CSIR Net Mathematics Exam june 2018- practice test

Test for CSIR Net Mathematics Exam- 
Real analysis Topic - Countability 

1. A  set S is said to be countable if
Options:
a) there exists an injection from S to N
b) there exists a surjection from  N to S
c) it is a subset of a countable set
d) all the these

2. which of the followings set is not countable?
Options:
a) subset of an uncountable set
b) countable union of countable set
c) finite product of countable sets
d) countably infinite product of countable sets

3. The power set of a finite set is
Options:
a) finite
b) infinite
c) uncountable
d) none of these

4. The set of all binary sequence is
Options:
a) countable
b) uncountable
c) countably infinite
d) denumberable

5. The cardinality of set of algebraic numbers is equal to that of
Options:
a) Natural numbers
b) Real numbers
c) set of all binary sequences
d) b,c

6. which of the following sets are uncountable?
a) set of all functions f such that f :R->R
b) set of all functions f such that f: N-> Z2
c) set of all functions f such that f: Z2 -> N
d) set of all polynomials P : R->R

Options:
a) c
b) a,b
c) a,b,d
d) b,d

7. The collections of all isolated points of any set is
Options:
a) countable
b) uncountable
c) not enough information
d) finite

8. cantor set is ?

Options:
a) countable
b) finite
c) uncountable
d) countably finite

9. The cardinality of all disjoint intervals is not equals to
Options:
a) natural numbers
b) real numbers
c) algebraic numbers
d) rational numbers

10. set of all subsets of N are
Options:
a) countable
b) uncountable
c) finite
d) countably finite