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

I am the largest in my family of fifty.
The youngest of our family lives separately from the rest of the family and so do I.
I am regarded as harsh and tough.
I am so large, you cut me in two equal halves,
each half would still be larger than the second largest member of the family.
Who am I?

There are three boxes of different sizes with three cupcakes inside each of the boxes in Christina's kitchen. At night her daughter wakes up and goes to the kitchen. She opens a box and eats all three cakes.

But in the morning Christina finds out that each box still had three cupcakes. How?

Speaking of rivers, a man calls his dog from the opposite side of the river. The dog crosses the river without getting wet, and without using a bridge or boat. How?

A man walked into a pub and went straight towards the Barman. He asked for a dirty martini from the Barman. The Barman thought something and then pulled out a pistol from his drawer and aimed it directly at the man. Why did he do that?

Find the number of squares in the below picture

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

A red house is made out of red bricks. A yellow house is made out of yellow bricks. And, a blue house is made out of blue bricks. So, what is a greenhouse made of?

Which point will the car reach to go out?