Recall the sensitivity of a moving coil galvanometer

For a moving coil galvanometer, the deflection is $\theta = \frac{N B A}{k} I$ where:

• $N$ = number of turns,
• $B$ = magnetic field,
• $A$ = area of coil,
• $k$ = torsional constant,
• $I$ = current.

Hence, current sensitivity is $\frac{\theta}{I} = \frac{N B A}{k}$

So, sensitivity increases if magnetic field $B$ increases.

Check Statement 1

Statement 1 says: The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.

This is true because inserting a soft iron core increases the magnetic field inside the coil due to its high magnetic permeability. Since sensitivity is proportional to $B$, the sensitivity increases.

Therefore, Statement 1 is True.

Check Statement 2

Statement 2 says: Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.

Now:

• Soft iron does have high magnetic permeability — this part is true.
• But soft iron can be easily magnetized and demagnetized — this part is false.

Therefore, the complete statement is false.

So, Statement 2 is False.

Choose the correct option

• Statement 1: True
• Statement 2: False

Hence, the correct option is: $\boxed{\text{C}}$

Comparison with stored answer

Stored correct answer = C.

Our derived answer also = C.

Therefore, the stored answer is correct.