Can you solve below mathematical equation?

2^1234 - 2^1233

A girl says this to her best friend: “I was born in 1955, and I celebrated my 17th birthday last weekend.” Her best friend thinks she’s lying, but she’s actually correct. How is that possible?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

Some friends went on a vacation to a resort. It was raining heavily and it kept raining for thirteen days.

When it rained in the morning, the afternoon was beautiful and when it rained in the afternoon, the day was blessed with a clear morning.

Overall, the friends experienced eleven nice mornings and twelve nice afternoons. Can you find out the number of days they spent on vacation?

What animal walks on four legs in the morning, two legs during the day, and three legs in the evening?

Oedipus, the king of Thebes, figured out the answer to the riddle:

Can you discover the missing number in this series?

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

John was piloting a plane behind a car but was never able to overtake it. Why?

John, Jack and Jill are in a desert. John doesn't like Jill and hence decides to murder him. He poisons the water supply of Jill. Since it is a desert area, Jill must drink or he will die of thirst.

Jack does not know of the actions of John and also decides to murder Jill. To succeed in his ill motives, he removes the water supply of Jill so he dies of thirst.

Jill dies due to thirst. Who murdered Jill?

I’m tall when I’m young, and I’m short when I’m old. What am I?

Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: 'I am not aware of those numbers.'
Jacob: 'I knew you wouldn't be. I am not aware myself.'
John: 'Now I know them!'
Jacob: 'Now I know them, too!'

What are the two numbers?