Directions for Questions 41 - 45: What value will come in place of the question mark (?) in the given questions?
${{?}^{2}}+{{164}^{2}}={{307}^{2}}-272$
151
189
211
259
None of these
Solution
$\begin{align}
& {{(?)}^{2}}+{{(164)}^{2}}={{(307)}^{2}}-272 \\
& \Rightarrow {{?}^{2}}={{307}^{2}}-{{164}^{2}}-272 \\
& \Rightarrow {{?}^{2}}=471\times 143-272 \\
& \Rightarrow {{?}^{2}}=67353-272 \\
& \Rightarrow ?=\sqrt{67081}=259 \\
\end{align}$