Mathematics - Binomial Theorem Question with Solution | TestHub

No. of terms in $(x+y{)}^{(2n-3)}\Rightarrow \left[\begin{array}{c}(2n-3+1)\\ (2n-2)\end{array}\right].$ $\therefore$ sum of all coefficients $=2^{2n-3}$ (Put $\mathrm{x}=\mathrm{y}=1$ ) $\therefore$ Arithmetic mean of all coefficients $\begin{array}{rl}& =\left(\frac{2^{2n-3}}{2n-2}\right)=16\\ & \Rightarrow 2^{2n-3}=2^5(n-1)\Rightarrow n=5\\ & \therefore P\left(2n-1,n^2-4n\right)=(9,5)\end{array}$
$\begin{array}{rl}& x+y=8\\ & \therefore PM=\left|\frac{9+5-8}{\sqrt{2}}\right|=\frac{6}{\sqrt{2}}=\frac{3\times 2}{\sqrt{2}}=3\sqrt{2}\end{array}$