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NDA 2022 Maths · Mathematics · Quadratic Equations · medium

The system x+2y=3, 2x+ky=6 has infinitely many solutions when k equals

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The system x+2y=3x+2y=3, 2x+ky=62x+ky=6 has infinitely many solutions when kk equals
  1. A. 44
  2. B. 22
  3. C. 33
  4. D. 66
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Answer: (A) 44

Infinitely many solutions need proportional equations: 21=k2=63\frac{2}{1}=\frac{k}{2}=\frac{6}{3}, which gives k=4k=4. For any other kk the determinant k−4k-4 is non-zero and the solution is unique.
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Original question written in the NDA 2022 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake