If $x = \tan 15^{\circ}$,$y = \operatorname{cosec} 75^{\circ}$ and $z = 4 \sin 18^{\circ}$,then :

Which of the following is concerned with eubacteria?
$(1)$ Methanogens $(2)$ Anabaena $(3)$ $N_2$ fixation $(4)$ Thermoacidophiles $(5)$ Eukaryotes $(6)$ Diatoms $(7)$ Gelatinous sheath $(8)$ Heterocyst

Let $f(x) = x^3 + bx^2 + cx + d$ where $0 < b^2 < c$. Then $f(x)$:

The equation of the parabola with focus $(0,0)$ and directrix $x+y=4$ is

If the direction ratios $(l, m, n)$ of two lines satisfy the equations $l+m+n=0$ and $mn-2ln+lm=0$,then the angle between the lines is

If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$,then the quadratic equation whose roots are $\alpha$ and $\beta$ is