NDA 2023 Maths · Mathematics · Binomial Theorem · hard

In the expansion of (1+x)^n, the coefficients of x^3 and x^4 are in the ratio 1:2. The value of n is

Single correct option

In the expansion of

(1+x)^n

, the coefficients of

x^3

and

x^4

are in the ratio

1:2

. The value of

n

Show answer and solution

Answer: (B) $11$

Using

\dfrac{\binom n4}{\binom n3}=\dfrac{n-3}{4}

, the ratio

\binom n3:\binom n4=1:2

gives

\dfrac{n-3}4=2

, so

n=11

. Check:

\binom{11}3=165

and

\binom{11}4=330

. Reversing the ratio gives

\tfrac{n-3}{4}=\tfrac12

and

n=5

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