The angle between the lines represented by $x^2 + xy = 0$ is .....$^o$

Four different pairs of lines are given in List-$I$ and the cosine of the angle between every pair of lines is given in List-$II$. Match the following:

List-$I$	List-$II$
$(A)$ $5x^2 + 2\sqrt{7}xy - y^2 = 0$	$(I)$ $\frac{\sqrt{3}}{2}$
$(B)$ $x^2 + \sqrt{11}xy + 2y^2 = 0$	$(II)$ $\frac{1}{2\sqrt{3}}$
$(C)$ $x^2 + 2\sqrt{2}xy + y^2 = 0$	$(III)$ $\frac{1}{2}$
$(D)$ $3x^2 + 4\sqrt{2}xy + y^2 = 0$	$(IV)$ $\frac{2}{3}$
	$(V)$ $\frac{1}{\sqrt{2}}$

The correct match is:

If $(m+3n)(3m+n)=4h^2$,then the acute angle between the lines represented by $mx^2+2hxy+ny^2=0$ is

The condition for the two lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ to be perpendicular is:

$ax^2-4xy-2y^2=0$ represents a pair of lines. If $\theta$ is the angle between these lines,$\cos \theta=\frac{1}{5}$ and the possible values of '$a$' are $a_1$ and $a_2$ $(a_1 < a_2)$,then $a_1+3a_2=$

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} = $