Question

The number of real solutions of the equation $|x-5|=[-2\pi ]+\left[e^2\right]$ is (where [.] denotes greatest integer function)

• A. one
• B. two
• C. zero
• D. none of these

Answer 1

The correct option is A one

$-7<-2\pi <-6$ and $7<e^2<8$

$\therefore [-2\pi ]=-7,\left[e^2\right]=7$

$\therefore |x-5|=0$

$\Rightarrow x=5$ is the only solution