An infinite number of tangents can be drawn (1, 2) to the circle $x^2+y^2-2x-4y+\lambda =0$, then the value of $\lambda$ is

Clearly the point (1, 2) is the centre of the circle $x^2+y^2-2x-4y+\lambda =0$ and infinite tangents can only be drawn on a point circle.

Hence radius $=0\Rightarrow \sqrt{g^2+f^2-c}=0$

$\Rightarrow \sqrt{1^2+2^2-\lambda }=0\Rightarrow \lambda =5$