35.

36.

87.

38.

39.

40.

Let R be a ring and C-denotes, a commutative ring with unity, D-denotes a commutative ring
with unity and without zero divisors, E-denotes integral domain and F-denotes a field.

Choose the incorrect option:
ധ IfRisC,then R[x]in also C ൪൫ 18180, then R[x] in also D
(C) IfRisE, then R[x]is also E (D) IfRifF,then Rlxlis also F

Which of the following is a correct statement?
(A) Every metric space is a topological space
(B) Every topological space is a metric space
(C) All topological spaces are pseudo metrisable

(D) All of the above

Which of the following statement is wrong about compactness of a topological space?
(A) Compactness in preserved under continuous function
൯) Compactness is an absolute property
(C) Compactness is hereditary
(D) Every infinite subset A of a compact space X has at least one accumulation point
inX
Strongest topology on the real line Ris
(A) Usual topology (B) Cofinite topology
(C) Semi open interval topology (D) Discrete topology

Which of the following is a connected subset of R with usual topology?
‏بم‎ (2) 0) 68066)
൭ {2,3} (D) The set N of natural numbers

Which of the following is true about a Hausdorff space (X,r)
(A) Limits of sequences are unique
(B) Every singleton set {x}is closed
(C) Every compact subset of X are closed
(D) All of the above

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[P.T.0.]