Number System and Digits

Let the ten's digit be x and the unit's digit be y. Then, the number = 10x + y. The number obtained by interchanging the digits = 10y + x (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.

8 is the correct answer because there are more than one such number which is the square of an odd number and their last digit is our answer. But according to the question, 8 is the correct answer.

Smallest 2-digit number = 10

Original number = 32576New number after inter changing the digits = 35276  Difference = 35276 - 32576 = 2700  Product of smallest 2 digit number and difference is 2700 x 10                                                                                                                                                                         =27000

7460 + 4115 = 11575 12000 is nearest to 11575 as compared to 11000.

1125 + 3420 = 4545 5000 is nearest to 4545 as compared to 4000.

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.