Question

The number of dissimilar terms in the expansion of ${(x+\frac{1}{x}+x^2+\frac{1}{x^2})}^{15}$ are

• A. $61$
• B. $121$
• C. $255$
• D. $16$

Answer 1

The correct option is A $61$

${(x+\frac{1}{x}+x^2+\frac{1}{x^2})}^{15}{\left(\frac{x^3+x+x^4+1}{x^{30}}\right)}^{15}$

Now ${(1+x+x^3+x^4)}^{15}$will have highest power $60$ & lest power $x^0$

Total no. of dissimilar term$=60+1=61$option $A$ is lowest