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

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

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

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

Identify like terms in the following: abc, ab^(2)c, acb^(2), c^(2)ab, b^(2)ac, a^(2)bc, cab^(2)

In the given figure AB is the diameter and AC is the chord of a circle such that /_BAC=30^(@) . The tangent at C intersects AB produced at D. Prove that :BC=BD.

In the given figure A, B and C are points on OP, OQ and OR respectively such that AB||PQ and BC||QR. Show that AC||PR.

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).