A) \[^{15}{{C}_{5}}\]
B) \[^{15}{{C}_{6}}\]
C) \[^{15}{{C}_{4}}\]
D) \[^{15}{{C}_{7}}\]
Correct Answer: C
Solution :
[c] : Let \[{{T}_{r+1}}\]term containing \[{{x}^{32}}\]. Clearly,\[{{T}_{r+1}}{{=}^{15}}{{C}_{r}}{{({{x}^{4}})}^{(15-r)}}{{\left( \frac{-1}{{{x}^{3}}} \right)}^{r}}\] \[{{=}^{15}}{{C}_{r}}{{x}^{60-4r}}{{(-1)}^{r}}{{x}^{-3r}}{{=}^{15}}{{C}_{r}}{{(-1)}^{r}}{{x}^{60-7r}}\] \[\Rightarrow \]\[60-7r=32\Rightarrow 7r=28\Rightarrow r=4\] Thus, coefficient of \[{{x}^{32}}\] is \[^{15}{{C}_{4}}\].
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