Question

Number of solutions of the equation $2\sin (\{x\})=1$ in $x\in [0,2\pi ]$ is equal to
[Note: $\{k\}$ denotes fractional part of $k$.]

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (C)

$2\sin \{x\}=1$
$\sin \{x\}=1/2$
$\{x\}=\pi /6\text{ is the only value }$
$x=\frac{\pi }{6},\frac{\pi }{6}+1,\frac{\pi }{6}+2,\frac{\pi }{6}+3,4+\frac{\pi }{6},5+\frac{\pi }{6}\Rightarrow 6$