Karnataka PGCET 2017 Question Paper Mathematics and Computer Science

POST GRADUATE COMMON ENTRANCE TEST-2017
DATE and TIME COURSE SUBJECT
Department of Post Graduate Studies
and Research in Mathematics and
01-07-2017 Computer Science, Kuvempu University MATHEMATICS AND
10.30 a.m. to 12.30 p.m. and Department of Studies in Computer COMPUTER SCIENCE
Science, University of Mysore
MAXIMUM MARKS TOTAL DURATION MAXIMUM TIME FOR ANSWERING
100 150 Minutes 120 Minutes
MENTION YOUR PGCET NO. QUESTION BOOKLET DETAILS
VERSION CODE SERIAL NUMBER

A-1 122115
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 2''d Bell i.e., after 10.25 a.m.
4. The Serial Number of this question booklet should be entered and the respective circles should also be shaded
completely 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 on the OMR answer sheet.
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 3" Bell rings at 10.30 a.m., till then;
• Do not remove the paper seal / polythene bag of this question booklet.
Do not look inside this question booklet.
DO not start answering on the OMR answer sheet.
IMPORTANT INSTRUCTIONS TO CANDIDATES
This question booklet contains 75 (items) questions and each question will have one statement and four answers.
(Four different options / responses.)
2. After the 3"' Bell is rung at 10.30 a.m., remove the paper seal I polythene bag 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 I 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 BALL POINT PEN
a°ainst the uestion number on the OMR answer sheet.
Correct Method of shading the circle on the OMR answer sheet is as shown below :

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 12.30 p.m., stop marking on the OMR answer sheet and affix your left hand thumb
impression on the OMR answer sheet as per the instructions.
6. Handover the OM R 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.
S. 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 EACII (I TO 50)
PART-2 : 25 QUESTIONS CARRY TWO MARKS EACH (51 TO 75)

M/C-Al 111111111111 is

MATHEMATICS AND COMPUTER SCIENCE
PART — A
Each question carries ONE mark. (50 x I = 50)

1. If two lines arc perpendicular then the 4. What is the derivative of f(x) lx1 at
product of their slopes is equal to .v = 0 ?

(A) 1 (A) 1
(B) —1
(B) —1
(C) 0
(C) 0
(D)
(D) does not exist
The equation of the straight line
parallel to x-axis is given by
x—a y—b z—e dx .
(A) 5. The value of the integral
1 1 1
—ay—bz—c
(B) (A) 0
0 0
x—ay—bz—c (B) 0.25
(C)
0
(C) 1
x—ay—bz—e
(D) (D) cc
0 0 1

3. The length of major and minor axes of 6. Maxima and minima occurs
r.2
the Ellipse + =1 is (A) simultaneously
25 16
(A) 25, 16 (B) once
(B) 10, 8
(C) Rarely
(C) 8, 10
(D) Alternatively
(D) 16, 25

M/C 3 A-I

7. The value of line (I +x) 1 ' is 10. Integrating factor for the differential
v dv
equation cos-x y tan x.
dx

(A) eianv

(B) cos 2x

(C) C rafty

(D) sin 2x
8. The pedal equation of the curve
r = a- sin- 0 is
11. L[e2t sin t] is
3
r
(A) p= S
a
(A) 2)2 + I

(B) p=
a (B)
(s-2)- +I
(C) p =
(C)
(s+2)2 —I
p-, a
(D) — --
r
(D)
(s — 2) 2 — 1
T 2
9. I cos xix is
( ,
x- + y-
12. If u then
5rr x+y
(A)
32 (711
x + 1, is
5
(B)
32
(A) cot u
It
(c) (B) sin u
32
(C) tan u
5Tr
(D)
16 (D) 0

A-1 4 NI/C

13. If the events A and B are independent 16. A man has 12 friends whom he wants
then P(AnB) is equal to to invite for lunch. In how many ways
(A) P(A) + P(B) can he invite atleast 10 of them
(B) P(A) — P(B)
(A) 66
(C) P(A) • P(B)
(B) 140
P(A)
(D)
P(B) (C) 153

(D) 79
14. Let A and B be two events with
1
P(A) = — P(B) = -I— and P (AnB) =
3
1 17. The four roots of x4 = 1 are
— then P(A/B) is
4
(A) 1, —1,
3
(A)
4 (B) 1, 1, 1. 1
4
(B) (C) 1, I, —1. —1
3

