frac frac 1 3 frac 1 3 frac 1 3 +

A. $$\frac{2}{3}$$

B. $$\frac{3}{4}$$

C. $$\frac{{47}}{{60}}$$

D. $$\frac{{49}}{{60}}$$

Answer: Option C

Solution(By Examveda Team)

$$\frac{{\frac{1}{3}.\frac{1}{3}.\frac{1}{3} + \frac{1}{4}.\frac{1}{4}.\frac{1}{4} - 3.\frac{1}{3}.\frac{1}{4}.\frac{1}{5} + \frac{1}{5}.\frac{1}{5}.\frac{1}{5}}}{{\frac{1}{3}.\frac{1}{3} + \frac{1}{4}.\frac{1}{4} + \frac{1}{5}.\frac{1}{5} - \left( {\frac{1}{3}.\frac{1}{4} + \frac{1}{4}.\frac{1}{5} + \frac{1}{5}.\frac{1}{3}} \right)}}$$

A³ + B³ + C³ - 3ABC = (A + B + C)(A² + B² + C² - AB - BC - CA)

$$\therefore \frac{{{{\left( {\frac{1}{3}} \right)}^3} + {{\left( {\frac{1}{4}} \right)}^3} - 3.\frac{1}{3}.\frac{1}{4}.\frac{1}{5} + {{\left( {\frac{1}{5}} \right)}^3}}}{{{{\left( {\frac{1}{3}} \right)}^2} + {{\left( {\frac{1}{4}} \right)}^2} + {{\left( {\frac{1}{5}} \right)}^2} - \frac{1}{3}.\frac{1}{4} - \frac{1}{4}.\frac{1}{5} - \frac{1}{5}.\frac{1}{3}}}$$
$$ = \frac{{\left( {\frac{1}{3} + \frac{1}{4} + \frac{1}{5}} \right)\left[ {{{\left( {\frac{1}{3}} \right)}^2} + {{\left( {\frac{1}{4}} \right)}^2} + {{\left( {\frac{1}{5}} \right)}^2} - \frac{1}{3}.\frac{1}{4} - \frac{1}{4}.\frac{1}{5} - \frac{1}{5}.\frac{1}{3}} \right]}}{{\left[ {{{\left( {\frac{1}{3}} \right)}^2} + {{\left( {\frac{1}{4}} \right)}^2} + {{\left( {\frac{1}{5}} \right)}^2} - \frac{1}{3}.\frac{1}{4} - \frac{1}{4}.\frac{1}{5} - \frac{1}{5}.\frac{1}{3}} \right]}}$$
$$\eqalign{ & = \frac{{20 + 15 + 12}}{{60}} \cr & = \frac{{47}}{{60}} \cr} $$

Solution(By Examveda Team)

Join The Discussion

Read More: MCQ Type Questions and Answers