Respuesta :
It is A, my friend. I have taken the test and got it right ;)
Solution:
A is the correct option.
Explanation:
We have been given that [tex](2r - 3s)^{12}[/tex]
The [tex]r^{th}[/tex] term of a binomial expansion [tex](a+b)^n[/tex] is given by
[tex]t_r=^{n}C_{r-1}a^{n-r+1}b^{r-1}[/tex]
For the given binomial expansion, we have
[tex]a=2r,b=-3s,r=2,n=12[/tex]
On plugging this value in the above formula, we have
[tex]t_2=^{12}C_{2-1}(2r)^{12-2+1}(-3s)^{2-1}\\\\t_2=^{12}C_1 (2r)^{11}(-3s)^{1}\\\\t_2=\frac{12!}{1!11!}(2)^{11}r^{11}(-3)s\\\\t_2=12\cdot (2)^{11}(-3)r^{11}s\\\\t_2=-73728r^{11}s[/tex]
Therefore, the second term is -73728r^11 s
A is the correct option.
