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# If T 2 / T 3 in the Expansion of ( a + B ) N and T 3 / T 4 in the Expansion of ( a + B ) N + 3 Are Equal, Then N = (A) 3 (B) 4 (C) 5 (D) 6 - Mathematics

MCQ

If  $T_2 / T_3$  in the expansion of $\left( a + b \right)^n \text{ and } T_3 / T_4$  in the expansion of $\left( a + b \right)^{n + 3}$  are equal, then n =

#### Options

• 3

•  4

•  5

•  6

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#### Solution

5

$\text{ In the expansion} (a + b )^n , \text{ we have }$

$\frac{T_2}{T_3} = \frac{^{n}{}{C}_1 a^{n - 1} \times b^1}{^{n}{}{C}_2 a^{n - 2} \times b^2}$

$\text{ In the expansion } (a + b )^{n + 3} , \text{ we have }$

$\frac{T_3}{T_4} = \frac{^{n + 3}{}{C}_2 a^{n + 1} b^2}{^{n + 3}{}{C}_3 a^n b^3}$

$\text{ Thus, we have }$

$\frac{T_2}{T_3} = \frac{T_3}{T_4}$

$\Rightarrow \frac{^{n}{}{C}_1 a}{^{n}{}{C}_2 b} = \frac{^{n + 3}{}{C}_2 a}{^{n + 3}{}{C}_3 b}$

$\Rightarrow \frac{2}{n - 1} = \frac{3}{n + 1}$

$\Rightarrow 2n + 2 = 3n - 3$

$\Rightarrow n = 5$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Q 19 | Page 47
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