The value of $\lambda$ , if the lines $3x+4y+10=0$ , $8x-11y+33=0$  and $2x-3y+\lambda =0$  are concurrent.

The given lines are concurrent if $\left|\begin{array}{ccc}3& 4& 10\\ 8& -11& 33\\ 2& -3& \lambda \end{array}\right|=0$

$3\left(-11\lambda +99\right)-4\left(8\lambda +66\right)+10\left(-24+22\right)=0$

$-33\lambda +297-32\lambda -254-20=0$

$-65\lambda +13=0$

$-65\lambda =-13$

$\lambda =\frac{13}{65}=\frac{1}{5}$