{"id":3126,"date":"2025-06-06T13:40:37","date_gmt":"2025-06-06T13:40:37","guid":{"rendered":"https:\/\/diznr.com\/?p=3126"},"modified":"2025-06-06T13:40:37","modified_gmt":"2025-06-06T13:40:37","slug":"previous-year-gate-question-papers-in-hindi-gate-2006-set-theory-what-is-cardinality-the","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/previous-year-gate-question-papers-in-hindi-gate-2006-set-theory-what-is-cardinality-the\/","title":{"rendered":"Previous year gate question papers in Hindi &#8211; GATE 2025 Set Theory What is the cardinality"},"content":{"rendered":"<p>Previous year gate question papers in Hindi &#8211; GATE 2025 Set Theory What is the cardinality<\/p>\n<p>[fvplayer id=&#8221;265&#8243;]<\/p>\n<p data-start=\"0\" data-end=\"156\">\u0906\u092a\u0928\u0947 GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0914\u0930 \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u092e\u093e\u0902\u0917\u0940 \u0939\u0948\u0964 \u0906\u0907\u090f \u0907\u0928 \u0926\u094b\u0928\u094b\u0902 \u0935\u093f\u0937\u092f\u094b\u0902 \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p data-start=\"158\" data-end=\"217\"><strong data-start=\"158\" data-end=\"217\">1. GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902:<\/strong><\/p>\n<p data-start=\"219\" data-end=\"682\">GATE (\u0917\u094d\u0930\u0947\u091c\u0941\u090f\u091f \u090f\u092a\u094d\u091f\u0940\u091f\u094d\u092f\u0942\u0921 \u091f\u0947\u0938\u094d\u091f \u0907\u0928 \u0907\u0902\u091c\u0940\u0928\u093f\u092f\u0930\u093f\u0902\u0917) \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u093e \u091a\u0941\u0928\u094c\u0924\u0940\u092a\u0942\u0930\u094d\u0923 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0905\u0927\u093f\u0915\u093e\u0902\u0936 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0905\u0902\u0917\u094d\u0930\u0947\u091c\u0940 \u092e\u0947\u0902 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u0915\u0941\u091b \u0911\u0928\u0932\u093e\u0907\u0928 \u092a\u094d\u0932\u0947\u091f\u092b\u093c\u0949\u0930\u094d\u092e \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0938\u0948\u0902\u092a\u0932 \u092a\u0947\u092a\u0930 \u0914\u0930 \u092e\u0949\u0921\u0932 \u092a\u0947\u092a\u0930 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0906\u092a\u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0915 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, Aglasem \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0938\u0948\u0902\u092a\u0932 \u092a\u0947\u092a\u0930\u094d\u0938 \u0909\u092a\u0932\u092c\u094d\u0927 \u0915\u0930\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0906\u092a \u0905\u092a\u0928\u0940 \u0938\u0941\u0935\u093f\u0927\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p data-start=\"684\" data-end=\"719\"><strong data-start=\"684\" data-end=\"719\">2. \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940:<\/strong><\/p>\n<p data-start=\"721\" data-end=\"921\">\u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 \u092e\u0947\u0902, <strong data-start=\"737\" data-end=\"753\">\u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940<\/strong> \u0915\u093f\u0938\u0940 \u0938\u0947\u091f \u092e\u0947\u0902 \u092e\u094c\u091c\u093c\u0942\u0926 \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0938\u0947\u091f A = {2, 4, 6, 8} \u0939\u0948, \u0924\u094b \u0907\u0938 \u0938\u0947\u091f \u0915\u0940 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940 4 \u0939\u094b\u0917\u0940, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0907\u0938\u092e\u0947\u0902 \u091a\u093e\u0930 \u0924\u0924\u094d\u0935 \u0939\u0948\u0902\u0964<\/p>\n<p data-start=\"923\" data-end=\"970\"><strong data-start=\"923\" data-end=\"934\">\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong> \u092f\u0926\u093f \u0938\u0947\u091f B = {a, e, i, o, u} \u0939\u0948, \u0924\u094b:<\/p>\n<ul data-start=\"972\" data-end=\"999\">\n<li data-start=\"972\" data-end=\"999\">\u0938\u0947\u091f B \u0915\u0940 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940 = 5<\/li>\n<\/ul>\n<p data-start=\"1001\" data-end=\"1108\">\u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940 \u0915\u0940 \u0938\u092e\u091d GATE \u091c\u0948\u0938\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u093e\u0913\u0902 \u092e\u0947\u0902 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0907\u0938\u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928 \u0905\u0915\u094d\u0938\u0930 \u092a\u0942\u091b\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p data-start=\"1110\" data-end=\"1343\"><strong data-start=\"1110\" data-end=\"1118\">\u0928\u094b\u091f:<\/strong> GATE 2025 \u0915\u0940 \u0906\u0927\u093f\u0915\u093e\u0930\u093f\u0915 \u0935\u0947\u092c\u0938\u093e\u0907\u091f \u092a\u0930 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u092a\u0948\u091f\u0930\u094d\u0928 \u0914\u0930 \u0905\u0928\u094d\u092f \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0964 \u0905\u0927\u093f\u0915 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u0947 \u0932\u093f\u090f \u0906\u092a GATE 2025 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u092a\u0948\u091f\u0930\u094d\u0928 \u092a\u0943\u0937\u094d\u0920 \u092a\u0930 \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p data-start=\"1345\" data-end=\"1490\">\u0905\u092a\u0928\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0947 \u0926\u094c\u0930\u093e\u0928, \u0906\u0927\u093f\u0915\u093e\u0930\u093f\u0915 \u0938\u094d\u0930\u094b\u0924\u094b\u0902 \u0914\u0930 \u0935\u093f\u0936\u094d\u0935\u0938\u0928\u0940\u092f \u0905\u0927\u094d\u092f\u092f\u0928 \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0947\u0902, \u0924\u093e\u0915\u093f \u0906\u092a \u0938\u091f\u0940\u0915 \u0914\u0930 \u0905\u0926\u094d\u092f\u0924\u093f\u0924 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0947\u0902\u0964<\/p>\n<h3 data-start=\"1345\" data-end=\"1490\"><a href=\"https:\/\/mrce.in\/ebooks\/Maths-Discrete%20Mathematics%20&amp;%20its%20Applications%208th%20Ed.pdf\" target=\"_blank\" rel=\"noopener\">Previous year gate question papers in Hindi &#8211; GATE 2025 Set Theory What is the cardinality<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics for Computer Science<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.gbpuat.ac.in\/entrance_exam\/2023\/01.03.2023_Prospectus-2023.pdf\" target=\"_blank\" rel=\"noopener\">PROSPECTUS<\/a><\/h3>\n<p data-start=\"0\" data-end=\"276\">\u0906\u092a\u0928\u0947 \u092a\u0942\u091b\u093e \u0939\u0948: <strong data-start=\"14\" data-end=\"108\">&#8220;\u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 GATE \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 &#8211; GATE 2025 \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940: \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0948\u0932\u093f\u091f\u0940 \u0915\u094d\u092f\u093e \u0939\u0948?&#8221;<\/strong><br data-start=\"108\" data-end=\"111\" \/>\u092f\u0939\u093e\u0901 \u0939\u092e <strong data-start=\"119\" data-end=\"133\">\u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940<\/strong> \u0915\u0947 <strong data-start=\"137\" data-end=\"153\">\u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0948\u0932\u093f\u091f\u0940<\/strong> \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 GATE \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0939\u0932\u094b\u0902 \u0915\u094b \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902, \u091c\u094b \u0906\u092a\u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0915 \u0939\u094b\u0902\u0917\u0947\u0964<\/p>\n<hr data-start=\"278\" data-end=\"281\" \/>\n<h2 data-start=\"283\" data-end=\"343\">\ud83d\udcd8 <strong data-start=\"289\" data-end=\"343\">\u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0948\u0932\u093f\u091f\u0940 (Cardinality) \u0915\u094d\u092f\u093e \u0939\u0948?<\/strong><\/h2>\n<p data-start=\"345\" data-end=\"489\"><strong data-start=\"345\" data-end=\"357\">\u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/strong><br data-start=\"357\" data-end=\"360\" \/>\u0915\u093f\u0938\u0940 \u0938\u0947\u091f \u092e\u0947\u0902 \u0909\u092a\u0938\u094d\u0925\u093f\u0924 \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u0940 \u0915\u0941\u0932 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0909\u0938 \u0938\u0947\u091f \u0915\u0940 <strong data-start=\"415\" data-end=\"431\">\u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0948\u0932\u093f\u091f\u0940<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0947 <span class=\"katex\"><span class=\"katex-mathml\">\u2223A\u2223|A|<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span> \u092f\u093e <span class=\"katex\"><span class=\"katex-mathml\">n(A)n(A)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p data-start=\"491\" data-end=\"548\"><strong