$\int\limits_0^∞[2 e^{-x}]dx$, where [.] denotes the greatest integer function, is equal to

0 ln 2 e2 2e-1

ln 2

Since 0 < 2e-x ≤ 2 ∀x ∈ [0 , ∞), [2e-x] = 0, for x > ln 2. Hence the given integral = $\int\limits_0^{In\,2}dx+0=In\,2$. Hence (B) is the correct answer.