Question:

<div class="solution"><p>Max value of each <span class="math-inline">$\sin^{-1}x_i=\pi/2$</span>. Sum = <span class="math-inline">$10\times\pi/2=5\pi$</span> only if every <span class="math-inline">$x_i=1$</span>. So <span class="math-inline">$\sum x_i^2=10$</span>.</p><p><strong>Answer: (2) 10</strong></p><div class="trap-box"><strong>Trap:</strong> Bounded sum at maximum forces every term to its maximum — no averaging possible.</div><div class="key-concept"><strong>Key Concept:</strong> Extreme sum of bounded terms forces every term to the extreme</div></div>