Karnataka PGCET 2015 Question Paper Mathematics and Computer Science

POST GRADUATE COMMON ENTRANCE TEST - 2015
DATE & TIME COURSE SUBJECT
Department of Post Graduate Studies and Research MATHEMATICS
08-08-2015 in Mathematics and Computer Science,
AND
02.30 PM TO 4.30 PM Kuvempu University and Department of Studies
in Computer Science, University of Mysore COMPUTER SCIENCE

MAXIMUM MARKS TOTAL DURATION MAXIMUM TIME FOR ANSWERING

100 150 MINUTES 120 MINUTES

QUESTION BOOKLET
MENTION YOUR PGCET NO.
SERIAL NUMBER
320073
VERSION CODE A -1
DOs :
1. Check whether the PGCET No. has been entered and shaded in the respective circles on the OMR
answer sheet.
2. Ensure whether the circles corresponding to course and the specific branch have been shaded on the
OMR answer sheet.
3. This question booklet is issued to you by the invigilator after the 2nd bell i.e., after 02.25 pm.
4. The serial number of this question booklet should be entered on the OMR answer sheet.
5. The version code of this question booklet should be entered on the OMR answer sheet and the
respective circles should also be shaded completely.
6. Compulsorily sign at the bottom portion of the OMR answer sheet in the space provided.
DON'Ts:
1. THE TIMING AND MARKS PRINTED ON THE OMR ANSWER SHEET SHOULD NOT BE DAMAGED /
MUTILATED / SPOILED.
2. THE 3RD BELL RINGS AT 02.30 PM, TILL THEN;
Do not remove the seal / staple present on the right hand side of this question booklet.
Do not look inside this question booklet.
Do not start answering on the OMR answer sheet.
IMPORTANT INSTRUCTIONS TO CANDIDATES
1. This question booklet contains 75 (items) questions and each question will have one statement and
four answers. (Four different options / responses.)
2. After the 3rd Bell is rung at 02.30 pm, remove the seal / staple stapled on the right hand side of this
question booklet and check that this booklet does not have any unprinted or torn or missing pages or
items etc., if so, get it replaced by a complete test booklet. Read each item and start answering on the
OMR answer sheet.
3. During the subsequent 120 minutes:
• Read each question (item) carefully.
• Choose one correct answer from out of the four available responses (options / choices) given
under each question / item. In case you feel that there is more than one correct response, mark
the response which you consider the best. In any case, choose only one response for each item.
• Completely darken / shade the relevant circle with a blue or black ink ballpoint pen against
the question number on the OMR answer sheet.
4. Use the space provided on each page of the question booklet for Rough Work. Do not use the OMR
answer sheet for the same.
5. After the last bell is rung at 04.30 pm, stop marking on the OMR answer sheet and affix your left
hand thumb impression on the OMR answer sheet as per the instructions.
6. Hand over the OMR answer sheet to the room invigilator as it is.
7. After separating the top sheet (KEA copy), the invigilator will return the bottom sheet replica (candidate's
copy) to you to carry home for self evaluation.
8. Preserve the replica of the OMR answer sheet for a minimum period of ONE year.
9. Only Non-programmable calculators are allowed.

MARKS DISTRIBUTION
PART - 1 50 QUESTIONS CARRY ONE MARK EACH (1 TO 50)
PART - 2 25 QUESTIONS CARRY TWO MARKS EACH (51 - 75)

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MATHEMATICS AND COMPUTER SCIENCE
PART - 1
(Each question carries one mark) (50 X 1 = 50)

1. Representing the various steps in the form 6. is a technique in which the main
of a pictorial representation is called memory of the computer system is organised
in the form of equal sized - blocks called
a. Language h Program pages.

c. Algorithm cl. Flowchart a. Segmentation b. Swapping
c. Paging cl. None

2. The processing of removing a bug from
alogrithm is called as 7. GVI is an acronomy for

a. Error a. Geo - graphical usage interface
b. Graphical user interface
b. Problem
c. Global union of internet
c. Debugging
d. Geometrical used interface
d. None of the above

8. The execution of a program written in a C
language begins from
3. is the extension for MS - Powerpoint
a. Main ( ) b. Scanf ( )
a. DOC b. XLS
c. Printf ( ) d. ALL of the above
c. PPT d. None of the above

9. How many classes of datatypes does ANSI C
supports
4. Resolution is measured in terms of
a. 1 b. 2
a. Dots per inch b. Dot per pitch
c. 3 d 4
c. Pixels d. ALL

10. What is the range of values for float

5. The common keyboard arrangement is called a. —128 to 127
layout b. —32,768 to 32,767
a. QWERTY b. QWETYR c. 3.4C-38 to 3.4C+38
c. QYWERT d. ALL d. 1.7C-308 to 1.7C + 308

