MCQ
Direction ratio of line joining $(2, 3, 4)$ and $(-1, -2, 1),$ are:
- ✓$(-3, -5, -3)$
- B$(-3, 1, -3)$
- C$(-1, -5, -3)$
- D$(-3, -5, 5)$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$(S_1)$ there exists $\mathrm{x}_{1}, \mathrm{x}_{2} \in(2,4), \mathrm{x}_{1}<\mathrm{x}_{2}$, such that $f^{\prime}\left(x_{1}\right)=-1$ and $f^{\prime}\left(x_{2}\right)=0$
$(S_2)$ there exists $\mathrm{x}_{3}, \mathrm{x}_{4} \in(2,4), \mathrm{x}_{3}<\mathrm{x}_{4}$, such that $f$ is decreasing in $\left(2, x_{4}\right)$, increasing in $\left(x_{4}, 4\right)$ and $2 f^{\prime}\left(x_{3}\right)=\sqrt{3} f\left(x_{4}\right)$.
Then