{"id":2960,"date":"2025-06-06T09:10:17","date_gmt":"2025-06-06T09:10:17","guid":{"rendered":"https:\/\/diznr.com\/?p=2960"},"modified":"2025-06-06T09:10:17","modified_gmt":"2025-06-06T09:10:17","slug":"discrete-mathematics-previous-year-paper-in-hindi-gate-2020-if-proposition-the","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/discrete-mathematics-previous-year-paper-in-hindi-gate-2020-if-proposition-the\/","title":{"rendered":"Discrete mathematics previous year paper in Hindi &#8211; GATE 2025 &#8211; If the proposition."},"content":{"rendered":"<p>Discrete mathematics previous year paper in Hindi &#8211; GATE 2025 &#8211; If the proposition.<\/p>\n<p>[fvplayer id=&#8221;190&#8243;]<\/p>\n<p data-start=\"0\" data-end=\"196\">\u200b<span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">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\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 <strong data-start=\"63\" data-end=\"87\">\u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938<\/strong> \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0937\u092f \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 <strong data-start=\"118\" data-end=\"139\">\u092a\u094d\u0930\u094b\u092a\u094b\u091c\u093f\u0936\u0928\u0932 \u0932\u0949\u091c\u093f\u0915<\/strong> (\u0935\u093f\u0927\u0947\u092f\u093e\u0924\u094d\u092e\u0915 \u0924\u0930\u094d\u0915) \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928 \u092d\u0940 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/span> \u092f\u0926\u093f \u0906\u092a \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \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\u0940 \u0916\u094b\u091c \u092e\u0947\u0902 \u0939\u0948\u0902, \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0941\u091d\u093e\u0935 \u0906\u092a\u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:\u200b<\/p>\n<ol data-start=\"198\" data-end=\"658\">\n<li data-start=\"198\" data-end=\"309\">\n<p data-start=\"201\" data-end=\"309\"><strong data-start=\"201\" data-end=\"226\">\u0906\u0927\u093f\u0915\u093e\u0930\u093f\u0915 GATE \u0935\u0947\u092c\u0938\u093e\u0907\u091f<\/strong>: <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">GATE \u0915\u0940 \u0906\u0927\u093f\u0915\u093e\u0930\u093f\u0915 \u0935\u0947\u092c\u0938\u093e\u0907\u091f \u092a\u0930 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u092f\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903 \u0905\u0902\u0917\u094d\u0930\u0947\u091c\u0940 \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0906\u092a \u0907\u0928\u094d\u0939\u0947\u0902 \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0915\u0930\u0915\u0947 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u0935\u093e\u0926\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span>\u200b<\/p>\n<\/li>\n<li data-start=\"311\" data-end=\"428\">\n<p data-start=\"314\" data-end=\"428\"><strong data-start=\"314\" data-end=\"345\">\u0936\u0948\u0915\u094d\u0937\u0923\u093f\u0915 \u092a\u0941\u0938\u094d\u0924\u0915\u0947\u0902 \u0914\u0930 \u0917\u093e\u0907\u0921\u094d\u0938<\/strong>: <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0915\u0908 \u092a\u094d\u0930\u0915\u093e\u0936\u0915 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 GATE \u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0947 \u0932\u093f\u090f \u092a\u0941\u0938\u094d\u0924\u0915\u0947\u0902 \u0914\u0930 \u0917\u093e\u0907\u0921\u094d\u0938 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0928\u092e\u0947\u0902 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/span>\u200b<\/p>\n<\/li>\n<li data-start=\"430\" data-end=\"538\">\n<p data-start=\"433\" data-end=\"538\"><strong data-start=\"433\" data-end=\"455\">\u0911\u0928\u0932\u093e\u0907\u0928 \u092a\u094d\u0932\u0947\u091f\u092b\u093c\u0949\u0930\u094d\u092e<\/strong>: <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\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 GATE \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0909\u092a\u0932\u092c\u094d\u0927 \u0915\u0930\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, Testbook \u0914\u0930 CollegeDekho \u091c\u0948\u0938\u0940 \u0935\u0947\u092c\u0938\u093e\u0907\u091f\u094d\u0938 \u092a\u0930 \u0906\u092a \u092f\u0942\u091c\u0940\u0938\u0940 \u0928\u0947\u091f \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u092a\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938 \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<\/span>\u200b<span class=\"ml-1 inline-flex max-w-full items-center relative top-[-0.094rem]\"><span class=\"relative bottom-0 left-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between\"><span class=\"max-w-full grow overflow-hidden truncate text-center\">Testbook<\/span><span class=\"-mr-1 ml-1 flex h-full items-center rounded-full px-1 text-[#8F8F8F]\">+1<\/span><\/span><span class=\"flex h-4 w-full items-center justify-between absolute\"><span class=\"max-w-full grow overflow-hidden truncate text-center\">CollegeDekho<\/span><span class=\"-mr-1 ml-1 flex h-full items-center rounded-full px-1 text-[#8F8F8F]\">+1<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"540\" data-end=\"658\">\n<p data-start=\"543\" data-end=\"658\"><strong data-start=\"543\" data-end=\"575\">\u0936\u0948\u0915\u094d\u0937\u0923\u093f\u0915 \u0938\u0902\u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0915\u0947 \u0938\u0902\u0938\u093e\u0927\u0928<\/strong>: <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0915\u0941\u091b \u0936\u0948\u0915\u094d\u0937\u0923\u093f\u0915 \u0938\u0902\u0938\u094d\u0925\u093e\u0928 \u0914\u0930 \u0915\u094b\u091a\u093f\u0902\u0917 \u0938\u0947\u0902\u091f\u0930 \u0905\u092a\u0928\u0947 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0905\u0927\u094d\u092f\u092f\u0928 \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0914\u0930 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0909\u092a\u0932\u092c\u094d\u0927 \u0915\u0930\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/span>\u200b<\/p>\n<\/li>\n<\/ol>\n<p data-start=\"660\" data-end=\"783\"><strong data-start=\"660\" data-end=\"681\">\u092a\u094d\u0930\u094b\u092a\u094b\u091c\u093f\u0936\u0928\u0932 \u0932\u0949\u091c\u093f\u0915<\/strong> \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0947 \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0947 \u0932\u093f\u090f, \u0906\u092a \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul data-start=\"785\" data-end=\"1130\">\n<li data-start=\"785\" data-end=\"906\">\n<p data-start=\"787\" data-end=\"906\"><strong data-start=\"787\" data-end=\"819\">\u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0938\u0924\u094d\u092f\u093e\u092a\u0928<\/strong>: <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f \u0915\u094b\u0908 \u092a\u094d\u0930\u094b\u092a\u094b\u091c\u093f\u0936\u0928 P \u0914\u0930 Q \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902, \u0924\u094b \u0909\u0928\u0915\u0947 \u0938\u0902\u092f\u094b\u091c\u0928 (P \u2227 Q), \u0935\u093f\u092f\u094b\u091c\u0928 (P \u2228 Q), \u0914\u0930 \u0928\u093f\u0937\u0947\u0927 (\u00acP) \u0915\u0947 \u0938\u0924\u094d\u092f \u092e\u0942\u0932\u094d\u092f \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u0923\u0964<\/span>\u200b<\/p>\n<\/li>\n<li data-start=\"908\" data-end=\"1018\">\n<p data-start=\"910\" data-end=\"1018\"><strong data-start=\"910\" data-end=\"931\">\u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e<\/strong>: <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0926\u094b \u092a\u094d\u0930\u094b\u092a\u094b\u091c\u093f\u0936\u0928\u0932 \u0915\u0925\u0928\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0928\u093e\u0964<\/span>\u200b<\/p>\n<\/li>\n<li data-start=\"1020\" data-end=\"1130\">\n<p data-start=\"1022\" data-end=\"1130\"><strong data-start=\"1022\" data-end=\"1043\">\u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0928\u093f\u0939\u093f\u0924\u093e\u0930\u094d\u0925<\/strong>: <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u090f\u0915 \u092a\u094d\u0930\u094b\u092a\u094b\u091c\u093f\u0936\u0928 \u0938\u0947 \u0926\u0942\u0938\u0930\u0947 \u092a\u094d\u0930\u094b\u092a\u094b\u091c\u093f\u0936\u0928 \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0928\u093e\u0964<\/span>\u200b<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"1132\" data-end=\"1217\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0907\u0928 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0947 \u0905\u092d\u094d\u092f\u093e\u0938 \u0938\u0947 \u0906\u092a \u092a\u094d\u0930\u094b\u092a\u094b\u091c\u093f\u0936\u0928\u0932 \u0932\u0949\u091c\u093f\u0915 \u092e\u0947\u0902 \u0928\u093f\u092a\u0941\u0923\u0924\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0915 \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0917\u093e\u0964<\/span>\u200b<\/p>\n<p data-start=\"1219\" data-end=\"1304\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0905\u0902\u0924 \u092e\u0947\u0902, \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f \u0906\u092a \u0928\u093f\u092f\u092e\u093f\u0924 \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u094d\u0930\u094b\u0924\u094b\u0902 \u0938\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u0939\u0932 \u0915\u0930\u0947\u0902 \u0924\u093e\u0915\u093f \u0906\u092a\u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0935\u094d\u092f\u093e\u092a\u0915 \u0914\u0930 \u0938\u0941\u0926\u0943\u0922\u093c \u0939\u094b\u0964<\/span><\/p>\n<h3 data-start=\"1219\" data-end=\"1304\"><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Discrete mathematics previous year paper in Hindi &#8211; GATE 2025 &#8211; If the proposition.<\/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=\"74\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u0906\u092a\u0928\u0947 GATE 2025 \u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0947 \u0932\u093f\u090f <strong data-start=\"32\" data-end=\"56\">Discrete Mathematics<\/strong> \u0935\u093f\u0937\u092f \u0915\u0947 \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\u0940 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u092e\u093e\u0902\u0917\u0940 \u0939\u0948, \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947 \u0909\u0928 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u091c\u094b &#8220;If the proposition&#8230;&#8221; \u092a\u094d\u0930\u093e\u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u0948\u0902\u0964<\/span><\/p>\n<hr data-start=\"76\" data-end=\"79\" \/>\n<h3 data-start=\"81\" data-end=\"144\">\ud83d\udcd8 GATE Discrete Mathematics: \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 (PYQs)<\/h3>\n<p data-start=\"146\" data-end=\"220\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 Discrete Mathematics \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0937\u092f \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091f\u0949\u092a\u093f\u0915\u094d\u0938 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<ul data-start=\"222\" data-end=\"510\">\n<li data-start=\"222\" data-end=\"261\">\n<p data-start=\"224\" data-end=\"261\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><strong data-start=\"0\" data-end=\"39\" data-is-last-node=\"\" data-is-only-node=\"\">Propositional and First-Order Logic<\/strong><\/span><\/p>\n<\/li>\n<li data-start=\"262\" data-end=\"303\">\n<p data-start=\"264\" data-end=\"303\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><strong data-start=\"0\" data-end=\"24\" data-is-last-node=\"\" data-is-only-node=\"\">Set Theory &amp; Algebra<\/strong><\/span><\/p>\n<\/li>\n<li data-start=\"304\" data-end=\"345\">\n<p data-start=\"306\" data-end=\"345\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><strong data-start=\"0\" data-end=\"16\" data-is-last-node=\"\" data-is-only-node=\"\">Graph Theory<\/strong><\/span><\/p>\n<\/li>\n<li data-start=\"346\" data-end=\"387\">\n<p