यदि a_(1) (gt 0), a_(2), a_(3), a_(4), a_(5) एक जीपी में हैं, a_(2)+a_(4)=2a_(3)+1 तथा 3a_(2) + ...

If a_(1),a_(2),a_(3),a_(4),,……, a_(n-1),a_(n) " are distinct non-zero real numbers such that " (a_(1)^(2) + a_(2)^(2) + a_(3)^(2) + …..+ a_(n-1)^(2))x^2 + 2 (a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) + ……+ a_(n-1) a_(n))x + (a_(2)^(2) +a_(3)^(2) + a_(4)^(2) +......+ a_(n)^(2)) le 0 " then " a_(1), a_(2), a_(3) ,....., a_(n-1), a_(n) are in

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 eqiual to

It a_(1) , a_(2) , a_(3) a_(4) be in G.P. then prove that (a_(2)-a_(3))^(2) + (a_(3) - a_(1))^(2) + (a_(4) +a_(2))^(2) = (a_(1)-a_(4))^(2)

Let A and B be two sets such that n(A) = 5 and n(B) = 2 . If (a_(1), 2), (a_(2), 3), (a_(3), 2), (a_(4), 3), (a_(5), 2) are in A xx B and a_(1), a_(2), a_(3), a_(4) and a_(5) are distinct, find A and B.

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

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