Can you solve below mathematical equation?

2^1234 - 2^1233

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

A maths symbol is hidden in the below Bar Graph. Can you decipher it?

Peter wakes up daily to pick up his cycle and crosses the border between Spain and France daily with a bag on his shoulder. He is investigated daily by the officials but they don't find anything suspicious.

If we tell you that he is smuggling something what would it be?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

What does below Rebus say?

XLR8

Consider this about a word: The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

If in a code language, DISTANCE is written as IDTUBECN and DOCUMENT is written as ODDVNTNE, the how will THURSDAY be coded as in the same language?

Accidentally, two trains are running in the opposite direction and enter a tunnel that is 200 miles long. A supersonic bird that has fled the lab and taken shelter in the tunnel starts flying from one train towards the other at a speed of 1000 mph. As soon as it reaches the second train, he starts flying back to avoid collision and meets the first train again at the other end. The bird keeps flying to and fro till the trains collide with each other.

What is the total distance that the supersonic bird has traveled till the trains collided?