A) Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement -1
B) Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
C) Statement -1 is true, Statement -2 is false.
D) Statement -1 is false, Statement -2 is true.
Correct Answer: C
Solution :
\[{{S}_{1}}=\sum\limits_{j=1}^{10}{j(j-1)}\frac{10!}{j(j-1)(j-2)!(10-j)!}\] \[=90\sum\limits_{j=2}^{10}{\frac{8!}{(j-2)!(8-(j-2))!}}=90\times {{2}^{8}}\] \[{{S}_{2}}=\sum\limits_{j=1}^{10}{j}\frac{10!}{j(j-1)!(9-(j-1))!}\] \[=10\sum\limits_{j=1}^{10}{\frac{9!}{(j-1)!(9-(j-1))!}}=10\times {{2}^{9}}\] \[{{S}_{3}}=\sum\limits_{j=1}^{10}{[j(j-1)+j]}\frac{10!}{j(10-j)!}\]\[=\sum\limits_{j=1}^{10}{{{(j-1)}^{10}}{{C}_{j}}}\] \[=\sum\limits_{j=1}^{10}{{{(j)}^{10}}{{C}_{j}}}={{90.2}^{8}}+{{10.2}^{9}}={{110.2}^{8}}={{55.2}^{9}}\] Hence statement 1 is true, statement 2 is falseYou need to login to perform this action.
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