The number of positive solution satisfying the equation `tan^(-1)((1)/(2x+1))+tan^(-1)((1)/(4x+1))=tan^(-1)(2/(x^2))` is

Match the following: List - I, List - II Let y(x)=cos(3cos^(-1)x) x in [-1,1],x!=+-(sqrt(3))/2 Then 1/(y(x)){(x^2-1)(d^2y(x))/(dx^2)+(dy(x))/(dx)} equals, 1 Let A_1,A_2, A_n(n >2) be the vertices of a regular polygon of n sides with its centre at the origin. Let vec a_k be the position vector of the point A_k ,k=1,2, ndot If |sum_(k=1)^(n-1)( vec a_k x vec a_(k+1))|=|sum_(k=1)^(n-1)( vec a_kdot vec a_(k+1))|, then the minimum value of n is, 2 If the normal from the point P(h ,1) on the ellipse (x^2)/6+(y^2)/3=1 is perpendicular to the line x+y=8 , then the value of h is, 8 Number of positive solutions satisfying the equation tan^(-1)(1/(2x)+1)+tan^(-1)(1/(4x+1))=tan^(-1)(2/(x^2)) is, 9

tan^(-1)((1)/(1+2x))+tan^(-1)((1)/(1+4x))=tan^(-1)((2)/(x^) (2)))

The root of the equation tan^(-1)((x-1)/(x+1))+tan^(-1)((2x-1)/(2x+1))=tan^(-1)((23)/(36)) is

Number of solutions of the equation tan^(-1)((1)/(a-1))=tan^(-1)((1)/(x))+tan^(-1)((1)/(a^(2)-x+1)) is :

Number of solutions of the equation tan^(-1)((1)/(a-1))=tan^(-1)((1)/(x))+tan^(-1)((1)/(a^(2)-x+1)) is :

Arithmetic mean of the non-zero solutions of the equation tan^(-1)((1)/(2x+1))+tan^(-1)((1)/(4x+1))=tan^(-1)((2)/(x^(2)))