A jeweller puts a diamond in a box weighing 1.2 kg. Find the total weight of the box and diamond with due regard to significant figures, if the weight of diamond is 5.42 g.

The correct option is 1.2 kg.

To find the total weight of the box and the diamond, we first need to express both weights in the same units (kilograms) and then apply the rules of significant figures for addition.

Step 1: Express both masses in kilograms (kg)
We are given:
Weight of the box = 1.2 kg
Weight of the diamond = 5.42 g

Since 1 kilogram is equal to 1000 grams:

$1\text{kg}=1000\text{g}$

We convert the weight of the diamond from grams to kilograms:

$\text{Weight of the diamond}=\frac{5.42}{1000}\text{kg}=0.00542\text{kg}$

Step 2: Calculate the total weight
Next, we add the two weights together:

$\text{Total weight}=1.2\text{kg}+0.00542\text{kg}=1.20542\text{kg}$

Step 3: Apply the rules of significant figures for addition
According to the rules of significant figures, when adding or subtracting physical quantities, the final result must be rounded off to the same number of decimal places as the measurement with the least number of decimal places.
- The weight of the box (1.2 kg) has only 1 decimal place (tenths place).
- The weight of the diamond (0.00542 kg) has 5 decimal places.

Since the weight of the box has the least number of decimal places (1 decimal place), the final sum must also be rounded off to exactly 1 decimal place.

Rounding 1.20542 kg to one decimal place yields:

$1.2\text{kg}$

Therefore, the total weight of the box and the diamond, keeping significant figures in mind, is 1.2 kg.