Step 1: The idea behind the question.
Glands release their products in different ways. Based on how much of the cell is lost during secretion, we name them merocrine, apocrine or holocrine. We must judge two statements about this.
Step 2: What merocrine means.
In merocrine glands the cell stays fully intact. It simply pushes out its product by exocytosis, like a small packet leaving the cell, and no part of the cell is destroyed.
Step 3: Check statement I about the pancreas.
The pancreas releases its enzymes by plain exocytosis without losing any cell parts. That makes it a merocrine gland. So statement I is true.
Step 4: What apocrine means.
In apocrine glands, the top part of the cell pinches off along with the secretion. So the cell loses a small bit of itself each time it secretes.
Step 5: Check statement II about mammary glands.
Mammary glands release milk with a little bit of the cell's apex breaking off, which is the apocrine style. So statement II is also true.
Step 6: Combine the results.
Both statements are correct, so any option saying one is false must be rejected.
Step 7: Conclusion.
Therefore the correct answer is "Both statements I and II are true". \[ \boxed{\text{Both I and II true}} \]