**Question:**

Consider the quadratic equation $(c-5) x^{2}-2 c x+(c-4)=0$, $\mathrm{c} \neq 5$. Let $\mathrm{S}$ be the set of all integral values of $\mathrm{c}$ for which one root of the equation lies in the interval $(0,2)$ and its other root lies in the interval $(2,3)$. Then the number of elements in $\mathrm{S}$ is:

Correct Option: 4

JEE Main Previous Year Jan. 10, 2019 (I)

**Solution:**