If `x_(1) x_(2) ......... x_(n)&(1)/(h_(1)) (1)/(h_(2)) ......(1)/(h_(n))` are two A.P.s such that `x_(3)=h_(2)=8 and x_(8)=h_(7)=20` then `x_(5)h_(10)` is

IF a_(1),a_(2),a_(3),"...."a_(10) be in AP and h_(1),h_(2),h_(3),"...."h_(10) be in HP. If a_(1)=h_(1)=2 and a_(10)=h_(10)=3 , then find value of a_(4)h_(7) .

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 f(x)=x-1, g(x)=3x , and h(x)=5/x , then f^(-1)(g(h(5))) =

Statement 1 : If two conics a_(1)x^(2)+ 2h_(1)xy+b_(1)^(2)=c_(1) , a_(2)x^(2) +2h_(2) xy +b_(2)y^(2) =c_(2) intersect in 4 concyclic points, then ( a_(1) -b_(1)) h_(2)=(a_(2)-b_(2))h_(1) . Statement 2 : For a conic to be a circle, coefficient of x^(2) = coefficient of y^(2) and coefficient of xy =0.

If f_(r)(x), g_(r)(x), h_(r) (x), r=1, 2, 3 are polynomials in x such that f_(r)(a) = g_(r)(a) = h_(r) (a), r=1, 2, 3 and " "F(x) =|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}| then F'(x) at x = a is ..... .

If int(dx)/(x+x^(2011))=f(x)+C_(1) and int(x^(2009))/(1+x^(2010))dx=g(x)+C_(2) (where C_(1) and C_(2) are constants of integration). Let h(x)=f(x)+g(x). If h(1)=0 then h(e) is equal to :

If f(x)=(h_1(x)-h_1(-x))(h_2(x)-h_2(-x))...(h_(2n+1)(x)-h_(2n+1)(-x)) and f(200)=0, then prove that f(x) is many one function.

If Delta_(f)H^(@)(C_(2)H_(4)) and Delta_(f)H^(@)(C_(2)H_(6)) are x_(1) and x_(2) kcal mol^(-1) , then heat of hydrogenation of C_(2)H_(4) is :

If x_1,x_2 …,x_(20) are in H.P and x_1,2,x_(20) are in G.P then Sigma_(r=1)^(19)x_rr_(x+1)

Let a_1,a_2 ,…. , a_10 be in A.P. and h_1,h_2 …. h_10 be in H.P. If a_1=h_1=2 and a_10 = h_10 =3 , then a_4 h_7 is :