For what value of $k$ does the equation $kx^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$ represent a pair of straight lines?

If the slope of one line of the pair of lines $2x^2 + hxy + 6y^2 = 0$ is thrice the slope of the other line,then $h =$

If $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ represents a pair of lines,which of the following statements is true?

If one of the lines given by the pair of lines $3x^2 + axy - 2y^2 = 0$ makes an angle of $60^{\circ}$ with the $x$-axis,then $a=$

The equation $2x^2 + 7xy + 3y^2 + 8x + 14y + \lambda = 0$ represents a pair of straight lines when $\lambda = $

If angles made by lines $x^2 - 4xy - y^2 = 0$ with the positive direction of the $x$-axis are $\theta_1$ and $\theta_2$,then the value of $\sec^2(\theta_1 + \theta_2) + |\frac{1}{\tan \theta_1} + \frac{1}{\tan \theta_2}|$ is