$A$ value of $k$ such that the straight lines $y-3kx+4=0$ and $(2k-1)x-(8k-1)y-6=0$ are perpendicular is

The slope of a line $L$ is $2$. If $m_1$ and $m_2$ are the slopes of two lines which are inclined at an angle of $\frac{\pi}{6}$ with $L$,then $m_1 + m_2 =$

The acute angle between the lines given by $y - \sqrt{3}x + 1 = 0$ and $\sqrt{3}y - x + 7 = 0$ is (in $^{\circ}$)

$A$ straight line through the point $(3, -2)$ is inclined at an angle $60^{\circ}$ to the line $\sqrt{3}x + y = 1$. If it intersects the $X$-axis, then its equation will be

Two equal sides of an isosceles triangle are along $-x+2y=4$ and $x+y=4$. If $m$ is the slope of its third side,then the sum of all possible distinct values of $m$ is:

If $3x + 4y - 5 = 0$ and $4x + ky - 8 = 0$ are two parallel lines,find the value of $k$.