Analysis of statements:
- Statement 1:
Alcohol is prepared from alkyl halide in the presence of aqueous KOH by elimination.
This statement is incorrect. Reaction of alkyl halide with aqueous KOH proceeds via $S_N1$ or $S_N2$ substitution, yielding alcohol, not elimination. Elimination occurs with alcoholic KOH.
- Statement 2:
Alkenes are prepared from alkyl halide with alcoholic KOH by $\beta$-elimination.
This statement is correct. Alcoholic KOH promotes $\beta$-elimination of alkyl halides, forming alkenes.
Conclusion: Statement-1 is false and Statement-2 is true. Thus, the correct option is (4) Statement-1 is false and Statement-2 is true.