A) \[-8\]
B) \[8\]
C) \[4\]
D) \[-4\]
Correct Answer: B
Solution :
Key Idea If three lines are concurrent, then the intersecting point of two lines lies on the third line. Given equation of lines are \[3x+4y+1=0\] ... (i) \[5x+\lambda y+3=0\] ... (ii) and \[2x+y-1=0\] ... (iii) The intersecting point of lines (i) and (iii) is\[(1,\,\,-1)\]. Since, the lines are concurrent, therefore the intersecting point \[(1,\,\,-1)\] lies on line (ii). \[\therefore \] \[5(1)+\lambda (-1)+3=0\] \[\Rightarrow \] \[\lambda =8\] Alternative Since, the given lines are concurrent. \[\therefore \] \[\left| \begin{matrix} 3 & 4 & 1 \\ 5 & \lambda & 3 \\ 2 & 1 & -1 \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[3(-\lambda -3)-4(-5-6)+1(5-2\lambda )=0\] \[\Rightarrow \] \[-3\lambda -9+20+24+5-2\lambda =0\] \[\Rightarrow \] \[-5\lambda +40=0\] \[\Rightarrow \] \[\lambda =8\]
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