Question:Let $S_{1}=\sum_{j=1}^{10} j(j-1)^{10} C_{J}, S_{2}=\sum_{j=1}^{10} j^{10} C_{j}$ and $S_{3}=\sum_{j=1}^{10} j^{2}{ }^{10} C_{j}$.
Statement -1: $S_{3}=55 \times 2^{9}$.
Statement – 2: $S_{1}=90 \times 2^{8}$ and $S_{2}=10 \times 2^{8}$.
Statement $-1$ is true, Statement $-2$ is true; Statement 2 is not a correct explanation for Statement $-1$.
Statement $-1$ is true, Statement $-2$ is false.
Statement $-1$ is false, Statement $-2$ is true .
Statement $-1$ is true, Statement 2 is true ; Statement $-2$ is a correct explanation for Statement $-1$.
Correct Option: 2
JEE Main Previous Year 1 Question of JEE Main from Mathematics Binomial Theorem and its Simple Applications chapter.
JEE Main Previous Year 2010
Solution:
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