data-start=\"348\" data-end=\"387\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><strong data-start=\"0\" data-end=\"17\" data-is-last-node=\"\" data-is-only-node=\"\">Combinatorics<\/strong><\/span><\/p>\n<\/li>\n<li data-start=\"388\" data-end=\"429\">\n<p data-start=\"390\" data-end=\"429\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><strong data-start=\"0\" data-end=\"24\" data-is-last-node=\"\" data-is-only-node=\"\">Recurrence Relations<\/strong><\/span><\/p>\n<\/li>\n<li data-start=\"430\" data-end=\"510\">\n<p data-start=\"432\" data-end=\"510\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><strong data-start=\"0\" data-end=\"29\" data-is-last-node=\"\" data-is-only-node=\"\">Groups, Monoids, Lattices<\/strong><\/span><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"512\" data-end=\"590\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u0907\u0928 \u0935\u093f\u0937\u092f\u094b\u0902 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 &#8220;If the proposition&#8230;&#8221; \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0905\u0915\u094d\u0938\u0930 \u092a\u0942\u091b\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<hr data-start=\"592\" data-end=\"595\" \/>\n<h3 data-start=\"597\" data-end=\"617\">\ud83d\udcdd \u0909\u0926\u093e\u0939\u0930\u0923 \u092a\u094d\u0930\u0936\u094d\u0928<\/h3>\n<p data-start=\"619\" data-end=\"727\"><strong data-start=\"619\" data-end=\"646\">\u092a\u094d\u0930\u0936\u094d\u0928 (GATE CSE 2020):<\/strong><br data-start=\"646\" data-end=\"649\" \/><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0926\u093f P \u0914\u0930 Q \u0926\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e\u090f\u0901 \u0939\u0948\u0902, \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u0947\u0902 \u0938\u0947 \u0915\u094c\u0928 \u0938\u093e \u0915\u0925\u0928 P \u2192 Q \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948?<\/span><\/p>\n<p data-start=\"729\" data-end=\"740\"><strong data-start=\"729\" data-end=\"740\">\u0935\u093f\u0915\u0932\u094d\u092a:<\/strong><\/p>\n<ol data-start=\"741\" data-end=\"951\">\n<li data-start=\"741\" data-end=\"783\">\n<p data-start=\"744\" data-end=\"783\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">P \u2227 Q<\/span><\/p>\n<\/li>\n<li data-start=\"784\" data-end=\"826\">\n<p data-start=\"787\" data-end=\"826\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u00acP \u2228 Q<\/span><\/p>\n<\/li>\n<li data-start=\"827\" data-end=\"869\">\n<p data-start=\"830\" data-end=\"869\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">P \u2228 Q<\/span><\/p>\n<\/li>\n<li data-start=\"870\" data-end=\"951\">\n<p data-start=\"873\" data-end=\"951\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u00acP \u2227 Q<\/span><\/p>\n<\/li>\n<\/ol>\n<p data-start=\"953\" data-end=\"1046\"><strong data-start=\"953\" data-end=\"967\">\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930:<\/strong><\/p>\n<ol start=\"2\" data-start=\"0\" data-end=\"9\" data-is-last-node=\"\" data-is-only-node=\"\">\n<li data-start=\"0\" data-end=\"9\" data-is-last-node=\"\">\u00acP \u2228 Q<\/li>\n<\/ol>\n<hr data-start=\"1048\" data-end=\"1051\" \/>\n<h3 data-start=\"1053\" data-end=\"1073\">\ud83d\udcda \u0905\u0927\u094d\u092f\u092f\u0928 \u0938\u0902\u0938\u093e\u0927\u0928<\/h3>\n<p data-start=\"1075\" data-end=\"1153\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\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\u0915\u0947 GATE Discrete Mathematics \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<ul data-start=\"1155\" data-end=\"1581\">\n<li data-start=\"1155\" data-end=\"1302\">\n<p data-start=\"1157\" data-end=\"1302\"><strong data-start=\"1157\" data-end=\"1183\">Unacademy (\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0939\u093e\u0901 \u092a\u0930 Discrete Mathematics \u0915\u0947 \u0935\u093f\u0937\u092f\u0935\u093e\u0930 GATE PYQs \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u092a\u093e\u0920\u094d\u092f\u0915\u094d\u0930\u092e \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964<\/span><\/p>\n<\/li>\n<li data-start=\"1304\" data-end=\"1443\">\n<p data-start=\"1306\" data-end=\"1443\"><strong data-start=\"1306\" data-end=\"1324\">GeeksforGeeks:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Discrete Mathematics \u0915\u0947 \u0935\u093f\u0937\u092f\u0935\u093e\u0930 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939\u0964<\/span><\/p>\n<\/li>\n<li data-start=\"1445\" data-end=\"1581\">\n<p data-start=\"1447\" data-end=\"1581\"><strong data-start=\"1447\" data-end=\"1462\">SelfStudys:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0939\u093e\u0901 \u092a\u0930 GATE \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964<\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1583\" data-end=\"1586\" \/>\n<h3 data-start=\"1588\" data-end=\"1608\">\ud83c\udfa5 \u0935\u0940\u0921\u093f\u092f\u094b \u0938\u0902\u0938\u093e\u0927\u0928<\/h3>\n<p data-start=\"1610\" data-end=\"1688\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0926\u093f \u0906\u092a \u0935\u0940\u0921\u093f\u092f\u094b \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u093e \u092a\u0938\u0902\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0935\u0940\u0921\u093f\u092f\u094b \u0906\u092a\u0915\u0940 \u092e\u0926\u0926 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<ul data-start=\"1690\" data-end=\"1907\">\n<li data-start=\"1690\" data-end=\"1802\">\n<p data-start=\"1692\" data-end=\"1802\"><strong data-start=\"1692\" data-end=\"1762\">Discrete Mathematics Previous Year Questions (PYQs) | BYJU&#8217;S GATE:<\/strong> <span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">YouTube<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"1804\" data-end=\"1907\">\n<p data-start=\"1806\" data-end=\"1907\"><strong data-start=\"1806\" data-end=\"1867\">GATE Question Solved CSE | Discrete Mathematics in HINDI:<\/strong> <span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">YouTube<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1909\" data-end=\"1912\" \/>\n<p data-start=\"1914\" data-end=\"2119\">\u092f\u0926\u093f \u0906\u092a \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 \u091f\u0949\u092a\u093f\u0915 (\u091c\u0948\u0938\u0947 Propositional Logic, Set Theory, Graph Theory \u0906\u0926\u093f) \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0940 \u0924\u0932\u093e\u0936 \u092e\u0947\u0902 \u0939\u0948\u0902, \u0924\u094b \u0915\u0943\u092a\u092f\u093e \u092c\u0924\u093e\u090f\u0902, \u092e\u0948\u0902 \u0906\u092a\u0915\u094b \u0909\u0938 \u0935\u093f\u0937\u092f \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928 \u0914\u0930 \u0905\u0927\u094d\u092f\u092f\u0928 \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0942\u0901\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Discrete mathematics previous year paper in Hindi &#8211; GATE 2025 &#8211; If the proposition. [fvplayer id=&#8221;190&#8243;] \u200bGATE (\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\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938 \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0937\u092f \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u092a\u094d\u0930\u094b\u092a\u094b\u091c\u093f\u0936\u0928\u0932 \u0932\u0949\u091c\u093f\u0915 (\u0935\u093f\u0927\u0947\u092f\u093e\u0924\u094d\u092e\u0915 \u0924\u0930\u094d\u0915) \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928 \u092d\u0940 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u0906\u092a \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \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\u0940 \u0916\u094b\u091c \u092e\u0947\u0902 [&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-2960","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2960","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=2960"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2960\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}