A) 0
B) 30
C) 31
D) 32
Correct Answer: D
Solution :
The general term in the expansion of\[{{(\sqrt{5}+4\sqrt{11})}^{124}}\]is \[{{T}_{r+1}}{{=}^{124}}{{C}_{r}}{{(\sqrt{5})}^{124-r}}{{(\sqrt[4]{11})}^{r}}\] \[{{=}^{124}}{{C}_{r}}\cdot {{5}^{(124-r)/2}}\cdot {{11}^{r/4}}\] For integer terms\[r=0,\,\,4,\,\,8,\,\,12,...,124\] \[\therefore \]Number of terms which are integers\[=32\]
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