Question

The number of non-zero terms in the expansion of $(\sqrt{7}+1{)}^{75}-(\sqrt{7}-1{)}^{75}$ is

• A. $36$
• B. $37$
• C. $38$
• D. $39$

Answer 1

The correct option is A $36$

$(\sqrt{7}+1{)}^{75}-(\sqrt{7}-1{)}^{75}$

$\Rightarrow \sqrt{7}{(1+\frac{1}{\sqrt{7}})}^{75}-\sqrt{7}{(1-\frac{1}{\sqrt{7}})}^{75}$

$\Rightarrow$ middle term = no of non zero terms=

$=36$