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NDA 2 2025 Maths, question 12

Topic: Matrices and determinants

Q12

The system of equations

2x−3y−5=0,15y−10x+50=02x-3y-5=0, 15y-10x+50=0

  1. (a) has a unique solution
  2. (b) has infinitely many solutions
  3. (c) is inconsistentCorrect answer
  4. (d) is consistent and has exactly two solutions

Solution.

Answer: (c) is inconsistent

  1. The first equation requires 2x−3y=5.
  2. Dividing the second by −5 gives 2x−3y=10.
  3. The same expression cannot equal both numbers, so the system is inconsistent.