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The decreasing basic order of the following is:
i). ${{\text{F}}^{\text{ - }}}$
ii). ${\text{C}}{{\text{l}}^{\text{ - }}}$
iii). ${\text{B}}{{\text{r}}^{\text{ - }}}$
iv). ${{\text{I}}^{\text{ - }}}$

Answer
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Hint: As these are halides, the basicity of halides depends upon the electronegativity. The order can be calculated using the fact that the order of conjugate base will be opposite to the order of acidic strength.

Complete step by step answer:
According to trends of the periodic table, as we go down the group the size of an atom increases. Similarly, the size of halide ions increases as we move down the group. It means the order of size will be:
${\text{I > Br > Cl > F}}$ .
Also, as the size increases, the bond dissociation energy decreases. It means that it will be easier to break ${\text{HI}}$ bond than ${\text{HF}}$ bond. So, the order will be:
${\text{HI > HBr > HCl > HF}}$.
The above order tells that fluorine being the most electronegative atom will make weak acid. So, ${\text{HI}}$ will be the strong acid due to the low electronegativity of iodine it will easily lose the hydrogen ion.
 Basically, the order of acidic strength will be:
${\text{HI > HBr > HCl > HF}}$.
The respective conjugate bases of the above acids will be ${{\text{I}}^{\text{ - }}}{\text{,B}}{{\text{r}}^{\text{ - }}}{\text{,C}}{{\text{l}}^{\text{ - }}}{\text{,}}{{\text{F}}^{\text{ - }}}$.
The order of conjugate bases will be the exact reverse of the order of the acidic strength.
${{\text{F}}^{\text{ - }}}{\text{ > C}}{{\text{l}}^{\text{ - }}}{\text{ > B}}{{\text{r}}^{\text{ - }}}{\text{ > }}{{\text{I}}^{\text{ - }}}$.
Hence option (A) is correct.

Note:
Conjugate bases are those when an acid loses a hydrogen ion. Remember, the order of conjugate bases of halogen acids is the reverse of their order of acidic strengths. Moreover, least is the electronegativity more easily the acid can lose hydrogen to form a conjugate base