The slope of the line through the origin which makes an angle of 30$$^\circ$$ with the positive direction of Y-axis measured anticlockwise is :

If the equation $$k x y+5 x+3 y+2=0$$ represents a pair of lines, then $$k=$$

If $$(a,-2 a), a>0$$ is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of the line is

If the angle between the lines given by the equation $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0, \lambda \geq 0$$, is $$\tan ^{-1}\left(\frac{1}{3}\right)$$, then $$\lambda=$$