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Statement 1 The sum of the products of n...

Statement 1 The sum of the products of numbers `pm a_(1),pma_(2),pma_(3),"....."pma_(n)` taken two at a time is `-sum_(i=1)^(n)a_(i)^(2)`.
Statement 2 The sum of products of numbers `a_(1),a_(2),a_(3),"....."a_(n)` taken two at a time is denoted by `sum_(1le iltjlen)suma_(i)a_(j)`.

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

Text Solution

Verified by Experts

The correct Answer is:
B
Statement 1 Let S be the required sum of product of numbers.
`(sum_(i=1)^(n)x_(i))^(2)=sum_(i=1)^(n)x_(i)^(2)+2sum_(1leiltjlen)sumx_(i)x_(j)`
`:.(a_(1)-a_(1)+a_(2)-a_(2)+"...."+a_(n)-a_(n))^(2)=2sum_(i=1)^(n)a_(i)^(2)+25`
`:. S=-sum_(i=1)^(n)a_(i)^(2)`
`:.` Statement 1 is true.
Statement 2 is true but not correct explanation for Statement 1.
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