Cut off of CSIR Net lecturership /JRF Mathematics (2014-2016)

REAL ANALYSIS QUIZ-
TOPIC- FUNCTIONS, CARDINALITY

Question 1: Let f:A->B  and g:B->C be functions such that gof is injective, then

(a)    f is injective

(b)   g is surjective

(c)    f is surjective

(d)   g is injective

Question 2 : which of the following are equivalent to the statement –     “A is a countable set”.

(a)    there exists a surjection of N onto S

(b)   there exists an injection of S into N

(c)    there exists a surjection of S onto N

(d)   there exists an  injection of N into S

Question 3 : Which of the following are true?

(a)    The set of algebraic numbers is countable.

(b)   The set of transcendental numbers  is countable.

(c)    The set of all binary sequence is uncountable .

(d)   Finite product  of countable set is countable.

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