JEE Math Practice Question

Statement - 1 : $$\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r} = \left( {n + 2} \right){2^{n - 1}}.} $$ Statement - 2 : $$\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r}{x^r} = {{\left( {1 + x} \right)}^n} + nx{{\left( {1 + x} \right)}^{n - 1}}.} $$

1. A.Statement - 1 is false, Statement - 2 is true
2. B.Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1
3. C.Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1
4. D.Statement - 1 is true, Statement - 2 is false