PrepRung
Sign inSign up free

NDA 2017 Maths · Mathematics · Determinants · hard

For the system x+y+z=6, x+2y+3z=14, x+3y+λ z=μ, the system does NOT have a unique solution when λ equals

Single correct option

For the system x+y+z=6x+y+z=6, x+2y+3z=14x+2y+3z=14, x+3y+λz=μx+3y+\lambda z=\mu, the system does NOT have a unique solution when λ\lambda equals
  1. A. 33
  2. B. 44
  3. C. 55
  4. D. 66
Show answer and solution

Answer: (C) 55

A unique solution exists iff the coefficient determinant is non-zero. ∣11112313λ∣=(2λ−9)−(λ−3)+(3−2)=λ−5\begin{vmatrix}1&1&1\\1&2&3\\1&3&\lambda\end{vmatrix}=(2\lambda-9)-(\lambda-3)+(3-2)=\lambda-5. It vanishes at λ=5\lambda=5.
Report a mistake

Original question written in the NDA 2017 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