MCQ
$\cos \frac{\pi }{5}\cos \frac{{2\pi }}{5}\cos \frac{{4\pi }}{5}\cos \frac{{8\pi }}{5} = $
- A$1/16$
- B$0$
- C$-1/8$
- ✓$-1/16$
$ = \frac{{\sin \frac{{{2^4}\pi }}{5}}}{{{2^4}\sin \frac{\pi }{5}}} = \frac{{\sin \frac{{16\pi }}{5}}}{{16\,\sin \frac{\pi }{5}}} $
$= \frac{{\sin \,\left( {3\pi + \frac{\pi }{5}} \right)}}{{16\,\sin \frac{\pi }{5}}}$
$ = \frac{{ - \sin \frac{\pi }{5}}}{{16\,\sin \frac{\pi }{5}}} = - \frac{1}{{16}}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| List $I$ | List $II$ |
| $P.$ For each $z_k$ there exists a $z_j$ such that $z_k \cdot z_j=1$ | $1.$ True |
| $Q.$ There exists a $k \in\{1,2, \ldots ., 9\}$ such that $z_{1 .} . z=z_k$ has no solution $z$ in the set of complex numbers. | $2.$ False |
| $R.$ $\frac{\left|1-z_1\right|\left|1-z_2\right| \ldots . .\left|1-z_9\right|}{10}$ equals | $3.$ $1$ |
| $S.$ $1-\sum_{k=1}^9 \cos \left(\frac{2 k \pi}{10}\right)$ equals | $4.$ $2$ |
Codes: $ \quad P \quad Q \quad R \quad S$