{"id":3085,"date":"2025-06-06T09:55:56","date_gmt":"2025-06-06T09:55:56","guid":{"rendered":"https:\/\/diznr.com\/?p=3085"},"modified":"2025-06-06T09:55:56","modified_gmt":"2025-06-06T09:55:56","slug":"previous-year-gate-question-in-hindi-gate-2015-discrete-math-let-r-be-a-relation-on-set-the","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/previous-year-gate-question-in-hindi-gate-2015-discrete-math-let-r-be-a-relation-on-set-the\/","title":{"rendered":"Previous year gate question in Hindi- Gate 2025 Discrete math Let R be a relation on the set."},"content":{"rendered":"<p>Previous year gate question in Hindi- Gate 2025 Discrete math Let R be a relation on the set.<\/p>\n<p>[fvplayer id=&#8221;245&#8243;]<\/p>\n<p data-start=\"0\" data-end=\"258\">GATE 2025 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930\u094b\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u093e \u0914\u0930 \u0909\u0928\u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u093e \u0906\u092a\u0915\u0940 \u0938\u092b\u0932\u0924\u093e \u0915\u0940 \u0915\u0941\u0902\u091c\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0917\u093e\u0907\u0921 \u092e\u0947\u0902 \u0926\u093f\u090f \u0917\u090f \u0938\u0941\u091d\u093e\u0935\u094b\u0902 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0915\u0947 \u0906\u092a \u0905\u092a\u0928\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u094b \u092c\u0947\u0939\u0924\u0930 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0928\u093f\u092f\u092e\u093f\u0924 \u0905\u092d\u094d\u092f\u093e\u0938 \u0914\u0930 \u0938\u0939\u0940 \u0930\u0923\u0928\u0940\u0924\u093f \u0915\u0947 \u0938\u093e\u0925 GATE \u092e\u0947\u0902 \u0938\u092b\u0932\u0924\u093e \u0938\u0902\u092d\u0935 \u0939\u0948\u0964<\/p>\n<p data-start=\"260\" data-end=\"593\">GATE 2025 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0947 \u0932\u093f\u090f \u0930\u0923\u0928\u0940\u0924\u093f\u0915 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923, \u0938\u092e\u0930\u094d\u092a\u0923 \u0914\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u090a\u092a\u0930 \u092c\u0924\u093e\u090f \u0917\u090f \u0924\u0948\u092f\u093e\u0930\u0940 \u0938\u0941\u091d\u093e\u0935\u094b\u0902 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0915\u0947, \u0909\u092e\u094d\u092e\u0940\u0926\u0935\u093e\u0930 \u0905\u092a\u0928\u0940 \u0938\u092b\u0932\u0924\u093e \u0915\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e\u0913\u0902 \u0915\u094b \u092c\u0922\u093c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0930\u0916\u0928\u093e, \u0928\u093f\u092f\u092e\u093f\u0924 \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u0928\u093e \u0914\u0930 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0940 \u092a\u0942\u0930\u0940 \u092f\u093e\u0924\u094d\u0930\u093e \u0915\u0947 \u0926\u094c\u0930\u093e\u0928 \u0916\u0941\u0926 \u0915\u094b \u092a\u094d\u0930\u0947\u0930\u093f\u0924 \u0930\u0916\u0928\u093e \u092f\u093e\u0926 \u0930\u0916\u0947\u0902\u0964<\/p>\n<p data-start=\"595\" data-end=\"852\">\u0906\u092a\u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u094b \u0914\u0930 \u092e\u091c\u092c\u0942\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930\u094b\u0902 \u0915\u093e \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u0928\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u092f\u0939 \u0906\u092a\u0915\u094b \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0948\u091f\u0930\u094d\u0928, \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930 \u0914\u0930 \u0915\u0920\u093f\u0928\u093e\u0908 \u0938\u094d\u0924\u0930 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0947\u0917\u093e\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u092e\u0949\u0915 \u091f\u0947\u0938\u094d\u091f \u0932\u0947\u0928\u093e \u0914\u0930 \u0905\u092a\u0928\u0940 \u0915\u092e\u091c\u094b\u0930\u093f\u092f\u094b\u0902 \u092a\u0930 \u0915\u093e\u092e \u0915\u0930\u0928\u093e \u092d\u0940 \u0938\u092b\u0932\u0924\u093e \u0915\u0940 \u0915\u0941\u0902\u091c\u0940 \u0939\u0948\u0964<\/p>\n<p data-start=\"854\" data-end=\"1082\">\u092f\u0926\u093f \u0906\u092a GATE 2025 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u0938\u094d\u0925\u093f\u0924 \u0939\u094b\u0928\u0947 \u0915\u0940 \u092f\u094b\u091c\u0928\u093e \u092c\u0928\u093e \u0930\u0939\u0947 \u0939\u0948\u0902, \u0924\u094b \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f \u0906\u092a \u0906\u0927\u093f\u0915\u093e\u0930\u093f\u0915 \u0905\u0927\u093f\u0938\u0942\u091a\u0928\u093e\u0913\u0902 \u0914\u0930 \u0905\u092a\u0921\u0947\u091f\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u0905\u092a\u0921\u0947\u091f\u0947\u0921 \u0930\u0939\u0947\u0902\u0964 \u092f\u0939 \u0906\u092a\u0915\u094b \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0924\u093e\u0930\u0940\u0916, \u0906\u0935\u0947\u0926\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0914\u0930 \u0905\u0928\u094d\u092f \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0935\u0930\u0923\u094b\u0902 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u0942\u091a\u093f\u0924 \u0930\u0916\u0947\u0917\u093e\u0964<\/p>\n<p data-start=\"1084\" data-end=\"1265\">\u0905\u0902\u0924 \u092e\u0947\u0902, \u0905\u092a\u0928\u0940 \u0938\u0947\u0939\u0924 \u0915\u093e \u0916\u094d\u092f\u093e\u0932 \u0930\u0916\u0947\u0902 \u0914\u0930 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f \u0906\u092a \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0928\u0940\u0902\u0926 \u0932\u0947\u0902, \u092a\u094c\u0937\u094d\u091f\u093f\u0915 \u092d\u094b\u091c\u0928 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0928\u093f\u092f\u092e\u093f\u0924 \u0935\u094d\u092f\u093e\u092f\u093e\u092e \u0915\u0930\u0947\u0902\u0964 \u0938\u094d\u0935\u0938\u094d\u0925 \u0936\u0930\u0940\u0930 \u0914\u0930 \u092e\u0928 \u0938\u0947 \u0906\u092a \u0905\u092a\u0928\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u094b \u0914\u0930 \u092a\u094d\u0930\u092d\u093e\u0935\u0940 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<h3 data-start=\"1084\" data-end=\"1265\"><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Previous year gate question in Hindi- Gate 2025 Discrete math Let R be a relation on the set.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/mrce.in\/ebooks\/Maths-Discrete%20Mathematics%20&amp;%20its%20Applications%208th%20Ed.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics and Its Applications, Eighth Edition<\/a><\/h3>\n<p data-start=\"0\" data-end=\"165\">\u092f\u0939\u093e\u0901 \u090f\u0915 GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u092a\u0942\u091b\u0947 \u0917\u090f \u090f\u0915 \u092a\u0942\u0930\u094d\u0935 \u0935\u0930\u094d\u0937 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u0915\u093e \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u0935\u093e\u0926 \u0914\u0930 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0939\u0948, \u091c\u094b <strong data-start=\"105\" data-end=\"123\">\u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u0917\u0923\u093f\u0924<\/strong> \u0915\u0947 <strong data-start=\"127\" data-end=\"145\">\u0930\u093f\u0932\u0947\u0936\u0928 (\u0938\u0902\u092c\u0902\u0927)<\/strong> \u0935\u093f\u0937\u092f \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948:<\/p>\n<hr data-start=\"167\" data-end=\"170\" \/>\n<h3 data-start=\"172\" data-end=\"202\">\ud83e\udde0 \u092a\u094d\u0930\u0936\u094d\u0928 (GATE CSE 2025):<\/h3>\n<p data-start=\"204\" data-end=\"314\"><strong data-start=\"204\" data-end=\"215\">\u092a\u094d\u0930\u0936\u094d\u0928:<\/strong><br data-start=\"215\" data-end=\"218\" \/>\u090f\u0915 \u0938\u0902\u092c\u0902\u0927 <span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0915\u094b \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u0915\u094d\u0930\u092e\u092c\u0926\u094d\u0927 \u092f\u0941\u0917\u094d\u092e\u094b\u0902 \u092a\u0930 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(x,y)\u2009R\u2009(u,v)\u2005\u200a\u27fa\u2005\u200ax&lt;u\u00a0\u0914\u0930\u00a0y&gt;v(x, y) \\, R \\, (u, v) \\iff x &lt; u \\text{ \u0914\u0930 } y &gt; v<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">v<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u27fa<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0<\/span><span class=\"mord brahmic_fallback\">\u0914\u0930<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">v<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"374\" data-end=\"430\">\u0924\u092c <span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u0947\u0902 \u0938\u0947 \u0915\u094c\u0928 \u0938\u093e \u0938\u0924\u094d\u092f \u0939\u0948?