If rth term in the expansion of (2x^ 2 -1 x )^ 12 is without x, t… - Vidyadip

MCQ

If rth term in the expansion of $\Big(2\text{x}^{2}-\frac{1}{\text{x}}\Big)^{12}$ is without x, then r is equal to:

A
8
B
7
✓
9
D
10

✓

Answer

Correct option: C.

9

rth term in the given expansion is ${^\text{20}}\text{C}_{\text{r}-1}\Big(2\text{x}^{2}\Big)^{12-\text{r}+1}\Big(\frac{-1}{\text{x}}\Big)^{\text{r}-1}$
$=(-1)^{\text{r}-1}\ {^\text{20}}\text{C}_{\text{r}-1}\ 2^{13-\text{r}}\ \text{x}^{26-2\text{r}-\text{r}+1}$
For this term to be independent of x, we must have,
$27-3\text{r}=0$
$\Rightarrow \text{r}=9$
Hence, the term in the expansion is independent.

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