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On (A={0,1,2,3,4}), (R={(a,b):a^2+b^2=a+b}). How many diagonal pairs are in (R)?समुच्चय (A={0,1,2,3,4}) पर (R={(a,b):a^2+b^2=a+b}) है। (R) में कितने विकर्ण युग्म हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 22
Step 1: On the diagonal, (2a^2=2a). Step 2: This becomes (a^2=a), i.e. (a(a-1)=0). Step 3: (a=0,1) work, so there are (2) diagonal pairs.चरण 1: विकर्ण पर (2a^2=2a) मिलेगा। चरण 2: इसे (a^2=a), यानी (a(a-1)=0) लिखते हैं। चरण 3: (a=0,1) काम करते हैं, इसलिए (2) विकर्ण युग्म हैं।
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