Q118 / 180 · COMEDK 2023 (Memory Based) · Mathematics
The total number of terms in the expansion of $(x+y)^{60}+(x-y)^{60}$ is
- A60
- B61
- C30
- Correct answerD31
Solution
$\begin{aligned}(x+y)^{60}={ }^{60} C_0 x^{60}-{ }^{60} C_1 x^{59} y+\ldots . . & \\ & +{ }^{60} C_{60} y^{60} \ldots(\mathrm{i})\end{aligned}$
By adding Eq. (i) and Eq. (ii) $\begin{aligned} & (x+y)^{60}+(x-y)^{60} \\ & =\underbrace{2\left({ }^{60} C_0 x^6+{ }^{60} C_2 x^{58} y^2+\ldots+{ }^{60} C_{60} y^{60}\right)}_{31 \text { terms }} \end{aligned}$ Hence, the expansion of $(x+y)^{60}+(x-y)^{60}$ has 31 terms.
By adding Eq. (i) and Eq. (ii) $\begin{aligned} & (x+y)^{60}+(x-y)^{60} \\ & =\underbrace{2\left({ }^{60} C_0 x^6+{ }^{60} C_2 x^{58} y^2+\ldots+{ }^{60} C_{60} y^{60}\right)}_{31 \text { terms }} \end{aligned}$ Hence, the expansion of $(x+y)^{60}+(x-y)^{60}$ has 31 terms.
Hence, the correct answer is option: 'D'.