In the given figure, x is (a) `(ab)`/(a + b)` , (b) `(ac)`/`(b + c)` (c) `(bc)`/`(b + c)`, (d)`(ac)`/`(a + c)`

If alpha,beta are the roots of the equation a x^2+b x+c=0 , then 1/(aalpha+b)+1/(abeta+b)= (a) c/(ab) (b) a/(bc) (c) b/(ac) (d) none of these

If distinct and positive quantities a ,b ,c are in H.P. then (a) b/c= (a-b)/(b-c) (b) b^2>ac (c) b^2< ac (d) a/c=(a-b)/(b-c)

If the four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) (a+b)/a , (b+c)/b , (c+d)/c are in H.P. (ii) (bc + ad) (b-c) = 2(ac^2 - b^2d)

If the four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) (a+b)/a , (b+c)/b , (c+d)/c are in H.P. (ii) (bc + ad) (b-c) = 2(ac^2 - b^2d)

In DeltaABC , if (sin A)/(c sin B) + (sin B)/(c) + (sin C)/(b) = (c)/(ab) + (b)/(ac) + (a)/(bc) , then the value of angle A is

If the four consecutive coefficients in any binomial expansion be a,b,c and d then (A) (a+b)/a,(b+c)/b,(c+d)/c are in H.P. (B) (bc+ad)(b-c)=2(ac^2-b^2d) (C) b/a,c/b,d/c are in A.P. (D) none of these

In a triangle ABC, 2B= A + C and b^(2) = ac , then (a(a+b+c))/(3bc) is

The determinant |{:(b^2-ab, b-c, bc-ac), (a b-a^2, a-b, b^2-ab) ,(b c-c a, c-a, a b-a^2):}| equals (a) a b c\ (b-c)(c-a)(a-b) (b) (b-c)(c-a)(a-b) (c) (a+b+c)(b-c)(c-a)(a-b) (d) none of these

(a-b)^3 + (b-c)^3 + (c-a)^3=? (a) (a+b+c)(a^2+b^2+c^2-ab-bc-ac) (b) 3(a-b)(b-c)(c-a) (c) (a-b)(b-c)(c-a) (d)none of these

Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c-a)(ab+bc+ca)