data-start=\"491\" data-end=\"502\">\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><br data-start=\"502\" data-end=\"505\" \/>\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">A={1,3,5}A = \\{1, 3, 5\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">3<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">5<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span>, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">\u2223A\u2223=3|A| = 3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/p>\n<hr data-start=\"550\" data-end=\"553\" \/>\n<h2 data-start=\"555\" data-end=\"608\">\ud83d\udcdd <strong data-start=\"561\" data-end=\"608\">GATE \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 (\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902):<\/strong><\/h2>\n<h3 data-start=\"610\" data-end=\"629\"><strong data-start=\"614\" data-end=\"627\">\u092a\u094d\u0930\u0936\u094d\u0928 1:<\/strong><\/h3>\n<p data-start=\"630\" data-end=\"709\">\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">A={1,3,5}A = \\{1, 3, 5\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">3<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">5<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span> \u0939\u0948, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">AA<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span> \u0915\u0947 \u092a\u093e\u0935\u0930 \u0938\u0947\u091f \u0915\u0940 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0948\u0932\u093f\u091f\u0940 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940?<\/p>\n<p data-start=\"711\" data-end=\"728\"><strong data-start=\"711\" data-end=\"728\">\u0909\u0924\u094d\u0924\u0930 \u0935\u093f\u0915\u0932\u094d\u092a:<\/strong><\/p>\n<ol data-start=\"729\" data-end=\"756\">\n<li data-start=\"729\" data-end=\"735\">\n<p data-start=\"732\" data-end=\"735\">4<\/p>\n<\/li>\n<li data-start=\"736\" data-end=\"742\">\n<p data-start=\"739\" data-end=\"742\">6<\/p>\n<\/li>\n<li data-start=\"743\" data-end=\"749\">\n<p data-start=\"746\" data-end=\"749\">9<\/p>\n<\/li>\n<li data-start=\"750\" data-end=\"756\">\n<p data-start=\"753\" data-end=\"756\">8 \u2705<\/p>\n<\/li>\n<\/ol>\n<p data-start=\"758\" data-end=\"1025\"><strong data-start=\"758\" data-end=\"765\">\u0939\u0932:<\/strong><br data-start=\"765\" data-end=\"768\" \/>\u092a\u093e\u0935\u0930 \u0938\u0947\u091f \u0915\u0940 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0948\u0932\u093f\u091f\u0940 = <span class=\"katex\"><span class=\"katex-mathml\">2n2^n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, \u091c\u0939\u093e\u0901 <span class=\"katex\"><span class=\"katex-mathml\">nn<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span> = \u0938\u0947\u091f \u092e\u0947\u0902 \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e<br data-start=\"845\" data-end=\"848\" \/>\u092f\u0939\u093e\u0901 <span class=\"katex\"><span class=\"katex-mathml\">n=3n = 3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span>, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">23=82^3 = 8<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><\/span><\/span><br data-start=\"882\" data-end=\"885\" \/><strong data-start=\"885\" data-end=\"901\">\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: 8<\/strong><br data-start=\"901\" data-end=\"904\" \/><a class=\"cursor-pointer\" target=\"_new\" rel=\"noopener\" data-start=\"904\" data-end=\"1025\">\u0938\u094d\u0930\u094b\u0924: Testbook<\/a><\/p>\n<hr data-start=\"1027\" data-end=\"1030\" \/>\n<h3 data-start=\"1032\" data-end=\"1051\"><strong data-start=\"1036\" data-end=\"1049\">\u092a\u094d\u0930\u0936\u094d\u0928 2:<\/strong><\/h3>\n<p data-start=\"1052\" data-end=\"1202\">\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">UU<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><\/span><\/span><\/span> \u090f\u0915 \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 100 \u0924\u0924\u094d\u0935 \u0939\u0948\u0902, <span class=\"katex\"><span class=\"katex-mathml\">n(A)=50n(A) = 50<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">50<\/span><\/span><\/span><\/span>, <span class=\"katex\"><span class=\"katex-mathml\">n(B)=60n(B) = 60<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">60<\/span><\/span><\/span><\/span>, \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">n(A\u2229B)=20n(A \\cap B) = 20<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><\/span><\/span><\/span> \u0939\u0948, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">n(A\u2032\u2229B\u2032)n(A&#8217; \\cap B&#8217;)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e?