A-1 3 M/C

11. Each variable must be initialized before they 17. What is the output of the following program
are used in the program or function
main ( )
a. True b. False {
Int m = 5;
c. Both d ALL of the above
if (m<3)printf("%d",m+1);
else (m<7) printf(` %d", m+2);
12. Which of the following is not a predifined C }
header file ? a. 5 b. 6
a. math. h b. conio. h c. 7 d. 8
c. scientific.h d. ctype.h
18. What is the symbol used for bitwise exclusive
OR
13. Which of the following operators are used for
obtaining the remainder in a division a. V b. A
operator?
c. — d 86
a. / b. %
c. ! d None of the above 19. are the variables which are
declared within a particular function
a. External variables
14. Which of the following is the correct
statement for computing logical AND ? b. Internal variables
a. a<b&x>y c. Global variables
b. A<b&x>y d ALL of the above

c. a<bANDx>y
d. None of the above 20. It is used when the number of repetitions is
not known before the loop begins executing.
It is known as
15. Which of the following has the highest a. Infinite lopp
precendence ? b. Counter - controlled loop
a. H b. ( ) c. Sentinel - controlled loop
c. {} d. <> d finite loop

16. The value of variables persists 21. An array is a sequenced collection
until the end of the program of elements of the same data type
a. Auto b. Static a. Non - fixed b. Fixed - size

c. Register d. None c. Size d. None of the above

A-1 4 M/C

22. How to do a initializing a two - dimensional 28. Three lines are coplanar if
array
a. They are concurrent
a. Int table (2, 3) b. Int table {2, 3}
b. A line is perpendicular to each of them
c. Int table [2, 3] d. Int table [2] [3] c. They are concurrent and a line is
perpendicular to each of them
23. Do not forget to initialize the elements; d. None of the above
otherwise they will contain values.
a. Zero b. No value
29. The nth derivative of xn is
c. Garbage d. ALL
a. n ! b. 0
c. n d. 1
24. Which of the following is used to represent
the end of a string value
a. Blank space 30. The curves are said to be orthogonal, if the
angle between the two curves is
b. Null character
c. Newline character a. 0 7T
h
4
d. Last element of the string
7r
c. 2 d. 1
25. A pointer variable is identified by which
symbol ?
a. #
31. If U = XY then au is
c. + ax

a. 0 h y xY -1
26. Curvature of a straight line is
c. x Y /og x d yxY
a. 1 h 0
c. A variable d. A constant
71.1
27. In three dimensions, the equation 32. The value of J cos7x dx is

x2 - y2 = a2 represents - x/2

a. a pair of straight lines a.
327T 32
35 — 35
b. a hyperbola
c. a cylinder c. 0 15
d. a cone d 35

A-1 5 M/C

33. The area of a loop of the curve r =a sin 30 37. If L (f (t)) = f (s) then L(e-at f (t))is
is

7ra 2 a. f(s-a) b. f(s + a)
a. b. '
14
12 12
c. f(s) d None of the above
Tr
c. d 0
12
38. The chance that a leap year selected at
random will contain 53 sundays
34. The series 1+ r+ r2 + r3 + co converges if
2 1
a. b.
a. Irl<1 b. r> 7 7
c. 1 d. 7
c. r<_ -1 d I r l >1

39. The median of the numbers 11, 10, 12, 13, 9 is
35. Integrating factor of the differential equation
a. 12.5 b. 12
dy
—+ y cos x= si n2x is
dx 2 c. 10.5 d 11

a. e sin 1x b e sin 3 x
8 180
40. The value of r for which
c. e sin x d sin x Cr+6 = "-'3r-24 is

a. 4 b. 12
c. -12 d -4
36. e' (c1 cos -6 x+c2sin x)+c3 e 2 is the
general solution of

(13 y 41. If A = { 0, 1, 2, 3 } , then which of the
a. +4y =0
d following is reflexive ?

a. { (1,1) (1,2) (3,3)
h d x3
Y 8y - 0

b. (0,0) (1,1) (2,2) (2,3)(3,3)
d 3y
C. +8y =0
d X3
c. (2,2) (3,3)
d 3y d 2y d y
d. 2 2± 2=0 { (1,1) (2,2) (3,3) }
dx dx dx

A-1 6 M/C

42. If A, B and C are any three sets then 47. From a pack of 52 cards two are drawn with
replacement. The probability, that the first
Au(Bnc)=
is a diamond and the second is a king is
a. (AnB)U(AUC) b. (AUB)NAUC)
a. 26 b' / 52
c. (AUB)n(AnC) d. (AnB)U(AnC)

17
c. 2704 d. None of the above
43. Some group ( G, 0) is known to be abelian.
Then which of the following is TRUE for G ?

a. g = g-1 for every g e G
48. The set of all real numbers under the usual
b. g = g2 for every g e G multiplication operation is not a group since

c. (goh)2 = g2o 17 2 for every g,n E G a. Multiplication is not a binary operation

d. G is of finite order b. Multiplication is not associative

c. Identity element does not exist
44. A numerical method used to solve
d. Zero has no inverse
x ex —cos x = 0 is
a. Picard's method
b. Weddle's Rule 49. The general solution of the differential

c. Newton - Raphson method equation p = log (px — y) is
d. Euler's method
a. y = px + e ' b. y = px — e

