{"id":3137,"date":"2025-06-01T14:15:12","date_gmt":"2025-06-01T14:15:12","guid":{"rendered":"https:\/\/diznr.com\/?p=3137"},"modified":"2025-06-01T14:15:12","modified_gmt":"2025-06-01T14:15:12","slug":"previous-year-gate-question-of-discrete-in-hindi-gate-1993-let-a-be-a-finite-set-of-size-n","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/previous-year-gate-question-of-discrete-in-hindi-gate-1993-let-a-be-a-finite-set-of-size-n\/","title":{"rendered":"Previous year gate question of Discrete in Hindi – GATE 1993 Let A be a finite set of size n."},"content":{"rendered":"

Previous year gate question of Discrete in Hindi – GATE 199 Let A be a finite set of size n.<\/p>\n

[fvplayer id=”270″]<\/p>\n

\u00a0GATE 1993 | Discrete Mathematics Previous Year Question in Hindi<\/strong><\/h3>\n

\u092a\u094d\u0930\u0936\u094d\u0928:<\/strong>
\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f AA<\/span>A<\/span><\/span><\/span><\/span> \u090f\u0915 \u092a\u0930\u093f\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f (Finite Set)<\/strong> \u0939\u0948 \u091c\u093f\u0938\u0915\u0940 \u0906\u0915\u093e\u0930 (Size) nn<\/span>n<\/span><\/span><\/span><\/span><\/strong> \u0939\u0948\u0964
\u0907\u0938 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u0947 Power Set (\u092a\u0949\u0935\u0930 \u0938\u0947\u091f)<\/strong> \u092e\u0947\u0902 \u0915\u0941\u0932 \u0915\u093f\u0924\u0928\u0947 \u0909\u092a\u0938\u092e\u0941\u091a\u094d\u091a\u092f (Subsets) \u0939\u094b\u0902\u0917\u0947?<\/p>\n

\u00a0\u0939\u0932 (Solution):<\/strong><\/h3>\n

\u0915\u093f\u0938\u0940 \u0938\u092e\u0941\u091a\u094d\u091a\u092f (Set) AA<\/span>A<\/span><\/span><\/span><\/span> \u091c\u093f\u0938\u0915\u093e \u0906\u0915\u093e\u0930 nn<\/span>n<\/span><\/span><\/span><\/span> \u0939\u094b<\/strong>, \u0909\u0938\u0915\u0947 \u092a\u0949\u0935\u0930 \u0938\u0947\u091f (Power Set) \u092e\u0947\u0902 \u0915\u0941\u0932 \u0909\u092a\u0938\u092e\u0941\u091a\u094d\u091a\u092f (Subsets)<\/strong> \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n

Total\u00a0Subsets=2n\\text{Total Subsets} = 2^n<\/span>Total\u00a0Subsets<\/span><\/span>=<\/span><\/span>2n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u091c\u0939\u093e\u0901 nn<\/span>n<\/span><\/span><\/span><\/span>, \u0938\u092e\u0941\u091a\u094d\u091a\u092f AA<\/span>A<\/span><\/span><\/span><\/span> \u092e\u0947\u0902 \u092e\u094c\u091c\u093c\u0942\u0926 \u0924\u0924\u094d\u0935\u094b\u0902 (Elements)<\/strong> \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0964<\/p>\n

\u00a0\u0909\u0926\u093e\u0939\u0930\u0923 (Example):<\/strong><\/h3>\n

\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f A={1,2,3}A = \\{1, 2, 3\\}<\/span>A<\/span>=<\/span><\/span>{<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>}<\/span><\/span><\/span><\/span> \u0939\u0948, \u092f\u093e\u0928\u0940 n=3n = 3<\/span>n<\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/strong>
\u27a1 \u0924\u094b \u0907\u0938\u0915\u0947 \u092a\u0949\u0935\u0930 \u0938\u0947\u091f \u092e\u0947\u0902 \u0915\u0941\u0932 \u0909\u092a\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u094b\u0902\u0917\u0947<\/strong><\/p>\n

23=82^3 = 8<\/span>23<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>8<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u092a\u0949\u0935\u0930 \u0938\u0947\u091f:<\/strong><\/p>\n

