A) \[\frac{13}{6}a-\frac{1}{12}{{b}^{3}}-\frac{1}{20}{{c}^{3}}\]
B) \[\frac{13}{6}a-\frac{21}{20}{{b}^{3}}+\frac{25}{12}{{c}^{3}}\]
C) \[\frac{13}{6}{{a}^{2}}+\frac{5}{12}{{b}^{3}}-\frac{1}{20}{{c}^{3}}\]
D) \[\frac{23}{6}{{b}^{2}}+\frac{25}{12}{{a}^{3}}-\frac{1}{20}{{c}^{3}}\]
Correct Answer: C
Solution :
(c) \[\left( \frac{{{a}^{2}}}{2}-\frac{{{b}^{3}}}{3}-\frac{{{c}^{3}}}{4} \right)+\left( \frac{2{{a}^{2}}}{3}-\frac{3{{b}^{3}}}{4}-\frac{4{{c}^{3}}}{5} \right)\]\[+\left( {{a}^{2}}+{{b}^{3}}+{{c}^{3}} \right)\] \[={{a}^{2}}\left( \frac{1}{2}+\frac{2}{3}+1 \right)+{{b}^{3}}\left( -\frac{1}{3}-\frac{3}{4}+1 \right)+{{c}^{3}}\left( -\frac{1}{4}-\frac{4}{5}+1 \right)\]\[=\frac{13}{6}{{a}^{2}}-\frac{{{b}^{3}}}{12}-\frac{{{c}^{3}}}{20}\]
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