If `(a - 2b - 3c + 4d)/(a + 2b - 3c - 4d) = (a - 2b + 3c - 4d)/(a + 2b + 3c + 4d), show that : `2ad = 3bc`.

If a : b = c : d , prove that : (6a + 7b) (3c - 4d) = (6c + 7d) (3a - 4b) .

If (a-2b-3c+4d)(a+2b+3c+4d) = (a+2b-3c-4d)(a-2b+3c-4d) then 2ad = "(a) 3bc (b) bc (c) 5bc (d) 2bc"

if a : b = e : d , show that : 3a + 2b : 3a - 2b = 3c + 2d : 3c - 2d .

(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)) .

Match List I ( Sub-structures) with List II (Functions and select the CORRECT answer using the codes given below the lists : (a) A - 2, B - 5 , C - 4, D - 3 (b) A - 3, B - 4 , C - 1, D - 2 (c) A - 3, B - 5 , C - 4, D - 2 (d) A - 2, B - 4 , C - 1, D - 3

If a, b, c, d satisfy the equation a + 7b + 3c + 5d = 0 , 8a + 4b + 6c + 2d = - 16 , 2a + 6b + 4c + 8d =16 and 5a + 3b + 7c + d = -16 then the value of (a + d) (b + c) =______

If (7a + 8b)/( 7c + 8d) = (7a - 8b)/(7c - 8d), prove that : (i) a:b=c:d (ii) (4a - 5b)/(4c - 5d)= (3a + 4b)/(3c + 4d)

If a: b= 2: 3, b: c= 4: 5 and c: d= 6: 7 , find : a: b: c:d .

If real numbers a, b, c, d, e satisfy a+1=b + 2 = c+ 3 = d + 4 = e + 5 = a + b + c + d + e + 3 then find the value of a^2 + b^2 + c^2 + d^2 + e^2

If a : b=3:4, then 4a :3b= (a) 4:3 (b) 3:4 (c) 1:1 (d) None of these