Which one of the following statements is NOT true?

1. In competitive inhibition, substrate and inhibitor compete for the same active site of an enzyme
2. Addition of a large amount of substrate to an enzyme cannot overcome uncompetitive inhibition
3. A transition state analogue in enzyme catalyzed reaction increases the rate of product formation
4. In non-competitive inhibition, $K_m$ of an enzyme for its substrate remains constant as the concentration of the inhibitor increases