Mathematics - Binomial Theorem Question with Solution | TestHub

Let$X={\left({}^{10}{C}_1\right)}^2+2{\left({}^{10}{C}_2\right)}^2+3{\left({}^{10}{C}_3\right)}^2+\dots +10{\left({}^{10}{C}_{10}\right)}^2$, where${}^{10}{C}_r, r\in \left\{\mathrm{1,2},\dots .,10\right\}$denote binomial coefficients. Then, the value of$\frac{1}{1430}X$is ______ .