<\/p>\n<p data-start=\"1204\" data-end=\"1221\"><strong data-start=\"1204\" data-end=\"1221\">\u0909\u0924\u094d\u0924\u0930 \u0935\u093f\u0915\u0932\u094d\u092a:<\/strong><\/p>\n<ol data-start=\"1222\" data-end=\"1253\">\n<li data-start=\"1222\" data-end=\"1229\">\n<p data-start=\"1225\" data-end=\"1229\">40<\/p>\n<\/li>\n<li data-start=\"1230\" data-end=\"1237\">\n<p data-start=\"1233\" data-end=\"1237\">20<\/p>\n<\/li>\n<li data-start=\"1238\" data-end=\"1245\">\n<p data-start=\"1241\" data-end=\"1245\">90<\/p>\n<\/li>\n<li data-start=\"1246\" data-end=\"1253\">\n<p data-start=\"1249\" data-end=\"1253\">10 \u2705<\/p>\n<\/li>\n<\/ol>\n<p data-start=\"1255\" data-end=\"1533\"><strong data-start=\"1255\" data-end=\"1262\">\u0939\u0932:<\/strong><br data-start=\"1262\" data-end=\"1265\" \/><span class=\"katex\"><span class=\"katex-mathml\">n(A\u222aB)=n(A)+n(B)\u2212n(A\u2229B)=50+60\u221220=90n(A \\cup B) = n(A) + n(B) &#8211; n(A \\cap B) = 50 + 60 &#8211; 20 = 90<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">50<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">60<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">90<\/span><\/span><\/span><\/span><br data-start=\"1330\" data-end=\"1333\" \/><span class=\"katex\"><span class=\"katex-mathml\">n(A\u2032\u2229B\u2032)=n(U)\u2212n(A\u222aB)=100\u221290=10n(A&#8217; \\cap B&#8217;) = n(U) &#8211; n(A \\cup B) = 100 &#8211; 90 = 10<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">U<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">100<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">90<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><\/span><\/span><br data-start=\"1389\" data-end=\"1392\" \/><strong data-start=\"1392\" data-end=\"1409\">\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: 10<\/strong><br data-start=\"1409\" data-end=\"1412\" \/><a class=\"cursor-pointer\" target=\"_new\" rel=\"noopener\" data-start=\"1412\" data-end=\"1533\">\u0938\u094d\u0930\u094b\u0924: Testbook<\/a><\/p>\n<hr data-start=\"1535\" data-end=\"1538\" \/>\n<h3 data-start=\"1540\" data-end=\"1559\"><strong data-start=\"1544\" data-end=\"1557\">\u092a\u094d\u0930\u0936\u094d\u0928 3:<\/strong><\/h3>\n<p data-start=\"1560\" data-end=\"1675\">\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">A={1,2,5,7}A = \\{1, 2, 5, 7\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">5<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">7<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">B={2,4,6}B = \\{2, 4, 6\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">4<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">6<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span> \u0939\u0948\u0902, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">A\u222aBA \\cup B<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span> \u0915\u0947 \u092a\u094d\u0930\u0949\u092a\u0930 \u0938\u092c\u0938\u0947\u091f\u094d\u0938 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940?<\/p>\n<p data-start=\"1677\" data-end=\"1694\"><strong data-start=\"1677\" data-end=\"1694\">\u0909\u0924\u094d\u0924\u0930 \u0935\u093f\u0915\u0932\u094d\u092a:<\/strong><\/p>\n<ol data-start=\"1695\" data-end=\"1727\">\n<li data-start=\"1695\" data-end=\"1703\">\n<p data-start=\"1698\" data-end=\"1703\">127<\/p>\n<\/li>\n<li data-start=\"1704\" data-end=\"1711\">\n<p data-start=\"1707\" data-end=\"1711\">64<\/p>\n<\/li>\n<li data-start=\"1712\" data-end=\"1721\">\n<p data-start=\"1715\" data-end=\"1721\">63 \u2705<\/p>\n<\/li>\n<li data-start=\"1722\" data-end=\"1727\">\n<p data-start=\"1725\" data-end=\"1727\">31<\/p>\n<\/li>\n<\/ol>\n<p data-start=\"1729\" data-end=\"1991\"><strong data-start=\"1729\" data-end=\"1736\">\u0939\u0932:<\/strong><br data-start=\"1736\" data-end=\"1739\" \/><span class=\"katex\"><span class=\"katex-mathml\">A\u222aB={1,2,4,5,6,7}A \\cup B = \\{1, 2, 4, 5, 6, 7\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">4<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">5<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">6<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">7<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><br