Q94 / 180 · COMEDK 2024 (Memory Based) · Mathematics

The coefficient of $x^{24}$ in the expansion of $\left(1-x^5\right)^{10}$ is

  • Correct answer
    A
    0
  • B
    ${ }^{10} C_5$
  • C
    ${ }^{10} C_4$
  • D
    110

Solution

$\begin{aligned}<br/>& \text { } \because \text { General term of }(x+y)^n={ }^n C_r(x)^{n-r}(y)^r \\<br/>& \Rightarrow \quad T_{r+1}={ }^{10} C_r(1)^{10-r}\left(-x^5\right)^r={ }_{}^{10} C_r(-1)^r(x)^{5 r} \\<br/>& \therefore \quad 5 r=24 \Rightarrow r=4.8<br/>\end{aligned}$
$\therefore r$ cannot be in fraction means no such terms are possible.
$\therefore$ Coefficient of $x^{24}=0$

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

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