Numerical: Number System MCQ - Practice Questions with Answers

Place value depends on the position of the digit, while face value is the digit itself. In 58647, the digit 8 is in the thousands place, so its place value is 8 × 1000 = 8000. The face value of 6 is simply 6, not 60. The required difference is 8000 − 6 = 7994. Therefore, the correct answer is 7994.

Place value depends on the position of a digit in the number. In 724638, 7 is in the lakh place, so its place value is 700000. The digit 4 is in the thousand place, so its place value is 4000. The question asks how much greater the first value is, so subtract the smaller place value from the larger one: 700000 − 4000 = 696000. Hence the required difference is 696000.

A number is divisible by 15 only when it is divisible by both 3 and 5. The number 47x5 already ends in 5, so it is divisible by 5 for every digit x. For divisibility by 3, the digit sum must be a multiple of 3: 4 + 7 + x + 5 = 16 + x. If x = 2, 16 + 2 = 18; if x = 5, 21; if x = 8, 24. All three are divisible by 3, so all three statements are correct.

Let the number be 10a + b, where a and b are its tens and units digits. The product condition gives ab = 12. Adding 36 reverses the digits, so 10a + b + 36 = 10b + a. This gives 9(b - a) = 36, hence b - a = 4. The digit pair with product 12 and units digit 4 more than the tens digit is 2 and 6. So the number is 26. The numbers 43, 34, and 62 fail the reversal-after-adding-36 condition.

A rational number has a terminating decimal expansion when, after reducing the fraction to lowest terms, the denominator has only the prime factors 2 and 5. For 3/40, the fraction is already in lowest terms and 40 = 2^3 × 5. Hence its decimal expansion terminates. For 7/30, 11/45 and 13/63, the denominators contain prime factors such as 3 or 7, so they do not give terminating decimals.