Kerala PSC Previous Years Question Paper & Answer

Title : HSST MATHS JR NCA
Question Code : A

Page:9


Below are the scanned copy of Kerala Public Service Commission (KPSC) Question Paper with answer keys of Exam Name 'HSST MATHS JR NCA' And exam conducted in the year 2018. And Question paper code was '057/2018/OL'. Medium of question paper was in Malayalam or English . Booklet Alphacode was 'A'. Answer keys are given at the bottom, but we suggest you to try answering the questions yourself and compare the key along wih to check your performance. Because we would like you to do and practice by yourself.

page: 9 out of 12
Excerpt of Question Code: 057/2018/OL

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
கட்டு ப
உறு பக (06
‏لامي‎ + (2/2 ௫6
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

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