If `a_(1) and a_(2)` aare two non- collineaar unit vectors and if `|a_(1)+a_(2)|=sqrt(3),` ,then value of `(a_(1)-a_(2)).(2a_(1)-a_(2))` is

If vec(a_(1)) and vec(a_(2)) are two non-collinear unit vectors and if |vec(a_(1)) + vec(a_(2))|=sqrt(3) , then the value of (vec(a_(1))-vec(a_(2))). (2 vec(a_(1))+vec(a_(2))) is :

If vec A_(1) and vec A_(2) are two non-collinear unit vectors and if |vec A_(1)+vec A_(2)|=sqrt(3) then the value of (vec A_(1)-vec A_(2))*(2vec A_(1)+vec A_(2)) is

A_(1) and A_(2) are two vectors such that |A_(1)| = 3 , |A_(2)| = 5 and |A_(1)+A_(2)| = 5 the value of (2A_(1)+3A_(2)).(2A_(1)-2A_(2)) is

If a_(1)=2 and a_(n)-a_(n-1)=2n(n>=2), find the value of a_(1)+a_(2)+a_(3)+....+a_(20)

If a_(1),a_(2),a_(3),a_(4) are positive real numbers such that a_(1)+a_(2)+a_(3)+a_(4)=16 then find maximum value of (a_(1)+a_(2))(a_(3)+a_(4))

If a_(1), a_(2), a_(3).... A_(n) in R^(+) and a_(1).a_(2).a_(3).... A_(n) = 1 , then minimum value of (1 + a_(1) + a_(1)^(2)) (a + a_(2) + a_(2)^(2)) (1 + a_(3) + a_(3)^(2))..... (1 + a_(n) + a_(n)^(2)) is equal to

If a_(i)gt0 for i u=1, 2, 3, … ,n and a_(1)a_(2)…a_(n)=1, then the minimum value of (1+a_(1))(1+a_(2))…(1+a_(n)) , is

If a_(n) is a geometric sequence with a_(1)=2 and a_(5)=18, then the value of a_(1)+a_(3)+a_(5)+a_(7) is equal to

If a_(1),a_(2),a_(3)….a_(n) are positive and (n-1)s = a_(1)+a_(2)+….+ a_(n) then prove that a_(1),a_(2),a_(3)…a_(n) ge (n-1)^(n)(s-a_(1))(s-a_(2))….(s-a_(n))

Let a_(1),a_(2),a_(3),...,...,a_(49),a_(50) are in airthmetic progression. If a_(1)=4 and a_(50)=144 ,then the value of , (1)/(sqrt(a_(1))+sqrt(a_(2)))+(1)/(sqrt(a_(2))+sqrt(a_(3)))+(1)/(sqrt(a_(3))+sqrt(a_(4)))cdots+(1)/(sqrt(a_(49))+sqrt(a_(50))) is equal to