The rate of decay of certain substance is directly proportional to the amount present at that instant. Initially, there are $$27 \mathrm{~gm}$$ of certain substance and $$3 \mathrm{~h}$$ later it is found that $$8 \mathrm{~gm}$$ are left, then the amount left after one more hour is

The direction cosines of a line which is perpendicular to lines whose direction ratios are $$3,-2,4$$ and $$1,3,-2$$ are

The points of discontinuity of the function

$$\begin{aligned} f(x) & =\frac{1}{x-1}, \text { if } 0 \leq x \leq 2 \\ & =\frac{x+5}{x+3} \text { if } 2< x \leq 4 \end{aligned}$$

in its domain are

If the angle between the lines given by the equation $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0, \lambda \geq 0$$, is $$\tan ^{-1}\left(\frac{1}{3}\right)$$, then $$\lambda=$$