If the constant term in Binomial expansion of (2x^r+1x^2)^10 is 180, then r is equal to An…

Question

If the constant term in Binomial expansion of $\left(2x^r+\dfrac{1}{x^2}\right)^{10}$ is 180, then $r$ is equal to

Answer: 8

Accepted Answer

$$T_{k+1}=\binom{10}{k}(2x^r)^{10-k}x^{-2k}=\binom{10}{k}2^{10-k}x^{10r-rk-2k}$$

Constant term: $10r-rk-2k=0\Rightarrow k=\dfrac{10r}{r+2}$

Testing $r=8$: $k=\dfrac{80}{10}=8$, and $\binom{10}{8}2^{2}=45\times4=180$

$r=8$

Solutions · 1