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Q.
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 $x$)
Binomial Theorem
Solution:
$(x+\frac{1}{x}+x^{2}+\frac{1}{x^{2}})^{15}=(\frac{x^{3}+x+x^{4}+1}{x^{2}})^{15}$
$=\frac{a_{o}+a_{1}x+a_{2}x^{2}+...+a_{60}x^{60}}{x^{30}}$
Hence, the total number of terms is 61.