Q174 / 270 · NDA 2019 (Phase 2) · Mathematics

How many terms are there in the expansion of $\left(1+2 x+x^2\right)^5+\left(1+4 y+4 y^2\right)^5$ ?

  • A
    12
  • B
    20
  • Correct answer
    C
    21
  • D
    22

Solution

$\begin{aligned} & \text { }\left(1+2 x+x^2\right)^5+\left(1+4 y+4 y^2\right)^5 \\ & =\left[(1+x)^2\right]^5+\left[(1+2 y)^2\right]^5 \\ & =(1+x)^{10}+(1+x y)^{10} \\ & \therefore \text { Total numbers of terms in each of them is } 11 \text { but constant } \\ & \text {term will be added } \\ & \therefore \quad \text { Total terms }=11+11-1 \\ & =21\end{aligned}$

Hence, the correct answer is option: 'C'.

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