data-start=\"1776\" data-end=\"1779\" \/>\u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e = 6<br data-start=\"1799\" data-end=\"1802\" \/>\u092a\u094d\u0930\u0949\u092a\u0930 \u0938\u092c\u0938\u0947\u091f\u094d\u0938 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e = <span class=\"katex\"><span class=\"katex-mathml\">26\u22121=632^6 &#8211; 1 = 63<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">63<\/span><\/span><\/span><\/span><br data-start=\"1847\" data-end=\"1850\" \/><strong data-start=\"1850\" data-end=\"1867\">\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: 63<\/strong><br data-start=\"1867\" data-end=\"1870\" \/><a class=\"cursor-pointer\" target=\"_new\" rel=\"noopener\" data-start=\"1870\" data-end=\"1991\">\u0938\u094d\u0930\u094b\u0924: Testbook<\/a><\/p>\n<hr data-start=\"1993\" data-end=\"1996\" \/>\n<h2 data-start=\"1998\" data-end=\"2034\">\ud83c\udfa5 <strong data-start=\"2004\" data-end=\"2034\">\u0935\u0940\u0921\u093f\u092f\u094b \u0938\u0902\u0938\u093e\u0927\u0928 (\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902):<\/strong><\/h2>\n<ul data-start=\"2036\" data-end=\"2228\">\n<li data-start=\"2036\" data-end=\"2125\">\n<p data-start=\"2038\" data-end=\"2125\">\u0938\u0947\u091f \u0915\u0940 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0948\u0932\u093f\u091f\u0940 \u0915\u094d\u092f\u093e \u0939\u0948? (\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902)<\/p>\n<\/li>\n<li data-start=\"2126\" data-end=\"2228\">\n<p data-start=\"2128\" data-end=\"2228\">\u092a\u093e\u0935\u0930 \u0938\u0947\u091f \u0914\u0930 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0948\u0932\u093f\u091f\u0940 \u092a\u0930 \u0905\u092d\u094d\u092f\u093e\u0938 \u092a\u094d\u0930\u0936\u094d\u0928 (\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902)<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"2230\" data-end=\"2233\" \/>\n<h2 data-start=\"2235\" data-end=\"2257\">\ud83d\udcda <strong data-start=\"2241\" data-end=\"2257\">\u0905\u0927\u093f\u0915 \u0938\u0902\u0938\u093e\u0927\u0928:<\/strong><\/h2>\n<ul data-start=\"2259\" data-end=\"2501\">\n<li data-start=\"2259\" data-end=\"2399\">\n<p data-start=\"2261\" data-end=\"2399\"><a class=\"cursor-pointer\" target=\"_new\" rel=\"noopener\" data-start=\"2261\" data-end=\"2399\">Testbook \u092a\u0930 \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 MCQs (\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902)<\/a><\/p>\n<\/li>\n<li data-start=\"2400\" data-end=\"2501\">\n<p data-start=\"2402\" data-end=\"2501\"><a class=\"cursor-pointer\" target=\"_new\" rel=\"noopener\" data-start=\"2402\" data-end=\"2501\">GATE 2022 \u0915\u0947 \u092a\u0941\u0930\u093e\u0928\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 (IIT \u0916\u0921\u093c\u0917\u092a\u0941\u0930)<\/a><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"2503\" data-end=\"2506\" \/>\n<p data-start=\"2508\" data-end=\"2608\">\u092f\u0926\u093f \u0906\u092a \u0907\u0928 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e <strong data-start=\"2530\" data-end=\"2537\">PDF<\/strong> \u092f\u093e <strong data-start=\"2541\" data-end=\"2555\">\u0905\u092d\u094d\u092f\u093e\u0938 \u0938\u0947\u091f<\/strong> \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0943\u092a\u092f\u093e \u092c\u0924\u093e\u090f\u0902\u0964 \u092e\u0948\u0902 \u0906\u092a\u0915\u094b \u0924\u0941\u0930\u0902\u0924 \u092d\u0947\u091c \u0926\u0942\u0902\u0917\u093e!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Previous year gate question papers in Hindi &#8211; GATE 2025 Set Theory What is the cardinality [fvplayer id=&#8221;265&#8243;] \u0906\u092a\u0928\u0947 GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0914\u0930 \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u092e\u093e\u0902\u0917\u0940 \u0939\u0948\u0964 \u0906\u0907\u090f \u0907\u0928 \u0926\u094b\u0928\u094b\u0902 \u0935\u093f\u0937\u092f\u094b\u0902 \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902: 1. GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937 \u0915\u0947 [&hellip;]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[76],"tags":[],"class_list":["post-3126","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3126","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=3126"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3126\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}