Can you find out the remainder when 3^300 is divided by 5?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

What do the following words have in common?

Assess
Banana
Dresser
Grammar
Potato
Revive
Uneven
Voodoo

When a clock is observed, the hour hand is at a minute mark and the minutes hand is six minutes ahead of it.

When the clock is observed again after some time, the hour hand is precisely on a different minute mark and the minute hand is seven minutes ahead of it.

Can you calculate how much time has elapsed between the two observations?

In a box, there is a jumble of 7 red balls, 6 blue balls, 5 green balls, and 4 yellow balls. What is the minimum number of balls, will you have to pick up so that you have at least 4 balls of the same colour?

One day, Birbal got late for a function and Akbar was highly disappointed.
Please forgive me Jahanpanah. I arrived late because my child was crying and I had to calm him down, explained Birbal.
Does it take this long to placate a child? questioned the emperor. I feel that you have no idea about how to raise a child. I order you to act like a child and I will act like your father to show you how you should have dealt with your child. Come on! Ask me all that he asked from you.
Father, I want a cow, said Birbal.
The emperor quickly ordered one of the servants to bring a cow to the kingdom.
I want to drink its milk, now, now, now! said Birbal, imitating the voice of his child.
Akbar asked his servants to milk the cow and give to Birbal.
The servants quickly milked the cow and offered the milk to Birbal. He sipped in a little and then gave the bowl to the emperor.
As Birbal put up the next demand that was put up by his child a few hours ago, the emperor was stunned and left the room.
What did Birbal say?

When is the top of a mountain similar to a savings account?

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

Who am I?

Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything.

"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'

"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?