The value of λ , for which the lines 3 x-4 y=13,8 x-11 y=33 and 2...

For concurrency of 3 lines the determinant of coefficients of equations should be 0. i.e. \left|$$\begin{array}{ccc}3 & -4 & -13 \\ 8 & -11 & -33 \\ 2 & -3 & \lambda\end{array}$$\right|=0\Rightarrow 3(-11 \lambda-99)+4(8 \lambda+66)-13(-24+22)=0\Rightarrow-33 \lambda-297+32 \lambda+264+312-286=0\Rightarrow-\lambda-583+576=0 \Rightarrow \lambda=-7