what does the below rebus means?

A pregnant woman is preparing to name her seventh child. Her children's names so far are Dominique, Regis, Michelle, Fawn, Sophie, and Lara. What will she name her next child -- Jessica, Katie, Abby or Tilly?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

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?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

A frog is at the bottom of a 30-meter well. Each day he summons enough energy for one 3-meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

Can you discover the missing number in this series?

37, 10, 82
29, 11, 47
96, 15, 87
42, ?, 15

While handling a project, the landscaper is asked by the owner of the mansion that he wants four trees in front of his mansion that are exactly equidistant from each other.

How will he do it?

2 ladies and 2 girls need to cross a river in a boat big enough for 1 LADY or 2 girls. How do they do it?

Can you find the largest Three-digit number whose sum is 14 and whose square is less than 5,00,000?