Statistical Inference — properties of the likelihood ratio

Consider the following statements regarding likelihood ratio tests: I. For a given size $\alpha$ of a test, the non-randomized Neyman-Pearson and likelihood ratio tests of a simple hypothesis against a simple alternative hypothesis are equivalent. II. The likelihood ratio $\lambda$ always lies between 0 and 1. III. For testing a null hypothesis against any alternative hypothesis, the likelihood ratio test is a function of every sufficient statistic for $\theta$. IV. If $\lambda$ is the likelihood ratio, then the asymptotic distribution of $-2\ln\lambda$ is normal with mean 0 and variance 1. Which of the statements given above are correct?