Number System and Digits

For n ≥ 5, n! ends in 0 (contains 2×5). So 5!+6!+...+100! ends in 0. Sum = 1!+2!+3!+4! = 1+2+6+24 = 33. Last digit = 3.

A PAN card contains exactly 10 alphanumeric characters in a specific format: 5 letters, 4 numbers, and 1 letter. This standardized structure is used for unique identification of taxpayers across India.

Let the number be 10x + y where x and y are digits. The interchange gives 10y + x. Their average is (11x + 11y)/2 = 9, so x + y = 18/11 which is not an integer. For a valid two-digit number, x + y must be an integer between 1 and 18. The conditions create an impossible scenario, so the difference cannot be uniquely determined from the given information.

COMP-5 performance degrades significantly with larger digit counts due to increased computational complexity. Using 10-18 digits is dramatically slower (over 20x) than using 1-4 digits because each additional digit requires more processing power for arithmetic operations and storage management.

The ARITH(EXTEND) compiler option extends the maximum number of digits allowed in numeric fields from the standard 18 digits to 31 digits. This extended precision enables handling of larger numeric values in computations without losing accuracy or requiring programmatic workarounds.

The ARITH(COMPAT) compiler option maintains compatibility with earlier COBOL compilers by limiting numeric precision to 18 digits maximum. This ensures consistent behavior with legacy systems and prevents precision-related issues when migrating or interfacing with older COBOL code.

Digital electronic circuits have two stable states (on/off or high/low voltage), which map naturally to binary digits 0 and 1. While it's true that binary can represent any data (option A), that's a consequence not the cause. Option C is too vague, and option D is incorrect - other number systems exist independently.

In standard COBOL, numeric fields (PIC 9 or PIC S9) can have a maximum of 18 total digits, regardless of where the decimal point falls. This includes both integer and fractional portions combined. The 18-digit limit is a fundamental constraint in COBOL numeric data types.

An ISIN is a 12-digit code consisting of both alphabets and numbers. The structure includes a 2-letter country code, a 9-character national security identifier (which can be alphanumeric), and a single check digit. It is never purely alphabetic or purely numeric - it always contains both.

The number trick works because subtracting the digit sum from a number makes the result divisible by 9. After deleting one digit and summing the remaining three, the missing digit can be deduced from the sum modulo 9. When the sum of three digits is 0, 9, or 18, there are exactly two possibilities for the deleted digit (0 or 9), making the maximum 2 possibilities.

In the 15-digit External CM number format, position 10 represents the Cycle Cut Number and position 12 is the Replacement digit. These specific positions are standardized within the CM numbering system to track card lifecycle events. Options A and C use incorrect position references.

The 8th digit in the external card number represents the billing cycle. This digit determines when the customer's statement is generated and payment is due. Billing digit and check digit are different concepts - check digits are for validation (often the last digit), and replacement digit would indicate a reissued card.

COBOL's standard allows a maximum of 18 digits in a numeric variable declaration, such as PIC S9(18) or PIC 9(18). This limit is enforced by the language specification and most COBOL compilers.

In telecom billing systems, Billing Account Numbers (BAN) typically have 10 digits, Customer Account Numbers (CAN) have 12 digits, and Cellular Telephone Numbers (CTN) representing subscription lines contain 10 digits. The other options are incorrect as they misrepresent the standard digit lengths for these distinct identifiers.

Binary system uses only two digits: 0 and 1, hence 'bi' meaning two. Option B includes 2 which is not valid in binary, and C/D are incomplete or incorrect.