\u0938\u092e\u093e\u0927\u093e\u0928<\/h5>\n<p>\u0939\u092e \u092a\u0930\u092e\u093e\u0923\u0941\u0913\u0902 \u0915\u094b \u0909\u0928 \u0930\u093f\u0915\u094d\u0924 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u090f\u0915 \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0915\u094b \u0938\u0902\u0917\u094d\u0930\u0939\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u090f\u0915 \u0938\u094d\u0925\u093e\u0928 \u092d\u0930\u093e \u0939\u0941\u0906 \u0939\u0948, \u0924\u094b \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u0915\u093f \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u0930\u092e\u093e\u0923\u0941 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0939\u0940 \u0905\u092a\u0928\u093e \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0930\u0916\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-zJa7H7iMOGY\/YF3QhG94SoI\/AAAAAAAAEuI\/olfdSHfeJOgKea3vHXEAyr5QCJ1ZjmcpgCLcBGAsYHQ\/s839\/cuantodeenergia.PNG\" \n               class=\"aligncenter lazyload\" alt=\"\u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902\" width=\"400\" height=\"200\" \/><\/center><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u0924\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0924\u0930\u0940\u0915\u094b\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0938\u0902\u092f\u094b\u091c\u0928\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\binom{n}{k}=\\dfrac{n!}{k!(n-k)!}<\/span><\/span><\/p>\n<p>\u092f\u0939 \u0917\u0923\u0928\u093e \u0939\u092e\u0947\u0902 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span> \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p><strong>(a)<\/strong> \u092f\u0926\u093f 10 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u092e\u0947\u0902 10 \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0935\u093f\u0924\u0930\u093f\u0924 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0907\u0938\u0947 \u0915\u0930\u0928\u0947 \u0915\u093e \u0915\u0947\u0935\u0932 \u090f\u0915 \u0939\u0940 \u0924\u0930\u0940\u0915\u093e \u0939\u0948\u0964 \u0905\u0924\u0903, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega=1<\/span><\/span>:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\Omega = \\binom{10}{10}=\\dfrac{10!}{10!(10-10)!} = \\dfrac{10!}{10!0!} = 1 <\/span><\/span><\/p>\n<p><strong>(b)<\/strong> 10 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u092e\u0947\u0902 5 \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0935\u093f\u0924\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0917\u0923\u0928\u093e \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\Omega &amp;= \\displaystyle\\binom{10}{5} \\\\ \\\\\n\n&amp;=\\dfrac{10!}{5!(10-5)!} = \\dfrac{10!}{5!\\cdot 5!} \\\\ \\\\\n\n&amp;= \\dfrac{5! \\cdot 6\\cdot 7\\cdot 8 \\cdot 9\\cdot 10}{5! \\cdot 2\\cdot 3\\cdot 4\\cdot 5} \\\\ \\\\\n\n&amp;= \\dfrac{ 7\\cdot 8 \\cdot 9\\cdot 10}{ 4\\cdot 5} = 7\\cdot 2 \\cdot 9 \\cdot 2 = 252\n\n\\end{array}<\/span>\n<p>\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, 252 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0935\u093f\u0928\u094d\u092f\u093e\u0938 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u092c\u0921\u093c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902<\/h2>\n<p>\u0905\u092c \u0924\u0915 \u0939\u092e\u0928\u0947 \u091c\u094b \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u093f\u092f\u093e \u0939\u0948, \u0935\u0939 \u0915\u0947\u0935\u0932 \u0936\u0941\u0930\u0941\u0906\u0924 \u0939\u0948\u0964 \u092f\u0926\u093f \u0939\u092e \u0915\u0947\u0938 (b) \u0915\u0940 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b 100 \u092a\u0930\u092e\u093e\u0923\u0941\u0913\u0902 \u0914\u0930 50 \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0924\u0915 \u092c\u0922\u093c\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega \\approx 10^{28}<\/span><\/span> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0917\u093e\u0964 \u0905\u092c \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0947\u0902 \u0915\u093f \u092f\u0926\u093f \u092f\u0939\u0940 \u0917\u0923\u0928\u093e \u090f\u0915 \u092e\u094b\u0932 \u092a\u0930\u092e\u093e\u0923\u0941\u0913\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0915\u0940 \u091c\u093e\u090f, \u0924\u094b \u092a\u0930\u093f\u0923\u093e\u092e \u0905\u0935\u093f\u0936\u094d\u0935\u0938\u0928\u0940\u092f \u0939\u094b\u0917\u093e\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0906\u0930\u094d\u0921\u0930 \u0911\u092b \u092e\u0948\u0917\u094d\u0928\u0940\u091f\u094d\u092f\u0942\u0921 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0947 \u0932\u093f\u090f \u0932\u0949\u0917\u0930\u093f\u0926\u092e \u0914\u0930 \u0938\u094d\u091f\u0930\u094d\u0932\u093f\u0902\u0917 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917<\/h3>\n<p>\u091c\u092c \u0939\u092e <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega = \\binom{n}{k}<\/span> \u091c\u0948\u0938\u0947 \u092e\u093e\u0928 \u0915\u0947 \u092a\u0930\u093f\u092e\u093e\u0923 \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">k=n\/2<\/span> \u0939\u094b, \u091c\u094b \u0905\u0927\u093f\u0915\u0924\u092e \u092e\u093e\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u092e\u093e\u092e\u0932\u093e \u0939\u0948, \u0924\u094b \u0938\u094d\u091f\u0930\u094d\u0932\u093f\u0902\u0917 \u0915\u0947 \u0932\u0949\u0917\u0930\u093f\u0926\u092e\u093f\u0915 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u0907\u0938 \u092a\u0930\u093f\u092e\u093e\u0923 \u0915\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0938\u0902\u092d\u093e\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0917\u0923\u0928\u093e \u0915\u094b \u0932\u0949\u0917\u0930\u093f\u0926\u092e \u0932\u0947\u0924\u0947 \u0939\u0941\u090f \u092a\u0941\u0928\u0903 \u0938\u094d\u0935\u0930\u0942\u092a\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\ln(\\Omega)=\\ln\\left(\\dfrac{n!}{k!(n-k)!}\\right)= \\ln(n!) - \\ln((n-k)!) - \\ln(k!)<\/span><\/span><\/p>\n<p>\u0907\u0938 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u094b \u0938\u094d\u091f\u0930\u094d\u0932\u093f\u0902\u0917 \u0915\u0947 \u0932\u0949\u0917\u0930\u093f\u0926\u094d\u092e\u093f\u0915 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0926\u094b \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u0902\u0938\u094d\u0915\u0930\u0923 \u0939\u0948\u0902: \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u0938\u0930\u0932\u0940\u0915\u0943\u0924:<\/p>\n<ul>\n<li><strong>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0905\u0928\u0941\u092e\u093e\u0928:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(n!) \\approx \\dfrac{1}{2}\\ln(2n\\pi) + n\\ln(n) - n<\/span><\/span> <\/li>\n<li><strong>\u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0905\u0928\u0941\u092e\u093e\u0928:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(n!) \\approx  n\\ln(n) - n<\/span><\/span> <\/li>\n<\/ul>\n<p><a name=\"4\"><\/a><\/p>\n<h4>\u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0935\u093f\u0915\u093e\u0938<\/h4>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/fnt99FeeHPM?si=H6r-5GhO2yqaeaXd\" title=\"YouTube \u0935\u0940\u0921\u093f\u092f\u094b \u092a\u094d\u0932\u0947\u092f\u0930\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\ln(\\Omega) &amp; \\approx n\\ln(n) - n - (n-k)\\ln(n-k) + (n-k) - k\\ln(k) + k \\\\ \\\\\n\n&amp;= n\\ln(n) - (n-k)\\ln(n-k) - k\\ln(k) \\\\ \\\\\n\n&amp;= n\\ln(n) - n\\ln(n-k) + k\\ln(n-k) - k\\ln(k) \\\\ \\\\\n\n&amp;= \\ln\\left[ \\left( \\dfrac{n}{n-k} \\right)^n \\right] + k\\ln\\left( \\dfrac{n-k}{k} \\right) \\\\ \\\\\n\n&amp;= \\ln\\left[ \\dfrac{1}{\\left(1 - \\dfrac{k}{n} \\right)^n} \\right] + k\\ln\\left( \\dfrac{n}{k} - 1 \\right)\n\n\\end{array}<\/span>\n<p>\u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u092c\u0921\u093c\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u0939\u092e \u0928\u093f\u092e\u094d\u0928 \u0938\u0902\u092c\u0902\u0927 \u0932\u093e\u0917\u0942 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{n\\to\\infty} \\left(1-\\dfrac{k}{n} \\right)^n = e^{-k} <\/span><\/span><\/p>\n<p>\u0907\u0938\u0932\u093f\u090f:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(\\Omega) \\approx \\ln(e^k) + k\\ln\\left( \\dfrac{n}{k} -1 \\right) = k + k\\ln\\left( \\dfrac{n}{k} -1 \\right) <\/span><\/span><\/p>\n<p>\u0905\u0902\u0924\u0924\u0903, \u0932\u0949\u0917\u0930\u093f\u0926\u092e \u0915\u0947 \u092c\u0947\u0938 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\log(\\Omega) = \\log(e)\\ln(\\Omega) \\approx k\\log(e)\\left[1 + \\ln\\left( \\dfrac{n}{k} - 1 \\right) \\right] <\/span><\/span><\/p>\n<p>\u091c\u093f\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0905\u0902\u0924\u093f\u092e \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\Omega \\approx 10^{k\\log(e)\\left[1 + \\ln\\left( \\dfrac{n}{k} - 1 \\right) \\right]}}<\/span><\/span><\/p>\n<p>\u0939\u093e\u0932\u093e\u0902\u0915\u093f \u092f\u0939 \u092a\u0930\u093f\u0923\u093e\u092e <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span> \u0915\u093e \u0938\u091f\u0940\u0915 \u092e\u093e\u0928 \u0928\u0939\u0940\u0902 \u0926\u0947\u0924\u093e \u0939\u0948, \u092f\u0939 \u0907\u0938\u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u092c\u0947\u0939\u0924\u0930 \u0905\u0928\u0941\u092e\u093e\u0928 \u0926\u0947\u0924\u093e \u0939\u0948 \u0914\u0930 \u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u092c\u0922\u093c\u0924\u093e \u0939\u0948, \u0907\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0914\u0930 \u092c\u0947\u0939\u0924\u0930 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, \u092f\u0939 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span> \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u092e\u093e\u0928 \u0915\u093e \u0924\u0947\u091c\u0940 \u0938\u0947 \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">k=n\/2<\/span> \u0939\u094b, \u0924\u094b \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Max}\\left(\\Omega\\right) \\approx 10^{\\dfrac{n}{2}\\log(e)\\left[1 + \\ln\\left( \\dfrac{n}{n\/2} - 1 \\right) \\right]} = 10^{ n\\log(e)\/2 } <\/span><\/span><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h4>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0935\u093f\u0915\u093e\u0938<\/h4>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/i3OO4lHV24Q?si=jEPCafXqgVxNYqH-\" title=\"YouTube \u0935\u0940\u0921\u093f\u092f\u094b \u092a\u094d\u0932\u0947\u092f\u0930\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u0939\u093e\u0932\u093e\u0902\u0915\u093f \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0935\u093f\u0915\u093e\u0938 \u0905\u0927\u093f\u0915 \u0938\u091f\u0940\u0915 \u092a\u0930\u093f\u0923\u093e\u092e \u0926\u0947\u0917\u093e, \u092f\u0939 \u0915\u0941\u091b \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u094b \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0947\u0917\u093e\u0964 \u0907\u0928 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u092c\u0921\u093c\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u094b\u0902\u0917\u0947\u0964 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u093e \u0935\u093f\u0915\u093e\u0938 \u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0905\u0928\u0941\u092e\u093e\u0928 \u092e\u0947\u0902 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0915\u0940 \u0917\u0908 \u0915\u0908 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u094b \u092a\u0941\u0928: \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\ln(\\Omega) &amp; = &amp; \\ln\\left(\\dfrac{n!}{k!(n-k)!