(D) i, i, —1, —i
(C)
4

3
(D)
— 4 18. Let A = 2, 3} then the power set of
A has
15. The mode of the number 7, 7, 7, 9, 10,
(A) 3 elements
11, 11, 11, 12 is

(A) 11 (B) 4 elements
(B) 12
(C) 6 elements
(C) 7

(D) 7 and 11 (D) 8 elements

M/C 5

19. If U= 11, 2, 3, 4, 5. 61, A 12. 4, 6;
then A' is
22. The series E 1 converges if
n=1 n

(A) p > 0
(A) 11, 3, 5
(B) p 1
(B) 12, 4, 6; (C) p> 1
(D) p < 0
(C) 12 41

(D) 11, 5; dy
23. If y x then -- is

1
(A)
2 '1(1+x)
20. If p and q are two propositions then
1
-(pvq) is (B)

(A) png

(B) pvq

(C)

(D) 24. From a pack of 52 cards, two cards are
drawn random, what is the probability
that both cards will be kings, if the
first card is not replaced
21. If a, bEG is a group then (ab)-i is
(A)
26
(A) a-1 b- I
(B)
52
(B) 13-1
1
(C)
(C) as I 169

(D)
(D) bb-1 221

A-1 6 111/C

25. lim (sin [LIFIX i s 28. The length of the string "pgcet" is

(A) 6
(A) I
(B) 8
(B) 0
(C)
(C) e
(D) 10
(D) 7/2

29. The value of an automatic variable that

26. UNIVAC is is declared but not initialized will be

(A) 0
(A) Universal Automatic Computer

(B)
(B) Unique Automatic Computer

(C)
(C) Universal Array Computer

(D) unpredictable
(D) Unvalued Automatic Computer

30. The statement int i = 5i then x = i
27. Which of the following is identified as
what is the value of x '?
cloud ?
(A) 4
(A) Web applications

(B) 5
(B) C

(C) 6
(C)

(D) Java (D) 7

M/C 7 A-1

31. If(a = 2) 34. The statement a>>2; indicates :

printf(" hello"); (A) shifts two bits towards left

else (B) shifts two bits towards right

printf("No"):, (C) adds 2 to a

what is the output ? (D) bitwise adds 2

(A) No

(B) hello No 35. UNIX is an example for

(C) hello (A) Command oriented OS

(D) No hello (B) GUI oriented OS

(C) A compiler

32. Use of functions (D) Assembler

(A) makes debugging task complex

(B) not enhance the logical clarity of 36. ROM is a
the program (A) Primary Memory
(C) makes the program complex (B) Secondary Memory
(D) helps to avoid repeating a set of (C) Random access Memory
statements many times.
(D) Flash Memory

33. Which of the following is not a low
level feature of C ? 37. ALU is nothing but

(A) Register class (A) all unit

(B) Bit fields (B) Arithmetic unit

(C) Bit wise operations (C) Arithmetic logic unit

(D) None (D) Algorithmetic unit

A-1 8 M/C

38. Intel P4 is a 41. Can you use social medial without
internet ?
(A) RAM
(A) Yes
(B) ROM
(B) True
(C) USB
(C) No

(D) Processor
(D)

39. E-mails can be accessed through 42. Word processor is an example for

(A) Network (A) compiler

(B) LAN (B) interpreter

(C) WAN (C) application software

(D) Internet (D) system software

43. Can we count no. of words characters,
40. Wchar is a valid datatype in C.
spaces in a file using MS-word.

(A) Yes
(A) Yes

(B) No (B) No

(C) May be (C) Only words

(D) Supports (D) Only characters

M/C 9 A-1

44. Extern is an example for 48. where is

(A) Storage class
(A) Pre decrementer
(B) Data type
(B) Pre incrementer
(C) Function

(D) Arrays (C) Post incremcnter

(D) Post decrementer
45. In the expression —x, where is

(A) Subtraction operator

(B) Decrement operator 49. Read only memory contents are
(C) Unary minus
(A) Volatile
(D) Binary minus
(B) Static

46. Size of(char) in bits
(C) Non-volatile
(A) 4
(D) Programmable
(B) 8

(C) 16

(D) 32
50. The loop for (: :); is valid.

