If the slope of one line of $ax^2 + 4xy + y^2 = 0$ is $3$ times the other,then the value of $a$ is:

If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

The plant part which consists of two generations,one within the other,is:

The differential equation of the family of parabolas with the focus at the origin and the axis along the $X$-axis is:

The enthalpy of formation of ammonia is $-46.0 \, kJ \, mol^{-1}$. The enthalpy change for the reaction $2NH_{3(g)} \longrightarrow N_{2(g)} + 3H_{2(g)}$ is ..... $kJ \, mol^{-1}$.

$A$ liquid drop having surface energy $E$ is spread into $512$ droplets of the same size. The final surface energy of the droplets is (in $E$)