Two of the lines represented by the equation $a y^4+b x y^3+c x^2 y^2+d x^3 y+e x^4=0$ will be perpendicular,then

Let $\overline{a}=\hat{i}+\hat{j}+\hat{k}$,$\overline{b}=\hat{i}-\hat{j}+\hat{k}$ and $\overline{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. $A$ vector $\overline{v}$ in the plane of $\overline{a}$ and $\overline{b}$,whose projection on $\overline{c}$ is $\frac{1}{\sqrt{3}}$,is given by

The equilibrium constant for the given reaction is $100$.
$N_{2(g)} + 2 O_{2(g)} \rightleftharpoons 2 NO_{2(g)}$
What is the equilibrium constant for the reaction given below?
$NO_{2(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + O_{2(g)}$

$A$ series $LCR$ circuit is connected across a source of alternating $emf$ of changing frequency and resonates at frequency $f_0$. Keeping capacitance constant,if the inductance $(L)$ is increased by $\sqrt{3}$ times and resistance $(R)$ is increased by $1.4$ times,the resonant frequency now is

If the wavelength of an electromagnetic radiation is $2000 \ \mathring{A}$,what is its energy in ergs?

$X-$ It is very important for the process of evolution.
$Y-$ Crossing over is the exchange of genetic material between two homologous chromosomes.