If Pen < Pencil, Pencil < Book and Book > Cap, then which one of the following is always true ?

The correct option/answer is Pen < Book.

Let us analyze the given relationships step-by-step to understand why this conclusion is always true.

We are given the following inequalities:
1. $\mathrm{Pen}<\mathrm{Pencil}$
2. $\mathrm{Pencil}<\mathrm{Book}$
3. $\mathrm{Book}>\mathrm{Cap}$ (which can also be written as $\mathrm{Cap}<\mathrm{Book}$)

By combining the first two inequalities:
Since $\mathrm{Pen}<\mathrm{Pencil}$ and $\mathrm{Pencil}<\mathrm{Book}$, we can apply the transitive property of inequality.
The transitive property states that if $a<b$ and $b<c$, then $a<c$.

Applying this property here gives:
$\mathrm{Pen}<\mathrm{Book}$

This relationship is established directly and is always true regardless of the value of "Cap". Therefore, the option "Pen < Book" is the correct choice.