If $\theta_1$ and $\theta_2$ are the acute angles between the pairs of lines $3x^2 - 7xy + 4y^2 = 0$ and $6x^2 - 5xy + y^2 = 0$ respectively,then:

If the lines given by $(x^2+y^2) \sin^2 \alpha = (x \cos \alpha - y \sin \alpha)^2$ are perpendicular to each other,then $\sin^2 \alpha + \tan^2 \alpha = $

If the slopes of both the lines given by $x^2 + 2hxy + 6y^2 = 0$ are positive and the angle between these lines is $\operatorname{Tan}^{-1}\left(\frac{1}{7}\right)$,then find the value of $h$.

If $\theta$ is the acute angle between the lines represented by the equation $x^2 - 3xy + 2y^2 = 0$, then $\frac{3 \sin \theta + 2 \cos \theta}{3 \sin \theta - 2 \cos \theta} = $

The pair of lines $l x^2 + 2(l+m) x y + m y^2 = 0$ lies along two diameters of a circle and divides the circle into $4$ sectors. If the area of the bigger sector is $5$ times the area of the smaller sector,then $\frac{l m}{(l+m)^2} = $

The angle between the pair of lines given by the equation $x^2 + 2xy - y^2 = 0$ is