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NDA 2021 Maths · Mathematics · Quadratic Equations · hard

The system kx+3y=k-3, 12x+ky=k has no solution when k equals

Single correct option

The system kx+3y=k−3kx+3y=k-3, 12x+ky=k12x+ky=k has no solution when kk equals
  1. A. 66
  2. B. −6-6
  3. C. 00
  4. D. 33
Show answer and solution

Answer: (B) −6-6

Parallel lines need k12=3k\dfrac k{12}=\dfrac3k, so k2=36k^2=36. For k=6k=6 the constants agree (12=12\tfrac12=\tfrac12) and there are infinitely many solutions; for k=−6k=-6 the ratio of constants is 32≠−12\tfrac32\neq-\tfrac12, so there is no solution.
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Original question written in the NDA 2021 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