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

If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d) , prove that: a : b = c : d .

In Figure, if A P=P B , then (a) A C=A B (b) A C=B C (c) A Q=Q C (d) A B=B C

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)

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

Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2) , and C = a^(2)c + ac^(2) - b^(2)c - bc^(2) , where a gt b gt c gt 0 and the equation Ax^(2) + Bx + C = 0 has equal roots, then a, b, c are in

(i) If a , b , c are in continued proportion, show that : (a^(2) + b^(2))/(b(a+c)) = (b(a + c))/(b^(2) + c^(2)) . (ii) If a , b , c are in continued proportion and a(b - c) = 2b , prove that : a - c = (2(a + b))/(a) . (iii) If (a)/(b) = (c)/(d) show that : (a^(3)c + ac^(3))/(b^(3)d +bd^(3)) = ((a + c)^(4))/((b + d)^(4)) .

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

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