Consider the following statements

(A) The difference between the place values of 9 and 5 in the number 639457 is 4.

(B) The number π is an irrational number.

(C) The sum of all the prime numbers from 1 to 20 is 67.

(D) The difference between the face values of 5 and 3 in number 475839 is 2.

Choose the correct answer from the options given below:

Place value means the value of a digit based on its position in the number.

In the number 639457:

• 9 is in the thousands place: $9 \times 1000 = 9000$
• 5 is in the tens place: $5 \times 10 = 50$

Difference $= 9000 - 50 = 8950$

Since $8950 \neq 4$, statement (A) is FALSE.

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An irrational number cannot be written as a ratio of two integers. Its decimal expansion goes on forever without repeating.

$\pi = 3.14159265...$ (non-terminating, non-repeating)

$\pi$ cannot be expressed as $\dfrac{p}{q}$ where $p$ and $q$ are integers.

Statement (B) is TRUE.

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A prime number is greater than 1 and has only two factors: 1 and itself.

Prime numbers from 1 to 20: $2, 3, 5, 7, 11, 13, 17, 19$

Sum $= 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19$

$= 5 + 5 + 7 + 11 + 13 + 17 + 19$

$= 10 + 7 + 11 + 13 + 17 + 19$

$= 17 + 11 + 13 + 17 + 19$

$= 28 + 13 + 17 + 19$

$= 41 + 17 + 19$

$= 58 + 19$

$= 77$

Since $77 \neq 67$, statement (C) is FALSE.

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Face value is the digit itself, regardless of its position in the number.

In the number 475839:

• Face value of 5 $= 5$
• Face value of 3 $= 3$

Difference $= 5 - 3 = 2$

Statement (D) is TRUE.

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Only statements (B) and (D) are TRUE.