Can you solve below mathematical equation?

2^1234 - 2^1233

I have a big mouth and I am also quite loud! I am NOT a gossip but I do get involved with everyone's dirty business.

I get hot but I never sweat,
I cook food but I am not a chef,
I have a door but you can't enter me,
I have a light but I am not a lamp.
Who am I?

They are the five precious gems of an everyday sort and all can be found on a Tennis Court. Who are they?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

Can you calculate the probability of getting a sum of six when a dice is thrown twice?

A guard is positioned at the one side of the bridge saying ‘A’. His task is to shoot all those who try to leave from ‘A’ to the other side and say ‘B’. He also need to welcome the person who comes from another side ‘B’ to his side ‘A’. The guard comes out of his post every 1 hour and looks down the bridge for any people trying to leave. You are at side ‘A’ and wish to go to another side ‘B’. you also know that it would take 1:45 hr to cross the bridge. How will you cross the bridge?

What jumps when it walks and sits when it stands?

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?

Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?