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26 JNUEE: Question Papers (2010-2012) Rs.SO

ENTRANCE EXAMINATION, 2012

M.Phil./Ph.0 . & M·.Tcch./Ph.D. ·COMPUTER & SYSTEM SCIENCES

't Field of Study Code : COMP-SCSP (158)/MTCP !157) J

120

Ttlll<' Ailowc:d 3 hou·rs Maximum Marks: 480 Weiyhwg<: : 70

INSTRUCTIONS FOR CANDIDATES

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INSTRUCTJONS FOR MARKING ANSWERS

\J~t· only Blue/Black Ballpoint P~'n (do not use pe rKil) to darken the apprnprwle Circle 2 Pk ast' d::irke11 thr whole Circle. J Dar ke n ONLY ON8 CJB~ fo r each question as s hown in exampl~ below ;

Wrong Wrong Wrong Wrong Correct

•@@• ® .@©@ @@©@ @@©• @@@• 4 . Once marked, no change 111 the answer is allowed. 5. l'le>1s1· do nnl mak,• any s tray marks on th<· Answe1 Sht'.Cl.

. 6 . Please clo not do a ny rough work on th<: Ansv. er Shr·ct . 7. Mark your ans wer only in the appropriate space ag;uns: the number corresponding·ro the qu1•st1on.

· S. 'Ensure that you have darkened the appropriate Circle of Question Paper Se.ries Code on the Answer Sheet .

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1. The binary number 10011101 is equal to the hexadecimal number

(a) 103

(b) 76

(c) 67

(d) . - 67

· 2. The probability that a le~p year has 53 ·Sundays is·

(a) 1/7

(b) 2/7

(c) 5/7

(d) 6/7

3. Consider the SOTS for the following AND operation :

'1..1

E --7 Ell) AND M E(2 )

4. -(

backpatch (E(l) .True, M.quad); E.True : = [:=J; . E.False : = Merge (E{t) .False, E(2l .False)

The missing term at [:=J must be

(a) -E(l) .True

(b) Ell). False

(c) E( 2 ) .False

(d) None of the above

Let a, b, .c be non.:.zero real numbers such that

.f1 (1 ~ COSS x)(ax 2 +bx+ tj dx = f 2

(1 +COSS x)(ax 2 +bx+ tj dx 0 0 .

Then the qua dratic equation ax2 +bx+ c = ·O has

(a) a double root in (0, 2)

(b) at least one root in (0, 2)

(c)" no root in .(0, ·2)

(d) two imaginary ront~

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5. Consider the following two theorems involving a language Land [, (complement of L)':

(i) T,he complement of a recursive language is recursive.

(ii) If a language Land its complement L are both recursively enume.rable, then L (and hence l) is recursive.

Which one of the following does not logically follow from theorems (i) and (ii)?

(a) Both l, ·and l are recursive

(b) One of L and l is recursive; the other is recursively enumerable

(c) Neither L nor l is recursively enumerable

(d) One of L and l is recursively enumerable but not recursive; the other is not recursively enumerable

6 . Wnich one of the following is an optimal substructure property?

(a) If Sis an optimal solution, then the components of Sare not necessarily optimal

(b) If S is an optimal solution, then t})e components of S are not dependent to S

(c) If S is an optimal solution, then the components of S are optirn~ solutions to subproblems

(d) None of the above

7. Consider the folio.wing Hasse diagrams (i) and (ii)

'(',

f

e c d

c

a a (i) (ii)

Which one of the following options is true?

(a) · Both (i) and (ii) are lattices

(b) (i) is a lattice and (ii) is not a lattice

(c) Ji) is not a lattice and (ii) is a lattice

(d) Neither (i) nor (ii) is n lnH;,...,,

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.'

8. Consider a stochastic process X(t), t e T, defined by X(t) = acos(cot + <!J), where a and w \~ are real constants, and <l> is a random variate uniformly distributed in the interval

JO, 2n]. We obtain E{X(t)} as

(a) 1t

(b) a

(c) 0

(d) a cos wt

9. The well-formed formula p v (- p /\ q) is equivalent to

(a) p/\q

(b) pvq

(c) -pAq

(d) -pvq

10. Imagine a 3 x 3 x 3-inch opaque cube divided into twenty-seven 1-.inch cub~s. What is the maximum number of 1-inch cubes that can be seen by one person from any point?

