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ISI2020-MMA: 11

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If ${ }^{n} C_{0},{ }^{n} C_{1},{ }^{n} C_{2}, \ldots,{ }^{n} C_{n}$ denote the binomial coefficients in the expansion of $(1+x)^{n}, p>0$ is a real number and $q=1-p$, then $$ \sum_{r=0}^{n} r^{2}{ }^{n} C_{r} p^{n-r} q^{r} $$ is

  1. $n p^{2} q^{2}$
  2. $n^{2} p^{2} q^{2}$
  3. $n p q+n^{2} p^{2}$
  4. $n p q+n^{2} q^{2}$
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