If `x_1, x_2, x_(20)` are in H.P. and `x_1,2,x_(20)` are in G.P., then `sum_(r=1)^(19)x_r x_(r+1)=` `76` b. `80` c. `84` d. none of these

If x_(1),x_(2),x_(3),......x2_(n) are in A.P, then sum_(r=1)^(2n)(-1)^(r+1)x_(r)^(2) is equal to

If x_(1),x_(2),….x_(20) are in H.P then x_(1)x_(2)+x_(2)x_(3)+….+x_(19)x_(20) =

If a, x_(1), x_(2) are in G.P. with common ration r, and b, y_(1), y_(2) are in G.P. with common ratio s where s-r=2 , then the area of the triangle with vertices (a, b), (x_(1), y_(1)) and (x_(2),y_(2)) is

If x^(2)+x+1=0 then sum_(r=1)^(25)(x^(r)+(1)/(x^(r)))^(2)=

If sum_(r=1)^(n)cos^(-1)x_(r)=0, then sum_(r=1)^(n)x_(r) equals to

If (x^(2)+x+1)/(1-x)=a_(0)+a_(1)x+a_(2)x^(2)+..., then sum_(r=1)^(50)a_(r) is equal to 148 b.146 c.149 d.none of these

If a, x_(1),x_(2) are in G.P with common ratio r and b, y_(1),y_(1) are in G.P with common ratio s where s-r=2 , then the area of the triangle with vertices (a,b),(x_(1),y_(1)),(x_(2),y_(2)) is

If a,x_(1),x_(2) are in G.P with common ratio r and b,y_(1),y_(2) are in G.P with common ratio s where s-r=2 , then the area of the triangle with vertices (a,b),(x_(1),y_(1)),(x_(2),y_(2)) is

If a,b,c, are in G.P. , a.x.b in A.P. and b,y,c in A.P., then : (a)/(x)+( c )/(y) = (A) 1/2 (B) 1 (C) 2 (D) none of these

if a,b,c are in G.P. and (a^(x+1))/(c^(x-1))=b^(2x) then x is equal to