Real Analysis quiz

Which of the following statements is incorrect?

• E ,set of even numbers is countable.

• Z is countable

• N is countable

• R is countable.

f:R→R defined by f(x)=x³. Then range=……….

• (-∞,0]

• (-∞,∞)

• [0,-∞)

Which of following sets are countable

• Z

• N

• R

• K

All the functions are relation

• Yes

• No

• May be true

• All the above options are incorrect

If a sequence is not convergent then

• 
• Always oscillates

• divergent

• May not be divergent always

• Bounded

• Unbounded

Identify the correct options:

Cantor set is

• Countable

• Connected

• finite

• Perfect

Set of natural number is

• bounded above

• Not bounded above

• finite

• None of these

In R with usual metric,the correct statement is ....

• [0,1] is an open set

• (0,1) is an open set

• Q is open

• Z is open

If A is open set and B is closed set, then____

• A – B is open set

• B – A is not open

• A – B is closed set

• B – A is open set