0:-0
Correct Answer:- Option-D
Question74:-Consider the metric space ("NN", d} where d is given by d(m, n} = |'1/m" — *1/n"| . Then which is false 7
A:-d is a bounded metric on *NN*
B:-d induces the discrete topology on "۰۷۰
C:-*{1/n}" converges to 0
D:-This space is Hausdorff
Correct Answer:- Option-C
Question75:-Which is not a productive property 7
A:-Connectedness
B:-Compactness
C:-Locally connectedness
D:-Path connectedness
Correct Answer:- Option-C
Question76:-Let X = (0, 1} and Y = "RR" . Then which is true 7
A:-X and Y are the same as metric spaces
B:-X and Y are the same as topological spaces
0:-000 (8) 2೧6 (0)
D:-Neither (a} nor (b}
Correct Answer:- Option-B
Question77:-Which of the following topological property is not preserved under a continuous function 7
A:-Connectedness
B:-Compactness
C:-First countability
D:-None of these
Correct Answer:- Option-C
Question78:-Which is true 7
A:-On "RR’ co-finite topology is weaker than usual topology
B:-On "RR* usual topology is weaker than co-finite topology
C:-On *RR" co-finite topology and usual topology are not comparable
D:-On "RR" co-finite topology and usual topology are the same
Correct Answer:- Option-A
Question79:-If every closed interval [a, b] with a < b is open with respect to some topology on "RR" ; then with respect to
this topology, closure of [27, 37115
ക:-[27. 37]
:-{-` 60 , 37]
6:27, 00 ` }
>.
Correct Answer:- Option-A
Question80:-For the space *RR™ with co-countable topology, which is false 7
A:-Unigueness of limits exists in this space for the convergence of sequences
B:-This space is not Hausdorff
C:-{"1/n"} is divergent in this space’ *
D:-None of these
Correct Answer:- Option-D
Question81:-If f: *RR’ *->' நாட்டி உங்க differentiable function with [൩ 0200)” (200 5 3£00 5 500) ട 0 with
“lim_(x->00)" f(x} = “lim_{x->00)" f'(x} = 1; then 1൩ 0500)” 0015
ಹಿಂ
B:-1
C:-10
0:-11
Correct Answer:- Option-D
Question82:-The third approximation ` ४ (3) 00 10೯0761
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உறு பக (06
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D:-None of these
Correct Answer:- Option-B
Question83:-Consider the vector space V= {f: 'RR* *->" *RR" such that f* — 2f + f = 0 over *RR" . Then which of the
following is a basis for v 7

„ ४" = 2x(1 + vy} ४(0) = 0 by Pickard's method 15