Question

The number of solution(s) for $\left\{x\right\}+\left\{\sin x\right\}=2,$ if $x\in [0,2\pi ],$ where $\{.\}$ is the fractional part function, is

• A. $0$
• B. $1$
• C. $2$
• D. infinitely many

Answer 1

The correct option is A $0$

We know that,
$0\le \left\{x\right\}<10\le \left\{\sin x\right\}<1\Rightarrow 0\le \left\{x\right\}+\left\{\sin x\right\}<2$

But given equation is $\left\{x\right\}+\left\{\sin x\right\}=2$
$\therefore$ No solution exists for given the equation.