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  • The coefficients of three successive terms in the expansion of  are 165, 330 and 462 respectiv

The coefficients of three successive terms in the expansion of (1+x)^n are 165, 330 and 462 respectively, then the value of n will be 

Option: 1

11


Option: 2

10


Option: 3

12


Option: 4

8


Answers (1)

best_answer

Let the coefficient of three consecutive terms i.e. (r+1)^{t h},(r+2)^{t h},(r+3)^{t h} in expansion of (1+x)^n are 165,330 and 462 respectively then,

Coefficient of (r+1)^{t h} term  ={ }^n C_r=165

Coefficient of (r+2)^{t h} term ={ }^n C_{r+1}=330  and 

Coefficient of (r+3)^{t h} term ={ }^n C_{r+2}=462

\begin{aligned} & \therefore \quad \frac{{ }^n C_{r+1}}{{ }^n C_r}=\frac{n-r}{r+1}=2 \\ & \text { or }{ }^{n-r=2(r+1)} \text { or } r=\frac{1}{3}(n-2) \\ & \text { and } \frac{{ }^n C_{r+2} }{{ }^nC_{r+1}}=\frac{n-r-1}{r+2}=\frac{231}{165} \end{aligned}

\begin{aligned} & \text { or } 165(n-r-1)=231(r+2) \text { or } 165 n-627=396 r \\ & \text { or } 165 n-627=396 \times \frac{1}{3} \times(n-2) \\ & \text { or } 165 n-627=132(n-2) \text { or } n=11 . \end{aligned}
 

 

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seema garhwal

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