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If coefficients of $r$ th and $(r + 1)$ th term in the expansion of ${(3 + 2 x)}^{74}$ are equal, then $r$ is equal to:

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Correct option is C

Tr+1=74Cr374−r(2x)r⇒ coeffcient of (r + 1)th term is 74Cr374−r2r We are given 74Cr−1374−r+12r−1=74Cr374−r2r⇒ 32=74!r!(74−r)!⋅(r−1)!(75−r)!74! =75−rr⇒ 3r=150−2r⇒r=30

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If coefficients of r th and (r + 1)th term in the expansion of (3 + 2x)74 are equal, then r is equal to:

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If coefficients of $r$ th and $(r + 1)$ th term in the expansion of ${(3 + 2 x)}^{74}$ are equal, then $r$ is equal to: