• # question_answer The set of values of p for which the equation $|\ln x|-\,px=0$ possess three roots is : A) (0, 1/e) B) (0, 1) C) $(0,\,\,\sqrt{3})$ D) (0, e)

 $1/{{x}_{1}}=p={{y}_{1}}/{{x}_{1}}$ $\Rightarrow$ ${{y}_{1}}=1$ & ${{x}_{1}}=e.$ Hence slope of $y=p\,x$ i.e.$p\in (0,\,\,1/e)$ for three roots