Which of the following is a correct order of basicity?

The correct order of basicity is CsOH > KOH > NaOH > LiOH.

Let's understand the chemical principles behind this order step-by-step:
1. Nature of hydroxides: All the given compounds ($\mathrm{LiOH}$, $\mathrm{NaOH}$, $\mathrm{KOH}$, and $\mathrm{CsOH}$) are hydroxides of alkali metals (Group 1 elements of the periodic table).
2. Trend in ionic size: As we move down Group 1 from Lithium ($\mathrm{Li}$) to Cesium ($\mathrm{Cs}$), the atomic and ionic radii of the metals increase due to the addition of new electronic shells:

${\mathrm{Li}}^{+}<{\mathrm{Na}}^{+}<K^{+}<{\mathrm{Cs}}^{+}$

3. Lattice energy and ionization: Because the ${\mathrm{Cs}}^{+}$ ion is much larger than the ${\mathrm{Li}}^{+}$ ion, the electrostatic force of attraction between the metal cation and the hydroxide anion (${\mathrm{OH}}^{-}$) is weakest in $\mathrm{CsOH}$ and strongest in $\mathrm{LiOH}$. Therefore, the bond between the metal and the hydroxide group becomes weaker and breaks more easily as we go down the group.
4. Basicity definition: Basicity in aqueous solution depends on the ease with which a substance dissociates to release hydroxide ions (${\mathrm{OH}}^{-}$). Since $\mathrm{CsOH}$ dissociates most readily to release ${\mathrm{OH}}^{-}$ ions, it is the strongest base. Conversely, $\mathrm{LiOH}$ holds its ${\mathrm{OH}}^{-}$ ion most tightly and is the weakest base among them.

Thus, the basic strength increases down the group in the following order:

$\mathrm{LiOH}<\mathrm{NaOH}<\mathrm{KOH}<\mathrm{CsOH}$

Which is represented as:

$\mathrm{CsOH}>\mathrm{KOH}>\mathrm{NaOH}>\mathrm{LiOH}$