[" Let "a_(1),a_(2),a_(3),...,a_(10)" be in G.P.with "a_(1)>0" for "i=1,2,...,10" and "S" be the set of pairs "(r,k),],[" rkeN(the set of natural numbers) for which "log_(n)a_(1)^(2)a_(1)^(2)log_(n)a_(1)^(prime)a_(1)^(k)log_(2)a_(1)^(prime)a_(1)^(2)],[log_(2)a_(1)^(2)a_(1)^(2)log_(1)a_(1)^(2)a_(1)^(k)],[" Then the number of elements in "S" ,is: "]

Let a_(1),a_(2),a_(3), …, a_(10) be in G.P. with a_(i) gt 0 for i=1, 2, …, 10 and S be te set of pairs (r, k), r, k in N (the set of natural numbers) for which |(log_(e)a_(1)^(r)a_(2)^(k),log_(e)a_(2)^(r)a_(3)^(k),log_(e)a_(3)^(r)a_(4)^(k)),(log_(e)a_(4)^(r)a_(5)^(k),log_(e)a_(5)^(r)a_(6)^(k),log_(e)a_(6)^(r)a_(7)^(k)),(log_(e)a_(7)^(r)a_(8)^(k),log_(e)a_(8)^(r)a_(9)^(k),log_(e)a_(9)^(r)a_(10)^(k))| = 0. Then the number of elements in S is

Let a_(1),a_(2),a_(3), …, a_(10) be in G.P. with a_(i) gt 0 for i=1, 2, …, 10 and S be te set of pairs (r, k), r, k in N (the set of natural numbers) for which |(log_(e)a_(1)^(r)a_(2)^(k),log_(e)a_(2)^(r)a_(3)^(k),log_(e)a_(3)^(r)a_(4)^(k)),(log_(e)a_(4)^(r)a_(5)^(k),log_(e)a_(5)^(r)a_(6)^(k),log_(e)a_(6)^(r)a_(7)^(k)),(log_(e)a_(7)^(r)a_(8)^(k),log_(e)a_(8)^(r)a_(9)^(k),log_(e)a_(9)^(r)a_(10)^(k))| = 0. Then the number of elements in S is

Let a_(1),a_(2),a_(3), …, a_(10) be in G.P. with a_(i) gt 0 for i=1, 2, …, 10 and S be te set of pairs (r, k), r, k in N (the set of natural numbers) for which |(log_(e)a_(1)^(r)a_(2)^(k),log_(e)a_(2)^(r)a_(3)^(k),log_(e)a_(3)^(r)a_(4)^(k)),(log_(e)a_(4)^(r)a_(5)^(k),log_(e)a_(5)^(r)a_(6)^(k),log_(e)a_(6)^(r)a_(7)^(k)),(log_(e)a_(7)^(r)a_(8)^(k),log_(e)a_(8)^(r)a_(9)^(k),log_(e)a_(9)^(r)a_(10)^(k))| = 0. Then the number of elements in S is

Let a_(1), a_(2), a_(3)……, a_(10) " be in GP with " a_(i) gt " for " I = 2,2,…..,10 and S be the set of pairs (r,k), r, k in N (the set of natural numbers) for which [{:("log"_(e)a_(1)^(r)a_(2)^(k), "log"_(e)a_(2)^(r)a_(3)^(k),"log"_(e)a_(3)^(r)a_(4)^(k)),("log"_(e)a_(4)^(r)a_(5)^(k), "log"_(e)a_(5)^(r)a_(6)^(k),"log"_(e)a_(6)^(r)a_(7)^(k)),("log"_(e)a_(7)^(r)a_(8)^(k), "log"_(e)a_(8)^(r)a_(9)^(k),"log"_(e)a_(9)^(r)a_(10)^(k)):}] = 0 ltbgt Then the number of elements is S, is

If a_(n)>1 for all n in N then log_(a_(2))a_(1)+log_(a_(3))a_(2)+....log_(a_(1))a_(n) has the minimum value of

If |(1+a_(1),a_(2),a_(3)),(a_(1),1+a_(2),a_(3)),(a_(1),a_(2),1+a_(3))|=0 then a_(1)+a_(2)+a_(3)=

If log_(3)M=a_(1)+b_(1) and log_(5)M=a_(2)+b_(2) where a_(1),a_(2)in N and b_(1),b_(2)in[0,1) .if a_(1)a_(2)=6 then find the number of integral values of M.

If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in

If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in