MCQ
$\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin 3\theta - \sin \theta }}{{\sin \theta }} = $
- A$1$
- ✓$2$
- C$1/3$
- D$3/2$
Aliter : $\mathop {\lim }\limits_{\theta \to 0} \,\frac{{\sin 3\theta - \sin \theta }}{{\sin \theta }} $
$= \mathop {\lim }\limits_{\theta \to 0} \,\frac{{\sin 3\theta }}{{\sin \theta }} - \mathop {\lim }\limits_{\theta \to 0} \,\frac{{\sin \theta }}{{\sin \theta }}$
$ = \frac{3}{1} - 1 = 2.$
You may also apply $L-$ Hospital rule.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Match each entry in List-$I$ to the correct entries in List-$II$.
| List-$I$ | List-$II$ |
| ($P$) The value of $\mathrm{d}\left(\mathrm{H}_0\right)$ is | ($1$) $\sqrt{3}$ |
| ($Q$) The distance of the point $(0,1,2)$ from $\mathrm{H}_0$ is | ($2$) $\frac{1}{\sqrt{3}}$ |
| ($R$) The distance of origin from $\mathrm{H}_0$ is | ($3$) $0$ |
| ($S$) The distance of origin from the point of intersection of planes $\mathrm{y}=\mathrm{z}, \mathrm{x}=1$ and $\mathrm{H}_0$ is | ($4$) $\sqrt{2}$ |
| ($5$) $\frac{1}{\sqrt{2}}$ |
The corret option is :
$x\,\, + \,\,y\,\, = \,\,\frac{{2\pi }}{3},\,{\rm{cos}}\,{\rm{x + }}\,{\rm{ cos}}\,{\rm{y}}\,{\rm{ = }}\,\frac{3}{2},$ where $x$ and $y$ are real in