Solution:

2 minutes (duration between 9:59 and 10:01)

Solution:

12345679

12345679 × 9 = 111111111 (only 1s)
12345679 × 18 = 222222222 (only 2s)
12345679 × 27 = 333333333 (only 3s)
12345679 × 36 = 444444444 (only 4s)
12345679 × 45 = 555555555 (only 5s)

Solution:

12:00

both minute and hour clock lie exactly between the number one and two in the number.

Solution:

5 leopard and one sheep

since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.

Solution:

None

The sum of numbers from 0-9(0,1,2,3,4,5,6,7,8,9) is 45 and therefore can be divisible by 3 and 9.

Solution:

40

Solution:

step 3 is wrong

Solution:

4

No Of circles in the number.

Solution:

He askes the god to beat him half to death.

Solution:

16-days

In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)