NDA 2025 Maths · Mathematics · Binomial Theorem · medium

In the expansion of (1+2x)^7, the ratio of the coefficient of x^3 to the coefficient of x^2 is

Single correct option

In the expansion of

(1+2x)^7

, the ratio of the coefficient of

x^3

to the coefficient of

x^2

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Answer: (A) $\dfrac{10}{3}$

Coefficient of

x^3

\binom73 2^3=280

and of

x^2

\binom72 2^2=84

. The ratio is

\frac{280}{84}=\frac{10}3

. Leaving out the powers of

2

gives

\frac{35}{21}=\frac53

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