}\\right)= \\ln(n!) - \\ln((n-k)!) - \\ln(k!) \\\\ \\\\\n\n&amp; \\approx &amp; \\color{red}\\dfrac{1}{2}\\ln(2n\\pi)\\color{black} + n\\ln(n) - n \\\\ \\\\\n\n&amp; &amp; \\color{red}-\\dfrac{1}{2}\\ln(2(n-k)\\pi)\\color{black} - (n-k)\\ln(n-k) + (n-k) \\\\ \\\\\n\n&amp; &amp; \\color{red}-\\dfrac{1}{2}\\ln(2k\\pi)\\color{black} - k\\ln(k) + k\n\n\\end{array}<\/span>\n<p>\u0932\u093e\u0932 \u0930\u0902\u0917 \u092e\u0947\u0902 \u091a\u093f\u0939\u094d\u0928\u093f\u0924 \u092d\u093e\u0917 \u0935\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0924\u0924\u094d\u0935 \u0939\u0948\u0902 \u091c\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0905\u0928\u0941\u092e\u093e\u0928 \u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e \u0905\u0928\u094d\u092f \u0917\u0923\u0928\u093e\u090f\u0902 \u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0902\u0964 \u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\ln(\\Omega) &amp; \\approx &amp; \\color{red}\\dfrac{1}{2}\\ln\\left( \\dfrac{2n\\pi}{2(n-k)\\pi \\cdot 2k\\pi} \\right)\\color{black} + k + k\\ln\\left(\\dfrac{n}{k} - 1\\right) \\\\ \\\\\n\n&amp; = &amp;  k + k\\ln\\left(\\dfrac{n}{k} - 1\\right) - \\dfrac{1}{2}\\ln\\left(\\dfrac{2k\\pi(n-k)}{n}\\right)\n\n\\end{array}<\/span>\n<p>\u0932\u0949\u0917\u0930\u093f\u0926\u092e \u0915\u0947 \u092c\u0947\u0938 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\log(\\Omega) = \\log(e)\\ln(\\Omega) \\approx \\log(e) \\left[ k + k\\ln\\left(\\dfrac{n}{k} - 1\\right) - \\dfrac{1}{2}\\ln\\left(\\dfrac{2k\\pi(n-k)}{n}\\right) \\right] <\/span><\/span><\/p>\n<p>\u0914\u0930 \u0905\u0902\u0924\u0924\u0903, 10 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0918\u093e\u0924\u093e\u0902\u0915 \u0932\u0947\u0924\u0947 \u0939\u0941\u090f:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\Omega \\approx 10^{\\log(e) \\left[ k + k\\ln\\left(\\dfrac{n}{k} - 1\\right) - \\dfrac{1}{2}\\ln\\left(\\dfrac{2k\\pi(n-k)}{n}\\right) \\right]}\n\n<\/span>\n<p>\u0905\u092c, \u091c\u0948\u0938\u0947 \u092a\u0939\u0932\u0947, \u0939\u092e <span class=\"katex-eq\" data-katex-display=\"false\">k=n\/2<\/span> \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0915\u0947 \u0907\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u092e\u093e\u0928 \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0939\u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u0930\u093f\u0923\u093e\u092e \u0926\u0947\u0917\u093e:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\text{Max}(\\Omega) &amp;\\approx &amp; 10^{\\log(e) \\left[ \\dfrac{n}{2} + \\dfrac{n}{2}\\ln\\left(\\dfrac{n}{(n\/2)} - 1\\right) - \\dfrac{1}{2}\\ln\\left(\\dfrac{2(n\/2)\\pi(n-n\/2)}{n}\\right) \\right]} \\\\ \\\\\n\n&amp; = &amp; 10^{\\log(e) \\left[\\dfrac{n}{2} - \\dfrac{1}{2}\\ln\\left(\\dfrac{n\\pi}{2} \\right) \\right]} = 10^{\\log(e)(n-\\ln(n\\pi\/2))\/2}\n\n\\end{array}<\/span>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0914\u0930 \u092a\u0930\u093f\u092e\u093e\u0923 \u0917\u0923\u0928\u093e \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/M7NrtICrSzU?si=6UT34333Wp5YwFU1\" title=\"YouTube \u0935\u0940\u0921\u093f\u092f\u094b \u092a\u094d\u0932\u0947\u092f\u0930\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u0915\u0947\u0938 1: \u092c\u0921\u093c\u0947 \u092b\u0948\u0915\u094d\u091f\u094b\u0930\u093f\u092f\u0932\u094d\u0938<\/h3>\n<p>\u0906\u0907\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(10^{50}\\right)!<\/span><\/span> \u0915\u0947 \u092a\u0930\u093f\u092e\u093e\u0923 \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u090f\u0902, \u092f\u093e\u0928\u0940 \u0907\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0932\u093f\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0905\u0902\u0915\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0964<\/p>\n<h5>\u0938\u092e\u093e\u0927\u093e\u0928<\/h5>\n<p>\u0907\u0938 \u0917\u0923\u0928\u093e \u0915\u094b \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0938\u094d\u091f\u0930\u094d\u0932\u093f\u0902\u0917 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\ln\\left[ \\left(10^{50}\\right)! \\right] &amp;\\approx 10^{50}\\ln\\left(10^{50}\\right) - 10^{50}\\\\ \\\\\n\n&amp;= \\left[\\ln\\left(10^{50}\\right) -1\\right]10^{50}  \\\\ \\\\\n\n&amp;= \\left[50\\ln(10)-1 \\right]10^{50} \\\\ \\\\\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0938\u0915\u0947 \u092c\u093e\u0926, \u0939\u092e \u0932\u0949\u0917\u0930\u093f\u0926\u092e \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\ln\\left[ \\left(10^{50}\\right)! \\right] = \\dfrac{\\log\\left[\\left(10^{50}\\right)!