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  • The number of integral terms in the expansion of <img alt="\left(5^{1 / 2}+7^{1 / 6}\right)^{642}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%285%5E%7B1%20/%202%7D&plus;7%5E%7

The number of integral terms in the expansion of \left(5^{1 / 2}+7^{1 / 6}\right)^{642} is

Option: 1

106


Option: 2

108


Option: 3

103


Option: 4

109


Answers (1)

best_answer

T_{r+1}={ }^{642} C_r\left(5^{1 / 2}\right)^{642-r} \cdot\left(7^{1 / 6}\right)^r

Obviously, r should be a multiple of 6. 
Total numbers   \frac{642}{6}=107; But first term for  is also integral. Hence total terms are 107 + 1 = 108.
 

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