Units place is 6, i.e. even number. So, the number is always divisible by 2.

Since last 3 digits ‘824’ of 91824 are divisible by 8, so 91824 is divisible by 8.

160358 = (6 + 3 + 8) – (1 + 0 + 5) = 17 – 6 = 11 Since ‘11’ is divisible by 11, so 160358 is divisible by 11.

2801* is divisible by 3. So, 11 + * should be divisible by 3. Nearest number to 11 is 12. Hence, * = 1

Since 21 is divisible by 3, so the number will be divisible by 3.

89047* is divisible by 5 It is possible if last digit is 0 or 5.

3857* is exactly divisible by 3. So, 23 + * is exactly divisible by 3. Number of possible values of * is 2.

The number 2001 is divisible by 3 but not by 2. If 3 is added to it, then it will be divisible by 3 and 2 also. So, the nearest number which is exactly divisible by 6 is 2004.

Hence, (2) is the correct option.  

8629a is exactly divisible by 11. (10 + a) – 15 should be 0 or multiple of 11. a – 5 = 0 a = 5

The greatest number between 1000 and 1100 will be the nearest number smaller than 1100. 1100 is divisible by 4 but not divisible by 3. We should subtract 8 to get it divisible by both 4 and 3. So, 1092 is divisible by 12.