Question

The number of distinct terms in the expansion of ${(x+\frac{1}{x}+x^2+\frac{1}{x^2})}^{15}$ is/are (with respect to different power of $x$)

• A. 255
• B. 61
• C. 127
• D. none of these

Answer 1

Answer: (B)

61

We have to expand ${(x+\frac{1}{x}+x^2+\frac{1}{x^2})}^{15}$

The Highest power of $x$ in the expansion is $2\times 15=30$

The least power of $x$ in the expansion is $2\times (-15)=-30$

The expansion of given expression covers all powers of $x$ between them

Therefore number of distinct terms in the expansion is $30+30+1=61$