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What is the value of (k) for the equations (3x+ky=12) and (9x+15y=36) to have infinitely many solutions?समीकरणों (3x+ky=12) और (9x+15y=36) के अनंत हल होने के लिए (k) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 55
For two linear equations to have infinitely many solutions, the ratios of corresponding coefficients must be equal: a₁/a₂ = b₁/b₂ = c₁/c₂. Here, 3/9 = 12/36 = 1/3. Therefore, k/15 = 1/3, giving k = 5. Hence, option C is correct. Exam tip: Find the common ratio using the coefficients of x and the constants, then use it to determine the coefficient of y.दो रैखिक समीकरणों के अनंत हल होने की शर्त है: a₁/a₂ = b₁/b₂ = c₁/c₂। यहाँ 3/9 = 12/36 = 1/3 है। इसलिए k/15 = 1/3, जिससे k = 5 प्राप्त होता है। अतः सही विकल्प C है। परीक्षा-टिप: पहले x और नियतांक के गुणांकों का अनुपात ज्ञात करके y के गुणांक का मान निकालें।
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