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What is the value of (b) for (5x+2y=9) and (10x+by=18) to have infinitely many solutions?समीकरण (5x+2y=9) और (10x+by=18) के अनंत हल होने के लिए (b) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 44
For a pair of linear equations to have infinitely many solutions, a₁/a₂ = b₁/b₂ = c₁/c₂ must hold. Here, 5/10 = 9/18 = 1/2, so 2/b = 1/2, which gives b = 4. Therefore, option C is correct. Exam tip: For infinitely many solutions, all three corresponding ratios must be equal, not just two of them.दो रैखिक समीकरणों के अनंत हल होने के लिए a₁/a₂ = b₁/b₂ = c₁/c₂ होना चाहिए। यहाँ 5/10 = 9/18 = 1/2 है, इसलिए 2/b = 1/2। अतः b = 4। इसलिए सही विकल्प C है। परीक्षा-टिप: अनंत हल के लिए तीनों अनुपात समान होने चाहिए; केवल दो अनुपातों का समान होना पर्याप्त नहीं है।
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