MCQ
The value of $(2 \hat{i}+3 \hat{j}-5 \hat{k}) \cdot(\hat{i}+\hat{j}+\hat{k})$ is
- ✓$0$
- B$-10$
- C$\sqrt{38}$
- D$15$
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$f(\mathrm{x})=\frac{\mathrm{x}[\mathrm{x}]}{1+\mathrm{x}^{2}},$ where $[\mathrm{x}]$ denotes the greatest
integer $\leq \mathrm{x} .$ Then the range of $f$ is
$(I)$ The curve $y=f(x)$ intersects the $x$-axis exactly at one point
$(II)$ The curve $y=f(x)$ intersects the $x$-axis at $\mathrm{x}=\cos \frac{\pi}{12}$
Then