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Below are the scanned copy of Kerala Public Service Commission (KPSC) Question Paper with answer keys of Exam Name 'LECTURER IN MATHEMATICS - NCA - EZHAVA/THIYYA/BILLAVA' And exam conducted in the year 2016. And Question paper code was '088/2016/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.

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Correct Answer:- Option-C

Question72:-Let G = (V, E) be asimple graph. Choose the wrong statement from below :

A:-G is bipartite implies G has a perfect matching

B:-Any plane Graph has a dual graph

C:-Two isomorphic graphs are having the same degree sequence

D:-Any Hamiltonian graph is 2-connected

Correct Answer:- Option-A

Question73:-Let (X, d) be a metric space and *(x_n)* be a sequence in X. Choose the correct statement from the following :

A:-If *(x_n)* is a Cauchy sequence, then it converges.

B:-If ‘(x_n)* converges in X, any subsequence converges to the same limit.

C:-If *(x_n)* is bounded, then it has a convergent subsequence.

D:-If 0൧൧) is unbounded, then it cannot have a convergent subsequence.

Correct Answer:- Option-B

Question74:-Let *X = R*2*. From the following maps from X to X, choose the one which is a linear homeomorphism :

ಡಿಸ (x_1, + 2) = (x_1-x_2,x_2-x1)

B:-F (x_1, x_2) = (2x_1-x_2, 0)°

CF (x_1, x_2) = (3x_1, 4x_1)°

D:-*F (x_1, x_2) = (x_1-x_2, x_1+x_2)°

Correct Answer:- Option-D

Question75:-Let E = { x ‘epsi’ R: x is rational, 0 °<=" x *<=* 2}. The Lebesgue measure of E is :

൧-2

8:-1

C:-not Lebesgue measurable

0:-0

Correct Answer:- Option-D

Question76:-Among the following equations, choose the exact differential equation :

A:-12x* 2ydx+4x*3dy=0°

(x+y)dx+3x*2ydy=0"

(:- (dx)/(x) + (dy)Axy*2) = 0°

D:-* (4x*2+3y)dx+6x*2y*2dy=0°

Correct Answer:- Option-A

Question77:-Let X = ("C*2 *, ` ||. || 1 ). 1 €! ^ 118 । (X) be defined by A*(x_1, x_2)=(2x_2, x_1).° Then ||Al| is :

3ھ

8:- 3/2.

C:-2

D:-1

Correct Answer:- Option-C

Question78:-Let ‘mu’ denote the Mobius function then ‘mu’ (75) is :

ا

B:-0

D:-

Correct Answer:- Option-B

Question79:-Consider the vector field defined by X ‘(x_1, x_2) = (x_1, x_2, - x_2, x_1).° Choose an integral curve of X from

the following :

A:-‘alpha*(t)=" (et, e*-t)*

Correct Answer:-Question Cancelled

Question80:-Let *X = R*2,* Y = {(x, 0): x ‘epsi* R} where, *||.||_1° is defined on X. Let g : Y ->* R be defined by g((x,

0))=x. From the following choose a Hahn-Banach extension of g :

D:f (1, x_2) = 3x1 + 4x2"

Correct Answer:- Option-C

Question81:-Which of the following is not a solution of the two-dimensional Laplace equation :

A: u=e*xsiny”

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