Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

The two consecutive terms in the expansion of (3 + 2x)74 whose coefficients are equal, are

1) 11, 12

2) 7, 8

3) 30, 31

4) None of the above

Solution: (3) 30, 31

\(\begin{array}{l}\text \ Let \ T_{r}, \ T_{r+1} \ be \ the \ consecutive \ terms,\ whose \ coefficients \ are \ equal.\\ 74 c_{r-1}(3)^{74-r+1}(2)^{r-1}=74 c_{r}(3)^{74-r}(2)^{r}\\ \Rightarrow \frac{3}{75-r}=\frac{2}{r}\\ \Rightarrow 3 r=150-2 r\\ \Rightarrow r=30\\ \therefore 30^{\text {th }}, 31^{\text {st }} \text \ term \ have \ equal \ coefficients.\end{array} \)

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