Deficiency of vitamin K causes :

Vitamin K is essential for the synthesis of prothrombin and several other clotting factors in the liver. It acts as a cofactor for the enzyme that carboxylates glutamic acid residues on these clotting proteins, which is necessary for them to bind calcium ions and function in the coagulation cascade.

When vitamin K is deficient, the body cannot produce adequate amounts of functional clotting factors, so the blood takes longer to clot. This means the blood clotting time increases.

Considering the other options: increased fragility of RBCs is associated with vitamin E deficiency, cheilosis (cracking at the corners of the mouth) is linked to vitamin B$$_2$$ (riboflavin) deficiency, and a decrease in blood clotting time is the opposite of what vitamin K deficiency causes.

The correct answer is option (1): increase in blood clotting time.