[A]: Prothrombin is necessory for blood clotting. ,
[R]: This is produced in pancreas in presence of vitamin K

a) If both A and R are true and R is the correct explanation of A
b) If both A and R are true but R is not the correct explanation of A
c) If A is true and R is false
d) If both A and R are false

Options

A. If both A and R are true and R is the correct explanation of A
B. If both A and R are true but R is not the correct explanation of A
C. If A is true and R is false
D. If both A and R are false

Answer

To solve the question regarding the statements about prothrombin, we will analyze both statements A and R step by step.

### Step 1: Analyze Statement A
**Statement A**: "Prothrombin is necessary for blood clotting."
- Prothrombin is indeed a crucial protein in the blood clotting process. It is one of the clotting factors that helps in the formation of blood clots, which prevent excessive bleeding. Therefore, Statement A is **true**.

### Step 2: Analyze Statement R
**Statement R**: "This is produced in pancreas in presence of vitamin K."
- Prothrombin is not produced in the pancreas; it is actually produced in the liver. While vitamin K is essential for the synthesis of prothrombin, the location of its production is incorrect. Therefore, Statement R is **false**.

### Step 3: Determine the Relationship Between A and R
- Since Statement A is true and Statement R is false, we need to identify the correct option from the given choices:
- a) If both A and R are true and R is the correct explanation of A.
- b) If both A and R are true but R is not the correct explanation of A.
- c) If A is true and R is false.
- d) If both A and R are false.

Given our analysis:
- A is true.
- R is false.

Thus, the correct option is **c) If A is true and R is false**.

### Summary of the Solution
- A is true (Prothrombin is necessary for blood clotting).
- R is false (Prothrombin is produced in the liver, not the pancreas).
- Therefore, the answer is option **c**.