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

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