[A=[[a,b,c],[b,c,a],[c,a,b]]" ,If trace "(A)=9," and "a,b,c" are "],[" positive integers such that "ab+bc+ca=26." Let "],[A," denote the adjoint of matrix "A_(1),A_(2)" represent "],[" adjoint of "A_(1)...." and so on,if value of "det(A_(4))" is "],[M" then "]

Let A = [a_(ij)] " be a " 3 xx3 matrix and let A_(1) denote the matrix of the cofactors of elements of matrix A and A_(2) be the matrix of cofactors of elements of matrix A_(1) and so on. If A_(n) denote the matrix of cofactros of elements of matrix A_(n -1) , then |A_(n)| equals

Let (a_(1),b_(1)) and (a_(2),b_(2)) are the pair of real numbers such that 10,a,b,ab constitute an arithmetic progression. Then, the value of ((2a_(1)a_(2)+b_(1)b_(2))/(10)) is

If the equation (a_(1)-a_(2))x+(b_(1)-b_(2))y=c represents the perpendicular bisector of the segment joining (a_(1),b_(1))(a_(2),b_(2)), then 2c=

If a and b are distinct positive real numbers such that a, a_(1), a_(2), a_(3), a_(4), a_(5), b are in A.P. , a, b_(1), b_(2), b_(3), b_(4), b_(5), b are in G.P. and a, c_(1), c_(2), c_(3), c_(4), c_(5), b are in H.P., then the roots of a_(3)x^(2)+b_(3)x+c_(3)=0 are

If the equation of the locus of a point equidistant from the points (a_(1),b_(1)) and (a_(2),b_(2)) is (a_(1)-a_(2))x+(b_(1)-b_(2))y+c=0 then the value of c is

If the equation of the locus of a point equidistant from the points (a_(1),b_(1)) and (a_(2),b_(2)) is (a_(1)-a_(2))x+(b_(1)-b_(2))y+c=0 then the value of c'is:

If the equation of the locus of a point equidistant from the points (a_(1),b_(1)) and (a_(2),b_(2)) is (a-1-a_(2))x+(b_(1)-b_(2))y+c=0, then the value of c is