A) 11, 12
B) 7, 8
C) 30, 31
D) None of these
Correct Answer: C
Solution :
General term of\[{{(3+2x)}^{74}}\]is \[{{T}_{r+1}}{{=}^{74}}{{C}_{r}}{{(3)}^{74-r}}{{2}^{r}}{{x}^{r}}\] Let two consecutive terms are\[{{T}_{r+1}}th\]and\[{{T}_{r+2}}th\]terms. According to the given condition, Coefficient of\[{{T}_{r+1}}=\]Coefficient of\[{{T}_{r+2}}\] \[\Rightarrow \] \[^{74}{{C}_{r}}{{3}^{74-r}}{{2}^{r}}{{=}^{74}}{{C}_{r+1}}{{3}^{74-(r+1)}}{{2}^{r+1}}\] \[\Rightarrow \] \[\frac{^{74}{{C}_{r+1}}}{^{74}{{C}_{r}}}=\frac{3}{2}\] \[\Rightarrow \] \[\frac{74-r}{r+1}=\frac{3}{2}\] \[\Rightarrow \] \[148-2r=3r+3\] \[\Rightarrow \] \[r=29\] Hence, two consecutive terms are 30 and 31.
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