A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

You have three orange, two pink and five purple balls in the drawer beside your bed. There is no electricity and the room is entirely dark. How many balls must you take out to ensure at least one ball of each colour at least?

There is a shop where written:
Buy 1 for $1
10 for $2
100 for $3
I needed 999 and still only paid $3. How could this be financially viable for the shop-keeper?

During which month do people sleep the least?

Can you make numbers like 24, using numbers 3,3,7 & 7 with any arithmetic operator?

Which digit occurred maximum times between the number 1 and 1000?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

There are nine letters in the below-given diagram. You have to form a nine-letter word using these letters.

Two prisoners Jack and Jill are locked in a cell.
There is open window approx 40 feet above the ground of the cell.
They are never able to reach there.

Then they plan to escape by a tunnel and they start digging out.
After digging for more than 20 days, Jill comes with the different plan and they escaped.

what was the plan ?

Buy me, smell me or deliver me, I do not change.

Who am I?