Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below.

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.