A) 35
B) 32
C) 33
D) 34
Correct Answer: C
Solution :
[c] \[{{T}_{r+1}}={{\,}^{256}}{{C}_{r}}{{(\sqrt{3})}^{256-r}}{{(\sqrt[8]{5})}^{r}}={{\,}^{256}}{{C}_{r}}{{(3)}^{\frac{256-r}{2}}}{{(5)}^{r/8}}\] Terms will be integral if \[\frac{256-r}{2}\And \frac{r}{8}\] both are +ve integer, which is so if r is an integral multiple of 8. As \[0\le r\le 256\] \[\therefore \,\,\,\,r=0,\,\,8,\,\,16,\,\,24,........256,\] total 33 values.
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