Question

The number of integral terms in the expansion of $(\sqrt{6}+\sqrt{7}{)}^{32}$ is:

• A. 16
• B. 18
• C. 20
• D. 17

Answer 1

The correct option is D

17

$T_{r+1}={}^{32}{C}_r(\sqrt{6}{)}^{32-r}.(\sqrt{7}{)}^r$
For integral terms r should be a multiple of 2 and 32-r should be a multiple of 2
This gives r the values 0,2,...., 32
No of integral terms is 17