{\u2205,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}\\{\\emptyset, \\{1\\}, \\{2\\}, \\{3\\}, \\{1,2\\}, \\{1,3\\}, \\{2,3\\}, \\{1,2,3\\} \\}<\/span>{<\/span>\u2205<\/span>,<\/span>{<\/span>1<\/span>}<\/span>,<\/span>{<\/span>2<\/span>}<\/span>,<\/span>{<\/span>3<\/span>}<\/span>,<\/span>{<\/span>1<\/span>,<\/span>2<\/span>}<\/span>,<\/span>{<\/span>1<\/span>,<\/span>3<\/span>}<\/span>,<\/span>{<\/span>2<\/span>,<\/span>3<\/span>}<\/span>,<\/span>{<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>}}<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u0905\u0917\u0930 AA<\/span>A<\/span><\/span><\/span><\/span> \u092e\u0947\u0902 5 \u0924\u0924\u094d\u0935 \u0939\u0948\u0902 (n=5n = 5<\/span>n<\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span>)<\/strong>
\u27a1 \u0924\u094b \u0907\u0938\u0915\u0947 \u092a\u0949\u0935\u0930 \u0938\u0947\u091f \u092e\u0947\u0902 \u0915\u0941\u0932 \u0909\u092a\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u094b\u0902\u0917\u0947<\/strong><\/p>\n

25=322^5 = 32<\/span>25<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>32<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u00a0\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 (Final Answer):<\/strong><\/h3>\n

\u092f\u0926\u093f AA<\/span>A<\/span><\/span><\/span><\/span> \u0915\u0947 \u0905\u0902\u0926\u0930 nn<\/span>n<\/span><\/span><\/span><\/span> \u0924\u0924\u094d\u0935 \u0939\u0948\u0902, \u0924\u094b \u0909\u0938\u0915\u0947 \u092a\u0949\u0935\u0930 \u0938\u0947\u091f \u092e\u0947\u0902 \u0915\u0941\u0932 2n2^n<\/span>2n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u0909\u092a\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u094b\u0902\u0917\u0947\u0964<\/strong><\/p>\n

GATE 1993 \u0915\u093e \u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930:<\/strong><\/p>\n

\\mathbf{2^n} \\]\u00a0\u0905\u0917\u0930 \u0906\u092a\u0915\u094b \u0915\u094b\u0908 \u0914\u0930 **GATE \u0915\u093e \u092a\u094d\u0930\u0936\u094d\u0928 \u0938\u092e\u091d\u0928\u093e \u0939\u094b, \u0924\u094b \u092c\u0924\u093e\u0907\u090f!<\/span><\/p>\n

Previous year gate question of Discrete in Hindi – GATE 1993 Let A be a finite set of size n.<\/a><\/h3>\n

Discrete Mathematics for Computer Science<\/a><\/h3>\n

Discrete Mathematical Structures<\/a><\/h3>\n

GATE CS – 1993<\/a><\/h3>\n

\u092f\u0939\u093e\u0901 \u092a\u0930 GATE 1993<\/strong> \u0915\u093e \u090f\u0915 \u092c\u0939\u0941\u0924 \u092a\u094d\u0930\u0938\u093f\u0926\u094d\u0927 \u0914\u0930 \u092c\u093e\u0930-\u092c\u093e\u0930 \u092a\u0942\u091b\u093e \u0917\u092f\u093e \u092a\u094d\u0930\u0936\u094d\u0928 \u0939\u0948 Discrete Mathematics<\/strong> \u0938\u0947 \u2014 \u091c\u093f\u0938\u0947 \u0939\u092e\u0928\u0947 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0938\u0930\u0932 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u092e\u091d\u093e\u092f\u093e \u0939\u0948\u0964<\/p>\n

\n

\ud83e\uddfe GATE 1993 \u2013 Discrete Mathematics (Set Theory)<\/strong><\/h2>\n

Question (In English):<\/strong>
\nLet A<\/strong> be a finite set of size n<\/strong>. The total number of relations<\/strong> on A<\/strong> which are reflexive<\/strong> and symmetric<\/strong> is:<\/p>\n

\n

\ud83e\udde0 \u092a\u094d\u0930\u0936\u094d\u0928 \u0915\u093e \u0939\u093f\u0902\u0926\u0940 \u0905\u0928\u0941\u0935\u093e\u0926:<\/strong><\/h2>\n

\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f A<\/strong> \u090f\u0915 \u0938\u0940\u092e\u093f\u0924 (finite) \u0938\u0947\u091f \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 n \u0924\u0924\u094d\u0924\u094d\u0935<\/strong> \u0939\u0948\u0902\u0964
\n\u0924\u094b \u0910\u0938\u0947 \u0915\u0941\u0932 \u0915\u093f\u0924\u0928\u0947 relations<\/strong> \u092c\u0928\u093e\u090f \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0915\u093f:<\/p>\n