Question bank/JEE Main/Mathematics
JEE MainMathematicsEasyStraight Lines
Find the number of the values of k for which the lines
are concurrent
k dk eku Kkr dhft, tcfd js[kk,sa
laxkeh
Show answer and solution
$\Delta = 0 \Rightarrow \left| \begin{matrix}
2\ \ \ \ k\ \ \ \ 3 \\
3\ \ \ \ 3\ \ \ \ k \\
k\ \ \ \ 2\ \ \ \ 2
\end{matrix} \right| = 0 \Rightarrow k^{3} - 19k + 30 = 0 \Rightarrow k = 2,3, - 5$
For k = 2, lines are parallel. k = 2
2\ \ \ \ k\ \ \ \ 3 \\
3\ \ \ \ 3\ \ \ \ k \\
k\ \ \ \ 2\ \ \ \ 2
\end{matrix} \right| = 0 \Rightarrow k^{3} - 19k + 30 = 0 \Rightarrow k = 2,3, - 5$
For k = 2, lines are parallel. k = 2
Source: Grass-G / M-25 Mathematics Paper 7 Jan.docx
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