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