According to CIP Sequence rule, the correct arrangement in order of decreasing priority is:
A. \[ - OH > C{H_2} > - CHO > - COOH\]
B. \[-OH > COOH > - CHO > C{H_2}OH\]
C. \[-COOH > OH > - COH > - C{H_2}OH\]
D. \[-COOH > CHO > - C{H_2}OH\; > - OH\]

Hint: The atom with the higher atomic number will have the higher priority which gives first priority to \[-OH\] , and the multiple-bonded atoms are counted thrice for triple bond by which \[-COOH\] is given priority over \[ - CHO\] .

Complete step by step answer:
CIP rule states to prioritize the four groups or atoms attached to a chiral centre according to atomic number. The highest atomic number is assigned first priority 1, and the lowest atomic number is assigned fourth priority. And if the atoms in the two groups have the same atomic number, then the priority of the group is decided by comparing the atomic number of the next atom of the group.
Thus, \[-OH\] which is bonded through hydrogen atom has the highest priority because the atomic number of oxygens is higher than that of carbon.
The next rule is that the multiple bonds are treated as separate single bonds. For example, if an atom A is double-bonded to an atom B, then A is treated as singly-bonded to two atoms. The multiple-bonded atoms are counted twice for double bond and thrice for triple bond.
Thus, \[-COOH\] is given priority over \[ - CHO\] .
So, the correct arrangement in order of decreasing priority is \[-OH > COOH > - CHO > C{H_2}OH\] according to the CIP sequence rule.

Therefore, the correct answer is option (B).

Note: A priority sequence, CIP, (Cahn Ingold Prelog) was proposed by Robert Cahn, Chris Ingold, and Vladimir Prelog in 1966. The purpose of CIP priority rule is to name a specific stereoisomer of a molecule which are compounds having the same molecular formula and same connectivity of atoms but they differ in their three-dimensional orientation.