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  • The first 3 terms in the expansion of <img alt="(1+a x)^n \quad(n \neq 0)" src="https://entrancecorner.oncodecogs.com/gif.

The first 3 terms in the expansion of (1+a x)^n \quad(n \neq 0)  are 1, 6x and 16x2. Then the value of a and n are respectively

 

 

Option: 1

2 and 9


Option: 2

3 and 2


Option: 3

2/3 and 9


Option: 4

3/2 and 6


Answers (1)

best_answer

$$ \begin{aligned} & T_1={ }^n C_0=1\ \ \ \ \ \ ....(i)\\ & T_2={ }^n C_1 a x=6 x\ \ \ \ \ \ ....(ii) \\ & T_3={ }^n C_2(a x)^2=16 x^2\ \ \ \ \ \ ....(iii)\\ \end{aligned}\\ $$ From (ii),\ \ \frac{n !}{(n-1) !} a=6 \quad \Rightarrow n a=6\\\\ From (iii), \frac{n(n-1)}{2} a^2=16

Only (c) is satisfying equation (iv) and (v).

 

 

Posted by

Gautam harsolia

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