<\/p>\n<p data-start=\"432\" data-end=\"443\"><strong data-start=\"432\" data-end=\"443\">\u0935\u093f\u0915\u0932\u094d\u092a:<\/strong><\/p>\n<ol data-start=\"444\" data-end=\"638\">\n<li data-start=\"444\" data-end=\"518\">\n<p data-start=\"447\" data-end=\"518\">\u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e (Partial Order) \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u092a\u0942\u0930\u094d\u0923 \u0915\u094d\u0930\u092e (Total Order) \u0928\u0939\u0940\u0902 \u0939\u0948<\/p>\n<\/li>\n<li data-start=\"519\" data-end=\"568\">\n<p data-start=\"522\" data-end=\"568\">\u090f\u0915 \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u0902\u092c\u0902\u0927 (Equivalence Relation) \u0939\u0948<\/p>\n<\/li>\n<li data-start=\"569\" data-end=\"616\">\n<p data-start=\"572\" data-end=\"616\">\u0928 \u0924\u094b \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e \u0939\u0948 \u0914\u0930 \u0928 \u0939\u0940 \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u0902\u092c\u0902\u0927<\/p>\n<\/li>\n<li data-start=\"617\" data-end=\"638\">\n<p data-start=\"620\" data-end=\"638\">\u090f\u0915 \u092a\u0942\u0930\u094d\u0923 \u0915\u094d\u0930\u092e \u0939\u0948<\/p>\n<\/li>\n<\/ol>\n<hr data-start=\"640\" data-end=\"643\" \/>\n<h3 data-start=\"645\" data-end=\"660\">\u2705 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923:<\/h3>\n<p data-start=\"662\" data-end=\"689\"><strong data-start=\"662\" data-end=\"687\">1. \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(x,y)\u2009R\u2009(u,v)\u2005\u200a\u27fa\u2005\u200ax&lt;u\u00a0\u0914\u0930\u00a0y&gt;v(x, y) \\, R \\, (u, v) \\iff x &lt; u \\text{ \u0914\u0930 } y &gt; v<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">v<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u27fa<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0<\/span><span class=\"mord brahmic_fallback\">\u0914\u0930<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">v<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"748\" data-end=\"769\"><strong data-start=\"748\" data-end=\"769\">2. \u0917\u0941\u0923\u094b\u0902 \u0915\u0940 \u091c\u093e\u0901\u091a:<\/strong><\/p>\n<ul data-start=\"771\" data-end=\"1431\">\n<li data-start=\"771\" data-end=\"983\">\n<p data-start=\"773\" data-end=\"983\"><strong data-start=\"773\" data-end=\"801\">\u092a\u094d\u0930\u0924\u093f\u092b\u0932\u0924\u093e (Reflexivity):<\/strong><br data-start=\"801\" data-end=\"804\" \/>\u0915\u093f\u0938\u0940 \u092d\u0940 <span class=\"katex\"><span class=\"katex-mathml\">(x,y)(x, y)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u0915\u094d\u092f\u093e <span class=\"katex\"><span class=\"katex-mathml\">x&lt;xx &lt; x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">y&gt;yy &gt; y<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span> \u0938\u0924\u094d\u092f \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948?