JEE Math Practice Question

Let $${s_1} = \sum\limits_{j = 1}^{10} {j\left( {j - 1} \right){}^{10}} {C_j}$$, $${{s_2} = \sum\limits_{j = 1}^{10} {} } j.{}^{10}{C_j}$$ and $${{s_3} = \sum\limits_{j = 1}^{10} {{j^2}.{}^{10}{C_j}.} }$$ Statement-1 : $${{S_3} = 55 \times {2^9}}$$. Statement-2 : $${{S_1} = 90 \times {2^8}}$$ and $${{S_2} = 10 \times {2^8}}$$.

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