Q53 / 100 · BITSAT 2024 (Memory Based Paper 1) · Mathematics

If the system of linear equations $2 x+y-z=7$ $x-3 y+2 z=1 ; x+4 y+\delta z=k$ where $\delta, k \in R$ has infinitely many solutions, then $\delta+k$ is equal to:

  • A
    $-3$
  • Correct answer
    B
    $3$
  • C
    $6$
  • D
    $9$

Solution

For getting infinite solutions $\mathrm{D}=0, \mathrm{D}_1=$ $\mathrm{D}_2=\mathrm{D}=0$ then check all the three equations Let $\Delta=\left|\begin{array}{ccc}2 & 1 & -1 \\ 1 & -3 & 2 \\ 1 & 4 & \delta\end{array}\right|=0 \quad \Rightarrow \delta=-3$ And $\Delta_1=\left|\begin{array}{ccc}7 & 1 & -1 \\ 1 & -3 & 2 \\ k & 4 & -3\end{array}\right|=0 \Rightarrow k=6$ $\Rightarrow \delta+k=3$

Hence, the correct answer is option: 'B'.

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