If the lines $ax + y + 1 = 0$,$x + by + 1 = 0$ and $x + y + c = 0$ (where $a, b$ and $c$ are distinct and different from $1$) are concurrent,then the value of $\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} = $

Let the line $L_1$ passing through the point of intersection of the lines $2x + 3y - 5 = 0$ and $4x - 5y + 7 = 0$ divide the line segment joining the points $(2, 3)$ and $(1, -1)$ in the ratio $2:1$. If the equation of $L_1$ is $ax + by = 1$,then $33(a - b) =$

The equation of the line parallel to the $y$-axis and passing through the point of intersection of the lines $ax + by + c = 0$ and $a'x + b'y + c' = 0$ is:

If the lines $x + q = 0$,$y - 2 = 0$,and $3x + 2y + 5 = 0$ are concurrent,then the value of $q$ is:

The point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ lies on the line

For all values of $\theta$,the line $(2 \cos \theta + 3 \sin \theta) x + (3 \cos \theta - 5 \sin \theta) y - (5 \cos \theta - 2 \sin \theta) = 0$ passes through which fixed point?