The correct answer is Option (4) → (B) and (D) only
Statement Analysis
- (A) The difference between the place values of 9 and 5 in the number 639,457 is 4.
- Place Value of 9: 9 is in the thousands place, so its value is $9 \times 1,000 = \mathbf{9,000}$.
- Place Value of 5: 5 is in the tens place, so its value is $5 \times 10 = \mathbf{50}$.
- Difference: $9,000 - 50 = 8,950$.
- The statement says the difference is 4 (which is the difference of their face values). Therefore, this statement is Incorrect.
- (B) The number $\pi$ is an irrational number.
- $\pi$ (Pi) is a mathematical constant whose decimal expansion is non-terminating and non-repeating. It cannot be expressed as a simple fraction $\frac{p}{q}$.
- Therefore, this statement is Correct.
- (C) The sum of all the prime numbers from 1 to 20 is 67.
- The prime numbers from 1 to 20 are: $2, 3, 5, 7, 11, 13, 17,$ and $19$.
- Sum: $2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = \mathbf{77}$.
- The statement says the sum is 67. Therefore, this statement is Incorrect.
- (D) The difference between the face values of 5 and 3 in number 475,839 is 2.
- Face Value: The face value of a digit is the digit itself, regardless of its position.
- Face value of $5 = 5$.
- Face value of $3 = 3$.
- Difference: $5 - 3 = \mathbf{2}$.
- Therefore, this statement is Correct.
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