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General Term of Binomial Expansion

If T 2/ T 3 i...

Question

If $\frac{T_{2}}{T_{3}}$ in the expansion of $(a + b)^{n}$ and $\frac{T_{3}}{T_{4}}$ in the expansion of $(a + b)^{n + 3}$ are equal, then n =

A

3

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B

4

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C

5

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D

6

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Solution

The correct option is C
5

In $(a + b)^{n}$ in $\frac{T_{2}}{T_{3}}$ = $\frac{^{n} C_{1} a^{n - 1} b}{^{n} C_{2} a^{n - 2} b^{2}}$ = $\frac{2 a}{(n - 1) b}$ and $(a + b)^{n + 3}$ $\frac{T_{3}}{T_{4}}$ = $\frac{^{n + 3} C_{2} a^{n + 1} b^{2}}{^{n + 3} C_{3} a^{n} b^{3}}$ = $\frac{3 a}{(n + 1) b}$

If these are equal then $\frac{2 a}{(n - 1) b}$ = $\frac{3 a}{(n + 1) b}$ so n = 5

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