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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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Question55:-Let f: R’->°R is differentiable for every x ‘epsi’ R, such that ‘lim_(x->00)° f'(x) = کل Then 1൩0൨-0൦)" 7

(40006:

ಡಿ

990 9

oh mle 2

0

Correct Answer:- Option-C

2

Question56:-Let t be a positive integer and define a sequence *{x_n}* by *x_(n+1)=t+* 3 for all n’ >="0 with *x_0=0". If

the sequence is convergent, then :

As t= U4

0:-1 (൮/൪)

Correct Answer:- Option-A

Question57:-Find the number of continuous onto maps from [0, 1] to (0, 1).

A:-Countably many

B:-None

C:-Exactly one

D:-Uncountably many

Correct Answer:- Option-B

Question58:-Let *f (x) = a_l* sin ‘x + a_2° sin ‘2x +...+ a_n’ sin nx such that |f (x)|"<="| sin x| ലാട. ന്ന

*Ja_1+2a_2+...+ 6:

A:-cannot find

B:-0

C:-greater than *(n (n+1))/2° 7

D:-less than or equal to 1

Correct Answer:- Option-D

Question59:-Let ` {5.0} ` 0€ a sequence of real numbers defined by *S_1=sqrt(2)* and “S_(n+1)=sqrt(2+S_n),*

then (51) 8:

A:-Monotonically increasing for all n

B:-Monotonically decreasing for all n

C:-Monotonically increasing for even n and decreasing for odd n

D:-Neither increasing nor-decreasing

Correct Answer:- Option-A

Question60:-Let f be a function on real line such that |f| is measurable. Then :

A:-f is measurable if it is monotonically increasing

B:-f is always measurable

C:-f need not be measurable

D:-none of the above

Correct Answer:- Option-C

Question61:-The value of ‘int_C***1/z*2 dz,* where C is the curve *|z - i] = 1/2,” is:

Ae

B:-0

“لمع

0; - 19/53:

Correct Answer:- Option-B

Question62:-Which of the following is a bounded complex valued function :

A--f (z) = sin z, in the complex plane

8:- (2) - e*z/z,* in the complex plane with |z| > 0

C:-f (z) = cosh z, in the complex plane

D:-None of the above (A), (B) and (C)

Correct Answer:- Option-D

Question63:-The function *g(z) = (z)/(e*z-1), z!= 0,` has:

A:-Essential singularity at z = 1

B:-Pole at the origin

C:-Essential singularity at the origin

D:-Removable singularity at the origin

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