Can you solve below mathematical equation?

2^1234 - 2^1233

John was born on March 5, 1970, in Delhi, India. Jacob was born 25 days before John. The year when they took birth, Republic Day fell on Monday.

Can you find out on what day was Jacob born?

Can you find out which triangle will have a bigger area among the following?
1. A triangle with sides 300, 400 and 500
2. A triangle with sides 300, 400 and 700

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

If you say my name, I will no longer exist. What am I?

A Club organizes a Running Race, and John, Jacob, Minda, and Tony participated.

The results are as follows

John beats Jacob
Minda beats Toni
Toni beats John

Who came first in the race?

A Monkey, a squirrel, and an Eagle are racing to the top of the mango tree. Assuming all these animals are in perfect shape, Which animal will reach to Banana first?

I am an odd number. Take away a letter and I become even. What number am I?

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?