The number of all possible 5-tuples `(a_(1),a_(2),a_(3),a_(4),a_(5))` such that ` a_(1)+a_(2) sin x+a_(3) cos x + a_(4) sin 2x +a_(5) cos 2 x =0` hold for all x is

find all the possible triplets (a_(1), a_(2), a_(3)) such that a_(1)+a_(2) cos (2x)+a_(3) sin^(2) (x)=0 for all real x.

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

The number of all three element subsets of the set {a_(1),a_(2),a_(3)......a_(n)} which contain a_(3) , is

Let (a_(1),a_(2),a_(3),a_(4),a_(5)) denote a re=arrangement of (3,-5,7,4-9), then a_(1)x^(4)+a_(2)x^(3)+a_(3)x^(2)+a_(4)+a_(5)=0 has

If a_(1),a_(2),a_(3),………. are in A.P. such that a_(1) + a_(5) + a_(10) + a_(15) + a_(20) + a_(24) = 225, then a_(1) + a_(2) + a_(3) + …… a_(23) + a_(24) =

Let a_(1), a_(2), a_(3) , … be a G. P. such that a_(1)lt0 , a_(1)+a_(2)=4 and a_(3)+a_(4)=16 . If sum_(i=1)^(9) a_(i) = 4lambda , then lambda is equal to :

If a_(0) = 0.4 and a_(n+1) = 2|a_(n)|-1 , then a_(5) =

Let a_(1),a_(2),a_(3),a_(4)anda_(5) be such that a_(1),a_(2)anda_(3) are in A.P., a_(2),a_(3)anda_(4) are in G.P., and a_(3),a_(4)anda_(5) are in H.P. Then, a_(1),a_(3)anda_(5) are in

The number of increasing function from f : AtoB where A in {a_(1),a_(2),a_(3),a_(4),a_(5),a_(6)} , B in {1,2,3,….,9} such that a_(i+1) gt a_(i) AA I in N and a_(i) ne i is

If log_(e )((1+x)/(1-x))=a_(0)+a_(1)x+a_(2)x^(2)+…oo then a_(1), a_(3), a_(5) are in