Our product and our sum always give the same answer. Who are we?

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?

The captain of a ship is telling you an interesting story and then poses a question. He says, “I have travelled the oceans far and wide. One time, two of my sailors were standing on opposite sides of the ship. One was looking west and the other one east. And at the same time, they could see each other clearly. Can you tell me how that was possible?”

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

Replace the question mark with the correct number in the below-given picture?

If,

Akriti = 631
Levis = 521
Sroti = 521
Aneel = 533
Then,
Sunil =?

I have eight fingers and two thumbs but I do not live. What Am I?

John is a strange liar.

He lies on six days of the week, but on the seventh day, he always tells the truth.

He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it"s Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."

On which day does John tell the truth?

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?