`(1/3 . 1/3 . 1/3 +1/4 . 1/4 . 1/4 - 3 1/3 . 1/4 . 1/5 + 1/5 . 1/5 . 1/5)/(1/3 . 1/3 + 1/4 . 1/4 + 1/5 . 1/5 - (1/3 . 1/4 + 1/4 . 1/5 + 1/5 . 1/3))` किसके बराबर है?

Options

A. `2/3`
B. `3/4`
C. `47/60`
D. `49/60`

Answer

C

Explanation

`(1/3xx1/3xx1/3+1/4xx1/1xx1/4-3xx1/3xx1/4xx1/5+1/5xx1/5xx1/5)/(1/3xx1/3+1/4xx1/4+1/5xx1/5-(1/3xx1/4+1/4xx1/5+1/5xx1/3))`
`A^(3)+B^(3)+C^(3)-3ABC=(A+B+C)(A^(2)+B^(2)+C^(2)-AB-BC-CA)`
`:. ((1/3)^(3)+(1/4)^(3)-3xx1/3xx1/4xx1/5+(1/5)^(3))/((1/3)^(3)+(1/4)^(2)+(1/5)^(2)-1/3xx1/4-1/4xx1/5-1/5xx1/3)`
`=((1/3+1/4+1/5)|__(1/3)^(2)+(1/4)^(2)+(1/5)^(2)-1/3xx1/4-1/4xx1/5-1/5xx1/3__|)/([(1/3)^(2)+(1/4)^(2)+(1/5)^(2)-1/3xx1/4-1/4xx1/5-1/5xx1/3])`
`=(20+15+12)/60=47/60`