A) is equal to 120.
B) does not exist (in R).
C) is equal to 0.
D) is equal to 15.
Correct Answer: A
Solution :
\[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,x\left[ \frac{1}{x}-\left\{ \frac{1}{x} \right\}+\frac{2}{x}-\left\{ \frac{2}{x} \right\}+.....+\frac{15}{x}-\left\{ \frac{15}{x} \right\} \right]\] \[=120-\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,x\underbrace{\left[ \left\{ \frac{1}{x} \right\}+\left\{ \frac{2}{x} \right\}+.....+\left\{ \frac{15}{x} \right\} \right]}_{finite}\] \[=120-0=120\].
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