Explanation

(c)
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 $T_{r + 2}$
$\Longrightarrow \ ^{74}C_{r}3^{74 - r}2^{r} = \ ^{74}C_{r + 1}3^{74 - (r + 1)}2^{r + 1}$
$\Longrightarrow \frac{\ ^{74}C_{r + 1}}{\ ^{74}C_{r}} = \frac{3}{2} \Longrightarrow \frac{74 - r}{r + 1} = \frac{3}{2}$
$\Longrightarrow 148 - 2r = 3r + 3 \Longrightarrow r = 29$
Hence, two consecutive terms are 30 and 31.