Question

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

Answer 1

Correct Answer - 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.