The determinant `|{:(2,a+b+c+d,ab+cd),(a+b+c+d,2(a+b)(c+d),ab(c+d)+cd(a+b)),(ab+cd,ab(c+d)+cd(a+b),2abcd):}|=0` for

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

If (7a + 8b)/( 7c + 8d) = (7a - 8b)/(7c - 8d), prove that : a:b= c:d

Factorise : ab (c^2 + d^2) - a^(2) cd - b^(2) cd

Factorise 2(ab + cd) - a^(2) - b^(2) +c^(2) +d^(2)

If a, b, c ,d be in G.P. , show that (i) (b -c)^(2) + (c - a)^(2) +(d -b)^(2) = (a - d)^(2) (ii) a^(2) + b^(2) + c^(2) , ab + bc + cd , b^(2) + c^(2) + d^(2) are in G.P.

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

If the points (a, 0), (b,0), (0, c) , and (0, d) are concyclic (a, b, c, d > 0) , then prove that ab = cd .

The lengths of the sides CB and CA of a triangle ABC are given by a and b and the angle C is (2pi)/(3) . The line CD bisects the angle C and meets AB at D . Then the length of CD is : (a) (1)/(a+b) (b) (a^(2)+b^(2))/(a+b) (c) (ab)/(2(a+b)) (d) (ab)/(a+b)

Factorise: a^(2) + b^(2) -c^(2)-d^(2)+2ab -2cd

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)