We start by testing each of the four statements one by one, because the question asks us to find the single statement that is not correct.
Statement A says: “Alcohols are weaker acids than water.”
To compare acidities we use the definition $$pK_a = -\log K_a.$$ A larger $$pK_a$$ means a smaller $$K_a$$ and therefore a weaker acid. Experimentally we have
$$pK_a(\text{H}_2\text{O}) \approx 15.7,$$
$$pK_a(\text{ROH})$$ (for a simple primary alcohol such as ethanol) $$\approx 16\text{--}18.$$
Because $$16-18 \gt 15.7,$$ the $$pK_a$$ of an alcohol is larger, so its $$K_a$$ is smaller, hence an alcohol is indeed a weaker acid than water. Therefore Statement A is correct.
Statement B claims: “Acid strength of alcohols decreases in the order $$\text{RCH}_2\text{OH} \gt \text{R}_2\text{CHOH} \gt \text{R}_3\text{COH}.$$”
Acidity depends on the stability of the conjugate base. After deprotonation an alkoxide ion $$\text{RO}^-$$ is formed. Alkyl groups are electron-donating by the inductive effect $$\left(+I\right).$$ More alkyl groups push electron density toward oxygen, destabilising the negative charge. Hence:
• A primary alkoxide $$(\text{RCH}_2\text{O}^-)$$ has one $$+I$$ group.
• A secondary alkoxide $$(\text{R}_2\text{CHO}^-)$$ has two $$+I$$ groups and is less stable.
• A tertiary alkoxide $$(\text{R}_3\text{CO}^-)$$ has three $$+I$$ groups and is the least stable.
Lower stability of the conjugate base means lower acidity of the conjugate acid, so the acid strength indeed falls in the sequence primary > secondary > tertiary. Hence Statement B is correct.
Statement C says: “Carbon-oxygen bond length in methanol, $$\text{CH}_3\text{OH},$$ is shorter than that of the C-O bond length in phenol.”
Let us recall typical experimental bond lengths:
• In methanol (a simple aliphatic alcohol) the $$\text{C-O}$$ bond is a pure single bond; its length is about $$143\ \text{pm}.$$
• In phenol, resonance causes partial double-bond character between the ring carbon and oxygen:
$$\text{Ar-O-H} \;\;\;\rightleftharpoons\;\;\; \text{Ar}=\text{O}^- -H^+$$
Because of this partial double-bond character the $$\text{C-O}$$ bond in phenol is shorter, about $$136\ \text{pm}.$$ Numerically, $$136\ \text{pm} \lt 143\ \text{pm},$$ so the bond in phenol is the shorter one. Statement C claims the opposite, therefore Statement C is not correct.
Statement D states: “The bond angle O-C-H in methanol is 108.9°.”
In methanol the carbon atom is $$sp^3$$-hybridised. An ideal $$sp^3$$ angle is $$109.5^\circ.$$ Slight differences arise because an $$\text{O-C}$$ bond and $$\text{C-H}$$ bonds are not identical in size or repulsion. Experimental gas-phase measurements give $$\angle(\text{O-C-H}) \approx 108.9^\circ,$$ well within normal error of the ideal tetrahedral value. Therefore Statement D is correct.
Summarising our findings:
• A is correct,
• B is correct,
• C is incorrect,
• D is correct.
Hence, the only statement that is not correct is Statement C, which corresponds to Option 3.
Hence, the correct answer is Option C.