" 12.If "[" 1"(x-11)/(b-A_(51))}-(bar(A_(1)-a))],[" If "a>0" ,then minimum value of "a+2a^(2)+a^(3)+15+a^(-1)+a^(-3)+a^(-4)" is "]

If a_(1)+a_(2)+a_(3)+a_(4)+a_(5)...+a_(n) for all a_(i)>0,i=1,2,3dots n. Then the maximum value of a_(1)^(2)a_(2)a_(3)a_(4)a_(5)..a_(n) is

If a_(1), a_(2), a_(3), ……. , a_(n) are in A.P. and a_(1) = 0 , then the value of (a_(3)/a_(2) + a_(4)/a_(3) + .... + a_(n)/a_(n - 1)) - a_(2)(1/a_(2) + 1/a_(3) + .... + 1/a_(n - 2)) is equal to

If (1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15), then the value of sum_(r=1) ^(15) r . (a_(r))/(a _(r-1)) is-

If (1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15), then the value of sum_(r=1) ^(15) r . (a_(r))/(a _(r-1)) is-

If a_(i)>0AA i=1,2,3,...50 and a_(1)+a_(2)+a_(3)+...+a_(50)=50 then the minimum value of (1)/(a_(1))+(1)/(a_(2))+(1)/(a_(3))+...+(1)/(a_(50))=

(1+x)^(5)=a_(0)+a_(1)x+a2x2+a_(3)x^(3)+a_(4)x^(4)+a_(5)x^(5) then the value of (a_(0)-a_(2)+a_(4))^(2)+(a_(1)-a_(3)+a_(5))^(2) is equal to 243 b.32 c.1 d.2^(10)

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_(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