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Let S(1) = sum(j=1)^(10) j(j-1).""^(10)...

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 xx 2^(9)`.
Statement 2 : `S_(1) = 90 xx 2^(8)` and `S_(2) = 10 xx 2^(8)`.

A

Statement-1 is ture ,Statement-2 is treu, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is ture ,Statement-2 is treu, Statement-2 is not a correct explanation for Statement-1

C

Statement-1 is true ,Statement-2 is false

D

Statement-1 is true ,Statement-2 is ture

Text Solution

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The correct Answer is:
B
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S_(1)= sum_(j=1)^(10) j (j -1)""^(10)C_(j) and S_(2)= sum_(j=1)^(10)j.""^(10)C_(j) . Statement-1 S_(3) = 50xx2^(9) . Statement-2 S_(1) = 90xx2^(8) and S_(2) = 10 xx 2^(8)

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"dot Statement-1: S_3=""55xx2^9 Statement-2: S_1=""90xx2^8a n d""S_2=""10xx2^8 . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Let S_1=sum_(j=1)^(10)j(j-1)^(10)C_j ,""S_2=sum_(j=1)^(10)j""^(10)C_i "andS"_"3"=sum_(j=1)^(10)j^2""^("10")"C"_"j"dot Statement-1: S_3=""55xx2^9 Statement-2: S_1=""90xx2^8a n d""S_2=""10xx2^8 . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

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