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The decreasing basic order of the following is:
(i) $C{H_3}^ - $ (ii) $O{H^ - }$ (iii) $C{H_3}CO{O^ - }$ (iv) ${H_2}O$
a) $i)\; > ii)\; > iii)\; > iv)$
b) $iv)\; > iii)\; > ii)\; > i)$
c) $iii)\; > i)\; > ii)\; > iv)$
d) $iv)\; > ii)\; > i)\; > iii)$

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Answer
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Hint:Basicity is defined as when the base can accept hydrogen ions and neutralizes an acid. It is measured on pH in the range $8 - 14$ . As we go from right to left in the periodic table the basicity increases.

Complete step by step answer:
In order to determine the basicity of these anions we will first check its acidic strength with its conjugate acids.
Conjugate acids are formed when a proton is added to the base. For example: conjugate acid of water $\left( {{H_2}O} \right) = $${H_3}{O^ + }$ . Here is the list of conjugate acids and bases as follows:
Conjugate acid of a strong base is weak, for example: $CH_3^ - $ is a strong base and $C{H_4}$ is a weak acid.
Conjugate acid of weak base is strong, for example: $N{H_3}$ is a weak base and $NH_4^ - $ is a strong acid.
Conjugate base of strong acid is weak, for example: $HCl$ is strong acid and $C{l^ - }$ is a weak base
Conjugate base of weak acid is strong, for example: $CH_4^{}$ is a weak acid and $C{H_3}^ - $ is a strong base.
Acidity is directly proportional to electronegativity. This means as we go from left to right in the period in the periodic table the acidity increases as electronegativity increases.
Also conjugate base of weak acid is strong.
Therefore, ${H_3}O < C{H_3}COOH < {H_2}O < C{H_4}$
So the basicity will be just the opposite of it. So the basicity will begin to increase as we go from right to left in the period.
Therefore, the basicity of these anions will increase as we go from right to left.
So the decreasing order of the basicity is: \[{H_2}O < C{H_3}CO{O^ - } < O{H^ - } < CH_3^ - \]
The correct answer is option B i.e $iv)\; > iii)\; > ii)\; > i)$

Note:
When the element is highly electronegative than the acidic character of that element will be more. If the electronegativity is less than the given element will be more basic. Basicity is inversely proportional to electronegativity.