\\right]}{\\log{e}}\n\n<\/span>\n<p>\u0907\u0938\u0932\u093f\u090f:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\log\\left[ \\left(10^{50}\\right)! \\right] \\approx \\log(e)\\left[50\\ln(10)-1 \\right]10^{50}\n\n<\/span>\n<p>\u0905\u0902\u0924\u0924\u0903, 10 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0918\u093e\u0924\u093e\u0902\u0915 \u0932\u0947\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\left(10^{50}\\right)!  \\approx  10^{\\log(e)\\left[50\\ln(10)-1 \\right]10^{50}} = 10^{49,5657 \\cdot 10^{50}}\n\n<\/span>\n<p>\u092f\u0939\u093e\u0902 10 \u0915\u0947 \u090a\u092a\u0930 \u0915\u093e \u0918\u093e\u0924\u093e\u0902\u0915 \u0909\u0938 \u092a\u0930\u093f\u092e\u093e\u0923 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u093e \u0939\u0948, \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">\\left(10^{50}\\right)!<\/span> \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0905\u0902\u0915\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"8\"><\/a><\/p>\n<h3>\u0915\u0947\u0938 2: \u092c\u0921\u093c\u0947 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938<\/h3>\n<p>\u090f\u0915 \u0914\u0938\u0924 \u0918\u0930 \u092e\u0947\u0902 \u0932\u0917\u092d\u0917 12 \u0932\u093e\u0907\u091f \u0938\u094d\u0935\u093f\u091a \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u091a\u093e\u0932\u0942 \u092f\u093e \u092c\u0902\u0926 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0914\u0938\u0924\u0928, \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0918\u0930 \u092e\u0947\u0902 4 \u0932\u094b\u0917 \u0930\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u090f\u0915 \u0936\u0939\u0930 \u092e\u0947\u0902 50 \u0932\u093e\u0916 \u0932\u094b\u0917 \u0939\u0948\u0902, \u0924\u094b \u0936\u0939\u0930 \u0915\u0947 \u0938\u094d\u0935\u093f\u091a\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0906\u0927\u0947 \u0938\u094d\u0935\u093f\u091a\u094b\u0902 \u0915\u0947 \u091a\u093e\u0932\u0942 \u0939\u094b\u0928\u0947 \u0915\u0947 \u0915\u093f\u0924\u0928\u0947 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902?<\/p>\n<h5>\u0938\u092e\u093e\u0927\u093e\u0928<\/h5>\n<p>\u0936\u0939\u0930 \u092e\u0947\u0902 \u0915\u0941\u0932 \u0938\u094d\u0935\u093f\u091a\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\nn &amp;=&amp;\\dfrac{\\text{\u0936\u0939\u0930 \u0915\u0940 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e}}{\\text{\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0918\u0930 \u092e\u0947\u0902 \u0932\u094b\u0917}} \\times \\text{\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0918\u0930 \u092e\u0947\u0902 \u0938\u094d\u0935\u093f\u091a} \\\\ \\\\\n\n&amp;=&amp; \\dfrac{5\\cdot 10^6}{4}\\cdot 12 = 15\\cdot 10^6\n\n\\end{array}\n\n<\/span>\n<p>\u0936\u0939\u0930 \u0915\u0947 \u0938\u094d\u0935\u093f\u091a\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0906\u0927\u0947 \u0915\u0947 \u091a\u093e\u0932\u0942 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u092e\u093e\u0907\u0915\u094d\u0930\u094b\u0938\u094d\u091f\u0947\u091f\u094d\u0938 \u0915\u093e \u092e\u0948\u0915\u094d\u0930\u094b\u0938\u094d\u091f\u0947\u091f \u0909\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u093e \u0939\u0948 \u091c\u094b \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u0938\u0902\u092d\u093e\u0935\u0928\u093e\u0913\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0905\u0927\u093f\u0915\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{max}<\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0905\u0928\u0941\u092e\u093e\u0928 \u0928\u093f\u092e\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u0915\u093f\u090f \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul>\n<ol><strong>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0905\u0928\u0941\u092e\u093e\u0928:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{max} = 10^{\\log(e)\\left[15\\cdot10^6 - \\ln\\left(15\\pi\\cdot10^6 \/ 2 \\right) \\right]\/2} \\approx 10^{6.514.413,542}<\/span><\/span><\/ol>\n<ol><strong>\u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0905\u0928\u0941\u092e\u093e\u0928:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{max} = 10^{\\log(e)\\left[15\\cdot10^6 \\right]\/2} \\approx 10^{6.514.417,229}<\/span><\/span><\/ol>\n<\/ul>\n<p>\u0939\u093e\u0932\u093e\u0902\u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0905\u0928\u0941\u092e\u093e\u0928\u094b\u0902 \u092e\u0947\u0902 \u0932\u0917\u092d\u0917 4 \u092a\u0930\u093f\u092e\u093e\u0923\u094b\u0902 \u0915\u093e \u0905\u0902\u0924\u0930 \u0939\u0948 (\u091c\u094b \u092c\u0939\u0941\u0924 \u0932\u0917 \u0938\u0915\u0924\u093e \u0939\u0948), \u0932\u0947\u0915\u093f\u0928 \u092f\u0939 65 \u0932\u093e\u0916 \u0938\u0947 \u0905\u0927\u093f\u0915 \u092a\u0930\u093f\u092e\u093e\u0923\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u092e\u0939\u0924\u094d\u0935\u0939\u0940\u0928 \u0939\u0948\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902 \u090f\u0915 \u0910\u0938\u0940 \u092d\u094c\u0924\u093f\u0915 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u091c\u093f\u0938\u092e\u0947\u0902 \u0932\u093e\u0916\u094b\u0902 \u0924\u0924\u094d\u0935 \u0939\u094b\u0902, \u0909\u0938\u0947 \u0915\u093f\u0924\u0928\u0947 \u0924\u0930\u0940\u0915\u094b\u0902 \u0938\u0947 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948? \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u093e \u0909\u0924\u094d\u0924\u0930 \u0926\u0947\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0917\u0923\u093f\u0924 \u0915\u0947 \u0909\u092a\u092f\u094b\u0917 \u0915\u094b \u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0926\u0947\u0916\u0947\u0902\u0917\u0947\u0964 \u0907\u0938\u092e\u0947\u0902 \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u0935\u093e\u0902\u091f\u093e \u0915\u0947 \u0935\u093f\u0924\u0930\u0923 \u0938\u0947 \u0932\u0947\u0915\u0930 \u092c\u0921\u093c\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30534,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[927,643],"tags":[],"class_list":["post-31203","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-927","category-643"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e 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property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902\" \/>\n<meta property=\"og:description\" content=\"\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092c\u0921\u093c\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0915\u0949\u092e\u094d\u092c\u093f\u0928\u0947\u091f\u0930\u093f\u0915\u094d\u0938 \u0914\u0930 \u0938\u094d\u091f\u0930\u094d\u0932\u093f\u0902\u0917 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e 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Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/31203","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=31203"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/31203\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/30534"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=31203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=31203"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=31203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}