(a) 9

(b) IS

(c) 19

(d) 21

11. Among the following sets, identify the set which is neither open nor closed.

\ (a) The empty set

(b) The Cantor set

(c) The set ·of rational numbers

(d) The set of real numbers

12. An LSI device. has a circuit complexity of

(a) 12 to 99 equivalent gates

(b) . 100 to 9999 equivalent gates

(c) 2000 to · 5000 equivalent gates

_(d) 10000 to 99999 equivalent gates

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13. Which of the following is true for a relocatable program?

(a) It can be loaded at one specific location

(b) It does not require a linker ·

(c) It can be loaded almost anywhere in the memory.

(d) It cannot be . used with fixed partitions

14. A car travels from point A to point B·(a distance of one mile) aJ 30 miles per hour. How fast would the car have· to travel from point B to point C (also a distance of one mile) to· average 60 miles per hour for the entire trip?

(a) 90 miles per hour

(b) · 120 miles per hour

(c) The car h as reached point C already (

(d) Not possible tq average 60 miles per hour

15. For which values of p, the following system of equations has solutions?

px + y = 1

16. Let T be a linear transformation from B1 to B2 , where 8i and B 2 are. Banach spaces. If T is continuous, then-

(i) its graph is a closed · set

(ii) G is an open set in B1 .implies T(G) is an open set in B2

(iii) for any sequence {Xn} in 8i converges to the origin impiies the ~equence {T(Xn)} also converges to the origin in B2

Identify the correct option from the following.

(a) All are false statements

(b) All are true statements

(c) Exactly two statements are true

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17. The simplified Boolean expression for X = A'BC+ AB'C' + A'B'C' + AB'C+ ABC is

(a) AB

(bl B'C

(c) AB+ (A'+ AB')C

(d) · AB'+ BC+ B'C'

18. A ladder was standing perfectly upright against a wall. Suddenly the foot of the ladder slid away from the wall and came to a stop 15 feet from the wall. The top of the ladder had moved one-fifth of the ladder's length before it came to rest firmly on a windowsill. Which of the following is true for the problem? ·

(a) Insufficient information to calculate the length of the ladder

(b) Sufficient infonn·ation .exist and length of the . ladder is 25 feet

(c) Sufficient information exist and length of the ladder is· 5 feet

(d) lnvalid question

19. Nine men and seven women pick as much com in five days as seven men.and eleven women pick in four days . Who are the better corn· pickers and by how much?

(a) Women are better workers by a ratio of 17 : 9

(b) Women are better workers by a ratio of 2 : 1

(c) Men are better workers by a ratio of 13. : 1

(d) Men a're better workers by a ratio of 2 : 1

20. Which one of t;he following is true for the matrix A = [ ~ ~] ?

(a) The. eigenvalues of A are (2, 4)

lb) . . F 1]

A has a unique eigenvector l i

(c) The trace of A is 8

(d) The rank of A is 1

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21.

23.

process? UNIX operating system does not .have a parent

(a) sh

(b) dev

(c) login

(d) kernel

How many distinct strings of length 10 can be constructed f~om the two digits 0 and 1 "\.th the restriction that five characters must be 0 and five must be 1?

(a)

(b) 272

(c) 302

(d)

I

dx (k is a positive constant). Find the limit lk as k =-t 00 •

(a) 0

(b) 1

(c) - 1

(d) e

24. In immediate addressing, where is

(a) In memory

(b) In stack

(c) In instruction after OP ·code

/.J I In CPU Register

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25. Let 8 =sin- 1(sin(-600")), then the value of8 is \l

26.

(a)

(b)

. /rl\ \'-'}

7t

3

7t

2

2n 3

The letters A, B, C, D, E, F and G, not nec~ssarily in that order, stand for ·.:;even consecutive integers from 1 to 1 O such that-

(i) D is 3 less than A

(ii) · B is the middle term

(iii) F i's as much less than B · as C is greater than D

(iv) G is greater than F

What is the value of (A - F)?

(a) 4

. (b} 3

(c) 2

(d) Cannot be determined

27. Among the SQL operations (i) Union, (ii) · Union ALL, (iii) Select and (iv) Intersection {l duplicates are preserved in

(a} (i) and (ii)

(b) (i) and (iv)

(c) (ii), (iii) and (iv)

(d) (ii) and (iii)

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28. The v'.3-lue of the game

is

(a) 1 /5

(b) 2/5

(c) 3/5

(d) 4/5

Player A

Player B

Bl B2 B3 .B4

~i.__~ __ o _ _ : __ -2_

2

_,I

29. Auxiliary carry is the carry generated from

(a) b_it D0 to · D1

(b) bit D3 to D4

(c) bit D7 to D 8

(d) bit 0 8 to D1

30. What is 1/2 of 2/3 of 3/5 of 135 divided by 1/3?

(a) 81

(b) 90

(c) 175

(d) 225

31. Study the following statements :

(i) There exists a finite group of order n. for each positive integer n.

