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Let $a_1, a_2, \ldots, a_{100}$ be non-zero real numbers such that $a_1+a_2+\ldots+a_{100}=0$ Then,

• ✓
  $\sum \limits_{i=1}^{100} a_i 2^{a_i} > 0$ and $\sum \limits_{i=1}^{100} a_i 2^{-a_i} < 0$
• B
  $\sum \limits_{i=1}^{100} a_i 2^{a_i} \geq 0$ and $\sum \limits_{i=1}^{100} a_i 2^{-a_i} \geq 0$
• C
  $\sum \limits_{i=1}^{100} a_i 2^{a_i} \leq 0$ and $\sum \limits_{i=1}^{100} a_i 2^{-a i} \leq 0$
• D
  The sign of $\sum \limits_{i=1}^{100} a_i 2^{a_i}$ or $\sum \limits_{i=1}^{100} a_i 2^{-a_i}$ depends on the choice of $a_i^{\prime} s$