Verbal Reasoning - Mental Ability Questions

Modern is used to refer to something new whereas antiquated is used with respect to something old.

In other words, both terms are the opposite of each other.

From the above analysis, the missing word should be a word that represents the opposite of weak. Strong is used to with great influence. Therefore, the apt word is strong or any synonym of strong like potent, powerful, keen,...

Hence, Modern : Antiquated :: Weak : Strong.

$$\begin{gathered} 63+6=222 \\ \end{gathered}$$ 

Similarly , 253+25=15650

Here the series of the form is x2 - 1, x2 - 2, x2 - 3,...

 53 x 2 - 4 = 106 - 4 = 102

Firstly Rain falls and then Sun comes and Rainbow forms. After that Child sees the rainbow and feels Happy.