Statement I : _ r =0 ^ n ( r +1) ^ n C _ r =( n +2) 2^ n -1 Statement II : _ r =0 ^ n ( r…
Mathematics · JEE Main · NTA Exams — Binomial Theorem And Its Simple Applications
Statement I : \(\sum_{\mathrm{r}=0}^{\mathrm{n}}(\mathrm{r}+1) \cdot{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=(\mathrm{n}+2) 2^{\mathrm{n}-1}\)
Statement II : \(\sum_{\mathrm{r}=0}^{\mathrm{n}}(\mathrm{r}+1)^{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \cdot \mathrm{x}^{\mathrm{r}}=(1+\mathrm{x})^{\mathrm{n}}+\mathrm{nx}(1+\mathrm{x})^{\mathrm{n}-1}\)
Statement II : \(\sum_{\mathrm{r}=0}^{\mathrm{n}}(\mathrm{r}+1)^{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \cdot \mathrm{x}^{\mathrm{r}}=(1+\mathrm{x})^{\mathrm{n}}+\mathrm{nx}(1+\mathrm{x})^{\mathrm{n}-1}\)
- Statement I is false, Statement II is true
- Statement I is true, Statement II is true;
Statement II is a correct explanation for Statement I - Statement I is true, Statement II is true;
Statement II is not a correct explanation for Statement I - Statement I is true, Statement II is false
Answer
(B) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
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