Number System and Digits

Let unit digit be x, then tens digit = 16 - x. Therfore, original number = 10 *(16 - x ) + x = 160-9x. On reversing the digits, we have x at tens place and 16-x at unit place.Therefore, new number = 10x + 16 - x = 9x + 16. Original number-New number = 18 (160-9x)-(9x+16) = 18160 - 9x - 9x - 16 = 18 - 18x + 144 = 1818x = 144-1818x = 126x = 7. In the original number, we have at unit place tens digit = 16 - 7 = 9. Therefore, original number = 97. It is the correct answer.

Correct

The binary (base-2) number system uses only two digits (0 and 1), fundamental to digital computing. Unlike decimal (base-10), binary represents all values using powers of 2. This is why computers use binary - electronic circuits have two states (on/off).

For a 4-digit number to be greater than 5000, the first digit must be 5, 6, or 7 (3 choices). After choosing the first digit, we have 4 choices for the second digit, then 3 for the third, and 2 for the fourth, with no repetition allowed. Total = 3 × 4 × 3 × 2 = 72.

For a 4-digit number from digits {0,1,2,3,4} with no repetition, the first digit cannot be 0 (otherwise it's a 3-digit number). So first digit has 4 choices (1,2,3,4). Second digit has 4 remaining choices (including 0), third has 3 choices, fourth has 2 choices. Total = 4 × 4 × 3 × 2 = 96.

  The 4!=24 permutations of the four digits and consider their sum.2468 2486 2648 2684 2846 28648246 8264 8426 8462 8624 +8642We find that each column has: six 2's, six 4's, six 6's, six 8's.The total of each column is 6*2 + 6*4 + 6*6 + 6*8 = 120Hence, the addition has the form:000120 001200 012000

+120000

133320

A PNR (Passenger Name Record) number in Indian Railways reservation system contains 10 digits. This unique alphanumeric identifier is essential for ticket management, tracking, and cancellation. The 10-digit format is standard across the railway computerized reservation system.

Unit's digit in 57¹ = 7 Unit's digit in 57² = 9 Unit's digit in 57³ = 3 Unit's digit in 57⁴ = 1 Unit's digit in 57⁵ = 7 => Digit is repeated in (4n+1) terms, where n = 1, 2. 3, 4......... => In 57²⁵ i.e. 57^(4*6+1), the unit's digit is 7 Thus, required digit = 7 + 1 = 8 So, option (2) is correct.

Placing 1 as indicated, shifts the given digits to the left, so that 't' is now the hundreds' digit and 'u' is the tens' digit. Therefore, 100t + 10u + 1. Hence, option (2) is the correct option.

Such a number can be written as follows: P * 103 + P = P (103 + 1) = P (1001) ...........where P is the block of three digits that repeat Therefore, option (4) is the correct option.

Smallest 5 digit number = 10000 Largest 5 digit number = 99999                                                                                                                                                                               The sum of the two numbers = 109999                                                    Hence, this option is the correct answer.

In the binary numbering system, every possible value can be represented using only the digits 0 and 1. These two digits are the fundamental building blocks of all data in digital computing.

The binary number system is base-2, meaning it uses exactly two digits: 0 and 1.

The binary system is a base-2 system that uses only the digits 0 and 1 to represent all values.

The International Standard Book Number (ISBN) was expanded from 10 digits to 13 digits in 2007 to increase the available numbering capacity.