Q. If $p,q,r$ are any real numbers, then
A) max $(p,q) = \max{\ (p,q,r)}$
B) $\min{(p,q) = \frac{1}{2}(P + q - |p - q|)}$
C) $\max{(p,q) < \min{(p,q,r)}}$
D) $\max{(p,q) = \frac{1}{2}(p + q - |p - q|)}$
Explanation
(b)
$|p - q| = \left\{ \begin{matrix}
p - q,p \geq q \\
q - p,\ p < q
\end{matrix} \right.\$
$\therefore\min{(p,q) = \left\{ \begin{matrix}
p,\ p < q \\
q,\ q < p
\end{matrix} \right.\ }$
$\Rightarrow RHS = \frac{1}{2}\left( p + q - |p - q| \right),if\ p > q$
$\Rightarrow \frac{1}{2}(p + q - p + q) = q$
and LHS $\min{(p,q) = q}$
$\therefore\min{(p,q) = \frac{1}{2}(p + q - |p - q|)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.