(ii) A group with the property that x 2 = e, for every element x from the group, where e is the identity element, must be Abelian.

(iii) A group of order n. with n.::; 4 must be Abelian.

Identify the number of correct statements.

(a) 3

(b) 2

(c) 1

(d) 0 ·-

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32. Consider the following statements _reg'.3-rding mutation testing :

(i) It is performed by cha..nging the test case.

(iij It is performed by changing the code.

'{iii) It tests if unit testing is correctly performed.

(iv) It is unnece~sary if unit testing is successful.

The correct statements are

{a) · both (i) and (iii)

(b) both {i) and (iv)

(c) both (ii) and (iii)

(d) both (ii) and (iv)

33. Computers operate with a fixed. number of digits and any excess digits produced in multiplication or division are lost. This type of error is called

ta) run-time error

(b) truncation error

(c) round-off error

(d) practical error

34. Which of the following algorithms is not a comparison-based algorithm?

(a) Heap sort -. (b) Quicksort

(c) Ra~ix sort

(d) Topological sort

· 35. Choose a correct alternative for the foll?wing relationship

Import Expo_rt .. Expenditure : ? ..

(a) Deficit

(b) Revenue

(c) Debt

(d) Tax

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36. ·suppose that the life of an industrial lamp (in thousands of hours) is exponentially distributed with failure rate A. = l f.3. The probability that the lamp will last longer than its mean life of 300_0 hours is/ given by

(a) 1 -1 -e

(b) e-1

(c) e-3

(d) 1 -3 - e

37. Modulation in which the two· binary values are 'represented by two different amplitudes of the capier frequency is known as

(a) amplitude

(b) amplitude modulation

(c) amplitude shift keying

(d) ALOHA

38. Which one of the following properties is true for a cyclic monoid?

(a) Every element has a unique inverse

{b) Only few elements have inverse· elements .. . (c) Every element is generated by an element called the generator element of the

monoid

(d) All of the above

39. Which one of the following is unlike the other three? .

(a) Kav.eri

(b) Krishna

(c) Mahanadi

(d) Narmada

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40. Th~ value of the definite integr~l J~ (1 + e-x2

) dx is

41.

(a) - 1

(b) 2 r

(c) l+e-1

(d) · None of the above

Assume that an upp~r triangular matrix a[O ... n - 1, 0 ... n - IJ is stored in a linear array

in.a lexicographical order. If a[O, OJ is stored in b(OJ, where is a [80, 90} stored in array b for n = 100?

(a) b(4851J

(b) . b[4855]

(c) b[4750J

(d) Non.e of the above ..

42. How many terms are there in the series 197, 204, 211, ... , .458?

43.

~'\

(a) 36

(b) 37

(c) 38

(d) 39 ·

The ·value of

(a) 0

(b) 1

(c) 4

(d) 8

. .

l 1 1 11 c; n + 2 c; n+ 4 c; is nc

2 n+2c . 2 n+4c

2

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44. The class 'Car' is derived from the class 'Vehicle'. The method start() is defined in the I .

Class 'Vehicle'. ~year is an instance of the class 'Car'. Assuming polymorphism, when MyCar.start() is executed, Vehide.siart() is not called, when

{a) Car.star t() does not refer to ·vehicle.start()

{b) 'Car' class does not define start() method

. .

{c) Car.~tart() calls Vehicle.start() and does nothing else

(d) user casts the M~Car object to 'Vehicle' class before . calling start()

45. . Which of the following statements is false?

2 2 {a) F(x, y) = x + Y is a homogenous function· of degree 1

x .,.- y

. 2

The differential equation of a ll non-horizontal lines . i~ a plane is d x = O (b) . dy2

(c) The general solution of the differential equation dy . dx + y sec x = tan x is

y(sec x - t.an x) =sec x - tan x + x + k

(d) (. e -21"-~ y J ·dx . dy 1

l r - r - = 1 (x ~ 0) when written in the form of- +Py= Q, then P = c

"x "x dy dx . "x

46. In the series 11 , 22, 44, ... ,what is th P 1 1th term?

(a) · 5635

(b} 7192

(c) 9999

(d) 11264

47. The beginning and the ending address for the data segment ~ssuming that register OS = EOOOH for microprocessor 808? will be

