If `a ,\ b ,\ c` are in proportion, then
(a) `a^2=b c`
(b) `b^2=a c`
(c) `c^2=a b`
(d) None of these

If a ,\ b ,\ c ,\ d are in proportion, then (a) a b=c d (b) a c=b d (c) a d=b c (d) None of these

If a ,b ,c ,d in R^+ and a ,b ,c,d are in H.P., then (a) a+d > b+c (b) a+b > c+d (c) a+c > b+d (d)none of these

If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a). 2a b c (b). 6a b c (c). 4a b c (d). none of these

If a, b, c are in continued proportion, prove that (a+b+c)(a-b+c)=a^(2)+b^(2)+c^(2) .

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=a b b. a^2+c^2=-a b c. a^2-c^2=-a b d. none of these

(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)) .

If a/2=b/3=c/4, then a : b : c= (a) 2:3:4 (b) 4:3:2 (c) 3:2:4 (d) None of these

In a A B C , A D is the bisector of /_B A C . If A B=6c m , A C=5c m and B D=3c m , then D C= 11. 3 c m (b) 2. 5 c m (c) 3:5c m (d) None of these

If a , b and c are in continued proportion, prove that : (i) (a^(2) + ab + b^(2))/(b^(2) + bc + c^(2)) = (a)/(c) (ii) (a^(2) + b^(2) + c^(2))/((a + b + c)^(2)) = (a - b + c)/(a + b + c) .

Given four quantities a , b , c and d are in proportion. Show that : (a - c)b^(2) : (b - d)cd = (a^(2) - b^(2) - ab) : (c^(2) - d^(2) - cd)