MATHS 1 Marks Question

• 12:1 + 2 = 3
• 23:2 + 3 = 5
• 34:3 + 4 = 7
• 45:4 + 5 = 9
• 56:5 + 6 = 11
Series shows increasing odd numbers.

45654 is a palindrome because it reads the same backward and forward.

18

(a)

(b)

Greatest number = 9870
Smallest number = 7809
Difference = 9870 – 7809
= 2061

In this arrangement, no cell is larger than its immediate neighbors: 1 2 3 4 5 6 7.

If all the digits are the same (like 1111 or 2222), subtracting the number from itself will always give you 0, and you can’t reach 6174.

You will always end up with 6174 which is Kaprekar constant.

98765 is the largest 5-digit number with unique digits.

The largest 4-digit number = 7510.
Smallest 4-digit number = 1057.
Therefore, the largest and smallest 4-digit numbers using each of digits 7, 1, 0, 5 only once is 7510 and 1057.

The smallest 4-digit number with different digits is 1023.
This number satisfies the given conditions of having four digits and each digit being unique.

Step to Solve:
1. 12 is even, so divide by 2→ 6
2. 6 is even, so divide by 2 → 3
3. 3 is odd, so multiply by 3 and add 1 → 10
4. 10 is even, so divide by 2 → 5
5. 5 is odd, so multiply by 3 and add 1 → 16
6. 16 is even, so divide by 2→ 8
7. 8 is even, so divide by 2 → 4
8. 4 is even, so divide by 2 → 2
9. 2 is even, so divide by 2 → 1
It takes 9 steps to reach 1.

7, 14, 21, 28, 35, 42, 49, 56, 63

Subtract 30 from 76 in mind 76 - 30 = 46.
Subtract the remaining 4: 46 - 4 = 42

Break it down in mind 87 + 40 = 127.
Then add 6: 127 + 6 = 133

02/02/2020, 12/02/2021, 22/02/2022

• 01:10
• 02:20
• 03:30
• 04:40
• 05:50
• 10:01
• 11:11
• 12:21

The interval is two minutes, between the times of 9:59 and 10:01.

If you start with 2222, all the digits are the same. Subtracting the number from itself gives 2222 – 2222 = 0. Since Kaprekar’s process requires distinct digits, it cannot reach 6174 from this number.

Yes, the Kaprekar process specifically works with 4-digit numbers and 3 digit numbers only. If you use a 5-digit or above number, the steps and the constant will not be the same. The process is designed to reach 6174 with 4-digit numbers and 495 with 3 digit numbers.

(a)

(b)

421 is a supercell because it is larger than 253 and 356.
789 is a supercell because it is larger than 356 and 345.
678 is a supercell because it is larger than 345 and 234.