The resonance point in `X_(L) - f` and `X_(C ) - f` curves is

The figure shows variation of R,X_(L) and X_(C) with frequency f in a series L,C,R circuit. Then for what frequency point, the circuit is inductive ?

If the tangent to the curve , y =f (x)= x log_(e)x, ( x gt 0) at a point (c, f(c)) is parallel to the line - segment joining the point (1,0) and (e,e) then c is equal to :

At an extreme point of a function f(X) the tangent to the curve is

If y=f(x) is a curve and if there exists two points A(x_(1),f(x_(1))) and B(x_(2),f(x_(2))) on it such that f'(x_(1))=-(1)/(f(x_(2))), then the tangent at x_(1) is normal at x_(2) for that curve. Now,answer the following questions.

If y=f(x) is a curve and if there exists two points A(x_(1),f(x_(1)) and B(x_(2),f(x_(2)) on it such that f'(x_(1))=-(1)/(f'(x_(2)))=(f(x_(2))-f(x_(1)))/(x_(2)-x_(1)) , then the tangent at x_(1) is normal at x_(2) for that curve. Now, anwer the following questions. Number of such lines on the curve y^(2)=x^(3) , is

If y=f(x) is a curve and if there exists two points A(x_(1),f(x_(1)) and B(x_(2),f(x_(2)) on it such that f'(x_(1))=-(1)/(f'(x_(2)))=(f(x_(2))-f(x_(1)))/(x_(2)-x_(1)) , then the tangent at x_(1) is normal at x_(2) for that curve. Now, anwer the following questions. Number of such lines on the curve y^(2)=x^(3) , is

If y=f(x) is a curve and if there exists two points A(x_(1),f(x_(1)) and B(x_(2),f(x_(2)) on it such that f'(x_(1))=-(1)/(f'(x_(2)))=(f(x_(2))-f(x_(1)))/(x_(2)-x_(1)) , then the tangent at x_(1) is normal at x_(2) for that curve. Now, anwer the following questions. Number of such lines on the curve y=|lnx|, is