45. The maximum slope of the curve
c. y= px — ec d. y = cx — e C
—x3 + 3x2 + 9x —27 is
a. 12 b. 14
c. 16 d. —14
50. A second order linear differential equation
has
46. The proposition p A (— p v q) is
a. Two arbitrary solutions
a. A tautulogy
b. One arbitrary solution
h A contradiction
c. Logically equivallent to p A q c. No aribtrary solution

d. All of the above d. None of the above

A-1 7 M/C

PART - 2
(Each question carries two marks) (25 X 2 = 50)

51. A set of rules that governs the 55. What is the output of the following code
communication process between the sender main ( )
and the receiver {
int a=10;
a. Message
while (a > 0)
b. Sender {
print f("hello I n");
c. Receiver }
d. Protocol }

a. Finite loop b. Runtime error
c. Infinite loop d. ALL of the above
52. Name of the keywords in the following
a. a, b 56. Identify the looping statements in the C
b. character, number programming language
a. if and else - if
c. int, char
b. else - if e switch
d_ None of the above
c. while and for loop
d. None of the above
53. The main use of session layer
a. Communication & notifying the errors 57. C programs are written in lower-case letters,
However uppercase letters are used for
b. Receiving and sending &

c. Internet and networks a. Variable & identifiers
b. Print & Read
d. ALL of the above
c. Symbolic names and output string
d. ALL of the above
54. A hexadecimal number is constituted with
the help of digits and letters 58. Do not use semicolon at the end of # define
directive
a. 0 -1 & AB
a. True
b. 0 - 6 & AD
b. False
c. 0 - 9 & A - F c. True or False
d. None of the above d_ None of the above

A-1 8 M/C

59. # include < stdio.h> includes two predefined 64. The direction cosines of the points ( -4, 9, 6 )
functions and and ( -1, 6, 6) is
a. getch( ) and clrscr( )
( 5,
1--1 0)
b. gets( ) and puts( ) a.( 2' ° h
1' -5'
c. printf( ) and scanf( )
d. putchar( ) and getchar( ) ( 1 1 0)
c. d. ( --I' 0)
2 ' ,ri ' \ 2 12 ' 1
60. Bitwise operators are used for testing the bits
or shifting them or
a. Right or left urn 2sinx— sin2x
65. is equal to
b. Right or top
x —> 0 x3
c. Right or bottom a. 1
d. ALL of the above
c. 0

61. How many types of category of functions are
there
a. 1 b. 2 66. If y = sin (log (x2 + 2x +1)) then
c. 4 d. 5
a. (x+ 1)2 y2 +(x +1) y1 + 4y = 0
62. How to initialize the double dimension array
b. (x + 02 y2 +(x+1)yi — 2y = 0
a. Int table (2, 2) - (0, 0, 0, 0)
b. Int table { 2, 2} = { 0; 0; 0; 0; } c. (x +02 y2 --(x+ 1)y, +4y = 0
c. Int table [2] [2] = { { 0, 0},{ 1, 1 } }
d. None of the above a. (x+1)2 y, — (x + 1) yi +2y = 0

63. Identify the correct syntax of user-defined
function x+ y
67. if u ,-. sin-i Nrx+ + j, then x ux ± y uy ,
a. Return type function name
(datatype argument )
b. No return type function name 1 i•n u
s b. —1 cos u
2
a. —
(argument ) 2
c. Return type function name ( data type )
tan u 1 cot u
d. -i-
d. ALL of the above c.
2

A-1 9 M/C

1 72. A pair of dice is tossed twice. The probability
2 )Y2 dx of scoring 7 points once is
68. The value of the integral f x4 (1— x is
0
equal to 5 5
h
a. 36 6
57r I
a. b. .17,-
8 5
cl. 18
3 71" 71"
c. d.
256 256

_n2
69. The differential equation formed, from the 73. E(1+ I) is
n
equation y = CI cos2x + C2 sin2x is
a. Convergent b. Oscillatory
22
y d y
a. dx +2
d2 y =0
b.
dx2
2y = 0 c. Divergent d. None of the above

d2 y d2y
c. 4y = 0 d. dx2 + 4y = 0
dx 2
74. The function ((p v (r v q)) A - (- qA — r)) is
equal to
70. The solution of the differential equation
a. q v r
(x + 2y3 ) —x = y is
dY

b. (p Aq)v(pAr)
a. x = y3 +cy b. x = y2 +cy
C. x=y+c d. None of the above C. (p Ar)v(p AO

d. pv r

71. The Laplace Transform of t e-2t sin4t is

75. If U = {0,1,2,3, 4,5,6,7,8}, A = {2,5,6,7} ,
8(s + 2)
8(s +2)
a. b. B = {0,2,5,7,8} then (AnBc) X (if ni3).
s2 +4s+20 (s2 + 4s + 20)2

8(s — 2) b. {(6,1) (6, 2)(6, 5)}
8(s — 2) a. 0
C. d. 2
s 2 —4s+20 (s 2 — 4s + 20) c. {(6, 0)(6,8)1 a. {(6, 0)(6, 7)}

A-1 10 M/C