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What is the value of (a) for the equations (4x+ay=32) and (12x+21y=96) to have infinitely many solutions?समीकरणों (4x+ay=32) और (12x+21y=96) के अनंत हल होने के लिए (a) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 77
For two linear equations to have infinitely many solutions, the ratios of the corresponding coefficients and constants must be equal: 4/12 = a/21 = 32/96. Since 4/12 and 32/96 are both 1/3, a/21 = 1/3, giving a = 7. Therefore, option C is correct. Exam tip: all three ratios must be equal; equality of only two ratios is not sufficient for infinitely many solutions.दो रैखिक समीकरणों के अनंत हल होने की शर्त है: 4/12 = a/21 = 32/96। यहाँ 4/12 और 32/96 दोनों 1/3 हैं, इसलिए a/21 = 1/3, अर्थात a = 7। अतः सही विकल्प C है। परीक्षा में ध्यान रखें कि अनंत हल के लिए तीनों अनुपात समान होने चाहिए; केवल दो अनुपातों का समान होना पर्याप्त नहीं है।
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