The absolute value of the tangent of the difference of the angles made by the lines $4x^2 - 24xy + 11y^2 = 0$ with the $X$-axis is

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=|x|$ and $g(x)=[x-3]$ for $x \in R$,then $\{g(f(x)):-\frac{8}{5} < x < \frac{8}{5}\}$ is equal to

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix}$,then $\det(A)$ is equal to

$A$ certain radioactive substance reduces to $25\%$ of its initial value in $16$ days. Its half-life is ........ $days$.

If ${}^n{P_4} : {}^n{P_5} = 1 : 2$,then $n = $

Choose the correct option regarding the following complex compounds which follows $(F)$ and does not follow $(NF)$ the Sidgwick $EAN$ rule:
$(I) \ [(Ph_3P)_2PdCl_2]$
$(II) \ [NiBrCl(en)]$
$(III) \ Na_4[Fe(CN)_5NOS]$
$(IV) \ Cr(CO)_3(NO)_2$
$(I) - (II) - (III) - (IV)$