(A) No
47. Pointer variable stores

(A) value (B) Error

(B) address
(C) Invalid Statement
(C) sum value

(D) decremented value (D) Yes-valid statement

A-1 10 M/C

PART - B
Each question carries TWO marks. (25 x 2 = 50)

4
51. L[t cos at] is 53. IX (— S
0

(A) 1
(s2 + 7T
(A)
256

s- - a -
(B) > „ 3
(s- + a`)- (B)
256

a- 37r
(C)
(C)
(s- -a- )- 256

1
s2 a 2 1
(D) 2 „ (D)
(s + a`)- 2 56

52. The solution of
54. 1 +— is
n
(D3 + D2 + 4D + 4) y = 0 is

(A) Converges
(A) y= + cos2x + sin2x

(B) Oscillatory
(B) y = c u e` + c2 cos2x + c3 sin2x

(C) Divergent
(C) y = (ci + c x + c3 x2 ) e-r

(D) Conditionally Convergent
(D) y= + c, e-2-v + C3 e-

M!C 11 A-1

55. is 58. Lt is
(s + a)- o 4
(A) e't
(A) ( abed) ) '4
(B) teat
(B) abed
(C) t
(D) e (C) log(abcd)
(D) 1

56. If P( A) P(B)
4
59. The points A(-4, 9, 6): B(-1. 6, 6);
P(AJB) - - then P(A/AI) is C(0, 7, 10) form a right angled
isosceles triangle, the direction cosines
1
(A) of AB are

1 (A),12,-h,0
(B)
3
1 -1
1 (B) 0
(C) v2 'i2
5
1 (C) - , Nr:;-
(D)
(D) 0, -F) -

57. Find the probability of drawing an ace
or spade or both from a deck of cards 60. The angle between two curves
rn = a" cos nO, r" = b" sin nO is
(A) --
13
(A) 0
17
(B)
52 (B)
4
13
(C)
52
(C)
4
(D)
13 (D)

A-1 12 NV('

61. The particular integral of 64. The following program fragment
(D2 + a2) y — sin ax is
for(i=1; i<5; ++i)
(A) — — cos ax
2a 4'(i-3)

(B) — cos ax continue;
2a
else
ax
(C) — cos av
printfi"%d", i);
ax
(D) cos ax result in printing of

(A) 1 ? 45
62. In a frequency distribution, mid-value
(B) 1 2 4
of a class is 15 and class interval is 4.
The lower limit of the class is (C) 2 4 5
(A) 14
(D) 1 2 34
(B) 13
(C) 12
(D) 10 65. for (i=3; i<15; i+=3)

63. Consider the function
find(int x, int y) printf("%d", i);

retum((x<y)?0 :(x—y));

let a, b be two non-negative integers. will result in
The call find (a, find (a, b)) can be
used to find the (A) 3 6 9 12
(A) maximum of a, b (B) 3 6 9 12 15
(B) positive difference of a, b
(C) 3 7 11
(C) sum of a, b
(D) minimum of a, b (D) 3 7 11 15

NI/C 13 A-1

66. Consider the array definition int 69. The purpose of the following program
num[ I 0] — 3, 3}; code is for
(A) num[9] is the last element of the
array num h s + b;

(B) the value of num[8] is 3 s— b— s
(C) the value of num[3] is 3
b=b—
(D) The value of num [4] is 3
where s, b are two integers is to

67. if a=5, b=5 then (A) transfer the contents of s to b.

x=++a; y—b+ ; then values of a, b, x
(B) transfer the contents of b to s.
and y are

(A) 66 65 (C) exchange the contents of s and b.

(B) 66 66
(D) negate the contents of s and h.
(C) 66 56

(D) 56 56

70. The statement

68. Forward declaration is absolutely
printf("%d", 25+±);
necessary

(A) if a function returns a non- prints:
integer quantity.
(A) error
(B) if the function call precedes its
definition.
(B) garbage
(C) if the function call precedes its
definition and the function (C) 25
returns a non-integer quantity.
(D) 26
(D) in an expression.

A-1 14 INI/C

71. Consider the following program code : 73. for(i=1; i<=1; i++)

int p=5, *ptr=4; fbr(j= 1 ; j<= 1 ; j++)

printf("%d\t%d", j);
printf("%d\t %d", p'*p+r);
(A) 1 1 1 2

(B) 1 2 1 1
the output will he
(C) 1 1 1 1

(A) an error (D) 1 1 2 1

(B) 5 and address of P
74. int i=5;

(C) 5 and garbage value +:

printtri=%dvt%d", *.] );
(D) 5 and 5
(A) 5 5

(B) 5 6

(C) 6 5

72. Any C program must contain (D) 6 6

(A) at least one function
75. in arr[ = 12, 5, 6, 71; then what is the
value of arr[3];
(B) one variable
(A) 2

(C) an array (B) 5

(C) 6
(D) constant
(D) 7

M/C 15 A-1

A-1 16 M/C