We need to evaluate two statements about vernier callipers.
Statement I: "In a vernier callipers, one vernier scale division is always smaller than one main scale division."
In a standard vernier callipers, n vernier scale divisions (VSD) coincide with (n-1) main scale divisions (MSD). So:
$$n \times VSD = (n-1) \times MSD$$
$$VSD = \frac{(n-1)}{n} \times MSD$$
This means one VSD is smaller than one MSD. However, the statement says "always." In some vernier callipers, n VSD = (n+1) MSD, which would make VSD larger than MSD. So the word "always" makes Statement I false, as there exist vernier callipers where VSD > MSD.
Statement II: "The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions."
The vernier constant (least count) is given by:
$$VC = 1 \text{ MSD} - 1 \text{ VSD} = MSD - \frac{(n-1)}{n} MSD = \frac{MSD}{n}$$
This equals one MSD divided by (not multiplied by) the number of vernier scale divisions. So Statement II is also false.
Both statements are false.
The correct answer is Option 3: Both Statement I and Statement II are false.