If $2x + 3y + 12 = 0$ and $x - y + 4\lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $\lambda$ is equal to

In the extraction of aluminium:
Process $X$: applied for red bauxite to remove iron oxide (chief impurity).
Process $Y$: (Serpeck's process) applied for white bauxite to remove $Z$ (chief impurity). Then,process $X$ and impurity $Z$ are:

Which of the following has the maximum boiling point?

If $a = \frac{1-i \sqrt{3}}{2}$,then the correct matching of List-$I$ with List-$II$ is:

List-$I$	List-$II$
$(i) \ a \bar{a}$	$(A) -\frac{\pi}{3}$
$(ii) \ \arg \left(\frac{1}{\bar{a}}\right)$	$(B) -i \sqrt{3}$
$(iii) \ a-\bar{a}$	$(C) \frac{2i}{\sqrt{3}}$
$(iv) \ \operatorname{Im}\left(\frac{4}{3a}\right)$	$(D) 1$
	$(E) \frac{\pi}{3}$
	$(F) \frac{2}{\sqrt{3}}$

Water is conveyed through a uniform tube of $8 \text{ cm}$ in diameter and $3140 \text{ m}$ in length at the rate of $2 \times 10^{-3} \text{ m}^3/\text{s}$. The pressure required to maintain the flow is (Viscosity of water $= 10^{-3} \text{ SI units}$):

If the charge on the capacitor is increased by $2 \ C$,the energy stored in it increases by $21 \%$. The original charge on the capacitor is: (in $C$)