The following equilibrium is established when $ ~HCl{{O}_{4}} $ is dissolved in weak acid $ HF. $
 $ HF+HCl{{O}_{4}}\rightleftharpoons ClO_{4}^{-}+{{H}_{2}}{{F}^{+}}. $
Which of the following is the correct set of conjugate acid base pairs?
(A) $ HF\text{ }and\text{ }HCl{{O}_{4}}. $
(B) $ HF\text{ }and\text{ }ClO_{4}^{-}. $
(C) $ HF\text{ }and\text{ }H{{F}_{2}}. $
(D) $ HCl{{O}_{4}}\text{ }and\text{ }{{H}_{2}}{{F}^{+}}. $

Hint: We know that this question is based on Bronsted-Lowry theory of acid and base. According to this compound that gives off ion in solution is considered as acid and compound that accepts in solution is considered as base. After giving off proton species that form is the conjugate base of the acid and after accepting proton species that form is the conjugate acid of the base.

Complete answer:
Bronsted-Lowry theory explains why compounds like ammonia act as a base and also explains why compounds like carboxylic acid show acidic behavior in alcoholic solution, which wasn’t explained by Arrhenius theory. Knowledge of conjugate acid-base pairs help us to identify the strength of acids and bases. If acid is strong its conjugate base will be weak and if acid is weak its conjugate base will be strong and vice versa. For example it is a weak acid that’s why its conjugate base is a very strong base, in fact it is a stronger base than hydroxide ion.
Conjugate acids are those acids which contain one more atom and one more positive charge than the base from which it is formed and the other hand conjugate base are those bases which contain one less atom and one more negative charge than the acid from which it is formed.
Whereas conjugate pair is made up by one conjugate acid and one conjugate base that’s why this is known by the name acid-base conjugate pair.
 $ \underset{acid}{\mathop{HX}}\,+\underset{base}{\mathop{B}}\,\rightleftharpoons \underset{\begin{smallmatrix}
 Conjugate \\
 acid
\end{smallmatrix}}{\mathop{H{{B}^{+}}}}\,+\underset{\begin{smallmatrix}
 Conjugate \\
 base
\end{smallmatrix}}{\mathop{{{X}^{-}}}}\, $
Conjugate acid base pair differ by a proton $ \left( {{H}^{+}} \right) $ ;
 $ \underset{\begin{smallmatrix}
 \text{Bronsted-Lowry } \\
 \text{Acid }
\end{smallmatrix}}{\mathop{HA}}\,+\underset{\begin{smallmatrix}
 \text{Bronsted-Lowry } \\
 \text{Acid }
\end{smallmatrix}}{\mathop{B}}\,\rightleftharpoons \underset{\begin{smallmatrix}
 \text{Conjugate } \\
 \text{Base }
\end{smallmatrix}}{\mathop{A}}\,+\text{ }\underset{\begin{smallmatrix}
 \text{Conjugate } \\
 \text{Acid }
\end{smallmatrix}}{\mathop{H{{B}^{+}}}}\,. $ ’
Therefore, the correct answer is option D.

Note:
Remember that buffer solutions achieve their property of resisting change in pH due to the presence of an equilibrium between a weak acid and its respective conjugate base or vice versa. For example it is a weak acid that’s why its conjugate base is a very strong base, in fact it is a stronger base than hydroxide ion.