<br data-start=\"883\" data-end=\"886\" \/>\u0928\u0939\u0940\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span class=\"katex\"><span class=\"katex-mathml\">x&lt;xx &lt; x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">y&gt;yy &gt; y<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span> \u0915\u092d\u0940 \u092d\u0940 \u0938\u0924\u094d\u092f \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u0947\u0964<br data-start=\"954\" data-end=\"957\" \/>\u27a4 <strong data-start=\"961\" data-end=\"983\">R \u092a\u094d\u0930\u0924\u093f\u092b\u0932 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/strong><\/p>\n<\/li>\n<li data-start=\"985\" data-end=\"1223\">\n<p data-start=\"987\" data-end=\"1223\"><strong data-start=\"987\" data-end=\"1010\">\u0938\u092e\u092e\u093f\u0924\u0924\u093e (Symmetry):<\/strong><br data-start=\"1010\" data-end=\"1013\" \/>\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">(x,y)\u2009R\u2009(u,v)(x, y) \\, R \\, (u, v)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">v<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u0939\u0948, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">x&lt;ux &lt; u<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">y&gt;vy &gt; v<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">v<\/span><\/span><\/span><\/span> \u0939\u094b\u0917\u093e\u0964<br data-start=\"1086\" data-end=\"1089\" \/>\u0932\u0947\u0915\u093f\u0928 <span class=\"katex\"><span class=\"katex-mathml\">(u,v)\u2009R\u2009(x,y)(u, v) \\, R \\, (x, y)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">v<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u0915\u0947 \u0932\u093f\u090f <span class=\"katex\"><span class=\"katex-mathml\">u&lt;xu &lt; x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">v&gt;yv &gt; y<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">v<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span> \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f, \u091c\u094b \u092a\u0939\u0932\u0947 \u0915\u0925\u0928 \u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924 \u0939\u0948\u0964<br data-start=\"1196\" data-end=\"1199\" \/>\u27a4 <strong data-start=\"1203\" data-end=\"1223\">R \u0938\u092e\u092e\u093f\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/strong><\/p>\n<\/li>\n<li data-start=\"1225\" data-end=\"1431\">\n<p data-start=\"1227\" data-end=\"1431\"><strong data-start=\"1227\" data-end=\"1256\">\u092a\u093e\u0930\u0917\u092e\u094d\u092f\u0924\u093e (Transitivity):<\/strong><br data-start=\"1256\" data-end=\"1259\" \/>\u092e\u093e\u0928 \u0932\u0947\u0902 <span class=\"katex\"><span class=\"katex-mathml\">(x,y)\u2009R\u2009(u,v)(x, y) \\, R \\, (u, v)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">v<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">(u,v)\u2009R\u2009(m,n)(u, v) \\, R \\, (m, n)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">v<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><br data-start=\"1327\" data-end=\"1330\" \/>\u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">x&lt;u&lt;mx &lt; u &lt; m<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">y&gt;v&gt;ny &gt; v &gt; n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">v<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span> \u0939\u094b\u0917\u093e<br data-start=\"1374\" data-end=\"1377\" \/>\u21d2 <span class=\"katex\"><span class=\"katex-mathml\">x&lt;mx &lt; m<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">y&gt;ny &gt; n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><br data-start=\"1407\" data-end=\"1410\" \/>\u27a4 <strong data-start=\"1414\" data-end=\"1431\">R \u092a\u093e\u0930\u0917\u093e\u092e\u0940 \u0939\u0948\u0964<\/strong><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"1433\" data-end=\"1729\"><strong data-start=\"1433\" data-end=\"1446\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937:<\/strong><br data-start=\"1446\" data-end=\"1449\" \/>R \u0928 \u0924\u094b \u092a\u094d\u0930\u0924\u093f\u092b\u0932 \u0939\u0948, \u0928 \u0938\u092e\u092e\u093f\u0924, \u0932\u0947\u0915\u093f\u0928 \u092a\u093e\u0930\u0917\u093e\u092e\u0940 \u0939\u0948\u0964<br data-start=\"1494\" data-end=\"1497\" \/>\u0907\u0938\u0932\u093f\u090f, \u092f\u0939 \u0928 \u0924\u094b \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e \u0939\u0948 (\u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0924\u093f\u092b\u0932\u0924\u093e \u0914\u0930 \u092a\u093e\u0930\u0917\u092e\u094d\u092f\u0924\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948), \u0914\u0930 \u0928 \u0939\u0940 \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u0902\u092c\u0902\u0927 (\u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0924\u093f\u092b\u0932\u0924\u093e, \u0938\u092e\u092e\u093f\u0924\u0924\u093e, \u0914\u0930 \u092a\u093e\u0930\u0917\u092e\u094d\u092f\u0924\u093e \u0938\u092d\u0940 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0902)\u0964<br data-start=\"1656\" data-end=\"1659\" \/>\u27a4 <strong data-start=\"1661\" data-end=\"1729\">\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: \u0935\u093f\u0915\u0932\u094d\u092a 3 \u2014 \u0928 \u0924\u094b \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e \u0939\u0948 \u0914\u0930 \u0928 \u0939\u0940 \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u0902\u092c\u0902\u0927<\/strong><\/p>\n<hr data-start=\"1731\" data-end=\"1734\" \/>\n<h3 data-start=\"1736\" data-end=\"1762\">\ud83c\udfaf \u0909\u0924\u094d\u0924\u0930: <strong data-start=\"1750\" data-end=\"1762\">\u0935\u093f\u0915\u0932\u094d\u092a 3<\/strong><\/h3>\n<hr data-start=\"1764\" data-end=\"1767\" \/>\n<p data-start=\"1769\" data-end=\"1899\">\u092f\u0926\u093f \u0906\u092a \u0907\u0938 \u0935\u093f\u0937\u092f \u092a\u0930 \u0914\u0930 \u0905\u0927\u093f\u0915 GATE \u0915\u0947 \u092a\u0942\u0930\u094d\u0935 \u0935\u0930\u094d\u0937 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0906\u092a \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0938\u093e\u0927\u0928\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul data-start=\"1901\" data-end=\"2138\">\n<li data-start=\"1901\" data-end=\"2024\">\n<p data-start=\"1903\" data-end=\"2024\"><a class=\"cursor-pointer\" target=\"_new\" rel=\"noopener\" data-start=\"1903\" data-end=\"2024\">GeeksforGeeks &#8211; Discrete Mathematics GATE Questions<\/a><\/p>\n<\/li>\n<li data-start=\"2025\" data-end=\"2138\">\n<p data-start=\"2027\" data-end=\"2138\"><a class=\"cursor-pointer\" target=\"_new\" rel=\"noopener\" data-start=\"2027\" data-end=\"2138\">Testbook &#8211; Discrete Mathematics GATE Questions<\/a><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2140\" data-end=\"2224\">\u0907\u0928 \u0938\u0902\u0938\u093e\u0927\u0928\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u0937\u092f\u0935\u093e\u0930 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939 \u0939\u0948, \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<\/p>\n<hr data-start=\"2226\" data-end=\"2229\" \/>\n<p data-start=\"2231\" data-end=\"2303\">\u092f\u0926\u093f \u0906\u092a \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 \u0935\u093f\u0937\u092f \u092f\u093e \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0930 \u0914\u0930 \u0938\u0939\u093e\u092f\u0924\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0943\u092a\u092f\u093e \u092c\u0924\u093e\u090f\u0902!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Previous year gate question in Hindi- Gate 2025 Discrete math Let R be a relation on the set. [fvplayer id=&#8221;245&#8243;] GATE 2025 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930\u094b\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u093e \u0914\u0930 \u0909\u0928\u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u093e \u0906\u092a\u0915\u0940 \u0938\u092b\u0932\u0924\u093e \u0915\u0940 \u0915\u0941\u0902\u091c\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0917\u093e\u0907\u0921 \u092e\u0947\u0902 \u0926\u093f\u090f \u0917\u090f \u0938\u0941\u091d\u093e\u0935\u094b\u0902 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0915\u0947 \u0906\u092a \u0905\u092a\u0928\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u094b \u092c\u0947\u0939\u0924\u0930 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0928\u093f\u092f\u092e\u093f\u0924 [&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-3085","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3085","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=3085"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3085\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}