Consider the function $$f:(0, \infty) \rightarrow \mathbb{R}$$ defined by $$f(x)=e^{-\left|\log _e x\right|}$$. If $$m$$ and $$n$$ be respectively the number of points at which $$f$$ is not continuous and $$f$$ is not differentiable, then $$m+n$$ is

Let a variable line passing through the centre of the circle $$x^2+y^2-16 x-4 y=0$$, meet the positive co-ordinate axes at the points $$A$$ and $$B$$. Then the minimum value of $$O A+O B$$, where $$O$$ is the origin, is equal to

Let $$A(a, b), B(3,4)$$ and $$C(-6,-8)$$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $$P(2 a+3,7 b+5)$$ from the line $$2 x+3 y-4=0$$ measured parallel to the line $$x-2 y-1=0$$ is

Let the mean and the variance of 6 observations $$a, b, 68,44,48,60$$ be $$55$$ and $$194$$, respectively. If $$a>b$$, then $$a+3 b$$ is