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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-B

Question37:-For any vector space V which of the following set is a subspace having a single element :

A:-{0}

ല്

D:-{{0}}

Correct Answer:- Option-A

Question38:-What is the largest possible value for the rank of a 2°xx*5 matrix ?

A:-10

B:-5

C:-3

D:-None of these

Correct Answer:- Option-D

Question39:-If atleast two elements a, b other than identity element are such that 0(a) = finite and 0(b) = ` 00", then the

group is called :

A:-Torsion free group

B:-Torsion group

C:-Mixed group

D:-P-group

Correct Answer:- Option-C

Question40:-Which of the following pair of groups are isomorphic ?

൧:-2 (24) and Z_8 0+ Z_(3)°

, (25) 2110 2 5 0+ 2 5`

©-2 (24) 270 2 5 ٠+ 2 5"

0:- 2 (20) 210 2 2 0+ 2 107

Correct Answer:- Option-A

Question41:-The point on the plane curve “f (x) = ~ * *x*3+3x+9x - 12° where the slope of the tangent is maximum is :

൧൦ (2,-12)"

B:-(1, 1)

(1, 1)

D:-None of these

Correct Answer:- Option-D

Question42:-The quadratic equation whose roots are the squares of the roots of the equation *2x*2-2x+5=0" is :

A: 4x*2+4x+25=0°

B:-4x*2+16x+25=0°

C:-°4x*2-4x-25=0°

D:-* 16x*2-4x-25=0°

Correct Answer:- Option-B

Question43:-If the sum of the distances of a point in the plane from two fixed perpendicular lines is |, then the locus of the

point is :

A:-Ellipse

B:-Hyperbola

C:-Square

D:-Parabola

Correct Answer:- Option-C

Question44:-The directional derivative of the scalar function *2xy+z*2+1° in the direction of the vector *i+2j-k> at the

point *(1,-1, 2)* is:

3ھ

8:-`15/2`

C:-0

0:۰17"

Correct Answer:-Question Cancelled

Question45:-The product of the eigen values of the matrix & = [[1, 2-1, 311 is :

A:5

8:-1

C:-4

D:-None of these

Correct Answer:- Option-A

Question46:-If *f (x) = (In (sin 2x))*2* then f' (x) is :

A:-4 cot 2x

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