Suppose 2-p, p, 2-alpha, alpha are the | vedclass

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Question

$2-p, p, 2-\alpha, \alpha$

Binomial coefficients are

$\begin{array}{ll} & { }^n C_r,{ }^n C_{r+1},{ }^n C_{r+2},{ }^n C_{r+3} 	ext { respec

Vedclass · Accepted Answer

$4$

Vedclass · Answer

$2-p, p, 2-\alpha, \alpha$

Binomial coefficients are

$\begin{array}{ll} & { }^n C_r,{ }^n C_{r+1},{ }^n C_{r+2},{ }^n C_{r+3} 	ext { respectively } \ \Rightarrow & { }^n C_r+{ }^n C_{r+1}=2 \ \Rightarrow & { }^{n+1} C_{r+1}=2 \quad \ldots \ldots .(1) \ & \quad 	ext { Also, } \quad{ }^n C_{r+2}+{ }^n C_{r+3}=2 \ \Rightarrow & { }^{n+1} C_{r+3}=2 \quad \ldots \ldots .(2) \ & \quad 	ext { From }(1) 	ext { and (2) } \ & { }^{n+1} C_{r+1}={ }^{n+1} C_{r+3}\end{array}$

$\begin{aligned} \Rightarrow \quad & 2 \mathrm{r}+4=\mathrm{n}+1 \ & \mathrm{n}=2 \mathrm{r}+3 \ & { }^{2 \mathrm{r}+4} \mathrm{C}_{\mathrm{r}+1}=2\end{aligned}$
Data Inconsistent

Suppose $2-p, p, 2-\alpha, \alpha$ are the coefficient of four consecutive terms in the expansion of $(1+x)^n$. Then the value of $p^2-\alpha^2+6 \alpha+2 p$ equals

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