The equation of the bisectors of the angle between the lines represented by $3 x^2-5 x y+4 y^2=0$ is

Consider the following reaction equilibrium:
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
Initially,$1 \text{ mole}$ of $N_2$ and $3 \text{ moles}$ of $H_2$ are taken in a $2 \text{ L}$ flask. At equilibrium state,if the number of moles of $N_2$ is $0.6$,what is the total number of moles of all gases present in the flask?

$\lim _{x \rightarrow 0} \frac{\sin x \sin ^{-1} x}{x^2}$ is equal to

$A$ line is at a constant distance $c$ from the origin and meets the coordinate axes in $A$ and $B$. The locus of the centre of the circle passing through $O, A, B$ is

$A$ point object is placed at a distance of $10\,cm$ and its real image is formed at a distance of $20\,cm$ from a concave mirror. If the object is moved by $0.1\,cm$ towards the mirror,the image will shift by about:

Equilibrium constant for the reaction $H_2O_{(g)} + CO_{(g)} \rightleftharpoons H_{2(g)} + CO_{2(g)}$ is $81$. If the velocity constant of the forward reaction is $162 \ L \ mol^{-1} \ s^{-1}$,what is the velocity constant (in $L \ mol^{-1} \ s^{-1}$) for the backward reaction?