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  • The sum of all those terms which are rational numbers in the expansion of <img alt="\left(2^{1 / 3}+3^{1 / 4}\right)^{12}" src="https://entrancecorner.codecogs.com/gif.latex?%5Cleft%282%5E%7B1%20/%203%7D&plus;3%5E%7B1%20/%204%7D%5Cright%29%5E%7B12%7D"

The sum of all those terms which are rational numbers in the expansion of \left(2^{1 / 3}+3^{1 / 4}\right)^{12} is:
Option: 1 89
Option: 2 27
Option: 3 35
Option: 4 43

Answers (1)

best_answer

General\,\, Term=\, ^{12}C_{r}\left ( 2 \right )^{\frac{12}{3}-\frac{r}{3}}\left ( 3 \right )^{\frac{r}{4}}
For rational term , r should be a multiple of 3 and 4 \Rightarrowa  multiple of 12

\therefore r= 0,12.

Terms: r= 0\Rightarrow \, ^{12}C_{0}\cdot 2^{4-0}\cdot 3^{0}= 16\, and
   r= 12\Rightarrow \, ^{12}C_{12}\cdot 2^{0}\cdot 3^{3}= 27

Sum\, of\, terms= 16+27= 43

Posted by

Kuldeep Maurya

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