Which of the following statements is/are incorrect?
(i) Eighty four in Roman numeral is written as CXXXIV.
(ii) There are seven zeroes in 1 crore.
(iii) There are ten thousand milligrams in 1 kg.
(iv) The smallest4-digitnumber formed by using all the digits 4, 3, 0, 8 without repetition is 3048.

Options

A. Both (i) and (iii)
B. Both (i) and (iv)
C. Only (i)
D. Only (iii)

Answer

To determine which statements are incorrect, we will evaluate each statement one by one.

### Step-by-Step Solution:

1. **Evaluate Statement (i)**: "Eighty four in Roman numeral is written as CXXXIV."
- The correct Roman numeral for 84 is LXXXIV (where L = 50, XXX = 30, and IV = 4).
- The statement claims it is CXXXIV, which is incorrect because C represents 100.
- **Conclusion**: Statement (i) is incorrect.

2. **Evaluate Statement (ii)**: "There are seven zeroes in 1 crore."
- 1 crore is written as 1,00,00,000.
- Counting the zeroes, we find there are indeed 7 zeroes.
- **Conclusion**: Statement (ii) is correct.

3. **Evaluate Statement (iii)**: "There are ten thousand milligrams in 1 kg."
- 1 kg is equal to 1000 grams.
- Since 1 gram = 1000 milligrams, then 1 kg = 1000 grams × 1000 milligrams/gram = 1,000,000 milligrams.
- The statement claims there are 10,000 milligrams in 1 kg, which is incorrect.
- **Conclusion**: Statement (iii) is incorrect.

4. **Evaluate Statement (iv)**: "The smallest 4-digit number formed by using all the digits 4, 3, 0, 8 without repetition is 3048."
- The digits available are 4, 3, 0, and 8.
- The smallest 4-digit number cannot start with 0, so we must start with the smallest non-zero digit, which is 3.
- Arranging the digits in ascending order after 3 gives us 3048.
- **Conclusion**: Statement (iv) is correct.

### Summary of Findings:
- Statement (i) is incorrect.
- Statement (ii) is correct.
- Statement (iii) is incorrect.
- Statement (iv) is correct.

### Final Answer:
The incorrect statements are (i) and (iii).

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