Why are all black people so quick ?

The following sentence is false. The preceding sentence is true.
Are these two sentences true or false?

Katrina wants to go on a date and prefers her date to be tall, dark and handsome.

Of the preferred traits - tall, dark and handsome - no two of Shahrukh, Ajay, Salman and Akshay have the same number.
Only Shahrukh or Akshay is tall and fair.
Only Ajay or Salman is short and handsome.
Shahrukh and Salman are either both tall or short.
Ajay and Akshay are either both dark or both fair.
Who is Katrina's date?

I travel all around the world but always stay in the corner. What am I?

There was a blind beggar living on the footpath of a street. Suddenly one day, the beggar's brother died. What was the relation of the blind beggar with the person who died?

PS: Brother is not the answer.

Solve the equation by replacing the alphabet with numbers.

MOM + MOM + NO = BOOK=

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?