A) 7
B) 3
C) 5
D) None
Correct Answer: B
Solution :
| \[\therefore {{(\sqrt{3}+\sqrt{7})}^{17}}=\sum\limits_{r=0}^{17}{^{17}{{C}_{r}}={{(\sqrt{3})}^{r}}\,{{(\sqrt{7})}^{17-r}}}\] |
| \[=\sum\limits_{r=0}^{17}{^{17}}{{C}_{r}}{{3}^{\frac{r}{2}}}\,\,{{7}^{\frac{17-r}{2}}}\] |
| \[\because \]Both \[\frac{r}{2}\] & \[\frac{17-r}{2}\] can?t be integer at same so all term are irrational |
| \[\therefore \]Total irrational terms are 18 |
| \[\therefore k=3\] |
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