(a) OOOOOH and EOOOOH

(b) OOOOOH and FFFFFH

(c)_ -EOOOOH and EFFFFH

(d) EFFFFH and FFFF __ _

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48. DDT is related to 'Abbreviation' in the same way as LASER is ·related to

(a) Epigram

(b) Epithet

(c) Acronym

· (d) Antithesis

49. The optimal solution of the line·ar programming .problem of \ maximizing Z = 1 OX + l SY

subject to

2X + Y ·:5 26 ··

X + 2Y :5 28

Y-X:55

X;?: 0 , Y;?: 0

is obtained as

· (a) X= 8 , y = 10

(b) X= 6 , y = 1

(c) x = 6, y = 10

(d) x = 8, Y =8

50. In McCabe's cyclomatic complexity metric, code is first repn:!.:>t!nted <.•~

(a)

(b)

(c)

(d)

a syntax graph

a data flow graph

a command flow graph .....

a control flow graph

·si. The equation tan- 1 x - cot.:1 x = tan- 1 ( ~) has

~ (a) infinite number of solutions

(b) two solutions

(c) a unique solution

(d) no solution

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-..

52. If VICTORY is coded as VJEWSW~, then the code for SUCCESS is

53.

\

(a) SVEFIXY

(b) SWFGJYZ

(c) SVEEIXX

(d) SWFFJYZ

Given the following pair of productions, where left-recurs ion exists in (i) and p in (ii) does- not begin with symbol A :

(i) A4Aa

(ii) A4P

Then which one of the following will be used to eliminate the left-recursion?

(a) ' A4PA' A' -ta A ' A'4e

(b)_ A4A'~ A '-ta.A' A' 4e

(c) A4PA' A'4A'a A' 4 e

(d) A4PA' A'4aA' A' 4A

54. For the function d efined by y = Ix I. an expression for dy for each value of x, where the . dx .

ti derivative exists, is

(a) x

lxl

(b) _ lxl

(c) - lxl

(d) -i

55. In a certain code language, '851' means 'gooc;I sweet fntit'; '783' means 'good red rose' and '341' means 'ros e and fruit'. Which of the following digits stands for 'sweet' in that language?

(a) 8

(b) 5

(c) 3

(d)

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56.

f"\

In a S~queen problem in which one queen is in tht; first column and second row, how many solutiorys a re possible?

(a )

(b) 2

(c) · 3

{d) 4

. 57. The e notation complexity for. the pseudocode

is

(a)

(b)

(c)

(d)

i = n

while (i<'!l)

for j = 1 to n x=x + i = i/2

tl (n)

~ (log 2 n)

tl (rt / log 2 n)

B (n log 2 n)

58. In a complete graph of n. ve:tices (n is .odd and greater than 3), how many edge-disjoint Hamiltonian circuits are possible?

(a)

(b)

(c )

(d)

n

2

n - l

2

n

n - 1

59. At the end of a cricket series, when five players were arranged in the ascending order of runs scored by them, 0 was fourth whi.le N was first. When they were arranged in descending order for wickets taken by them, K replaces 0 while 0 replaces L . . The position of M remains unchanged. K has scored more runs than M. L has the first rank in one ranking and fifth in tne other. Who has taken the lowest riumber of wickets?

(a) M

{b} 0

(c) L

(d) K

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60. The tangent of the curve given by x = et . cos t, y = et. sin t at t = ~ m~kes with x-axis 4

an angle

(a) rt

4

(bl n

3

(c) rt

2

(d) 0

61. Which of the follo\Yihg gives the least upper bound for the value of /(N), where f is a t<' solu tion to the recurrence f(2N + 1) = /(2 N) = f(N) +log N for N ~ 1 with f(l) = 0?

62.

r

63.

(a) O((log N) 2 )

(b) O(log N) + 0(1)

(c) O(Nlog N)

(d) None of the above

. . : r a bl Let a, b, c be given numbers with at 0. Then the value of d, . so that the matrix l . J

. c a

has rank 1, will be . . ; :

(a) be

(b) ab

(c) ac

(d) None of the above

A snail is at the bottom of a 20-meter deep pit. Everyday the snail climbs 5 meters upwards, but at night it slides 4 meters back downwards. How many days does it take before the snail rea.ches the top of the pit?

(a) 20

(b) 19

(c) 17

(d) 16

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64. A class template with typ~ Tis fi~st instantiated with int and then with double. In such a case

(a)

(b)

there is no need of the prefix int or double

you must precede each function call with the word int or double

(c) instantiation with double is not perl'!litted once you instantiate with int

(d) · you. cannot perform this in C++

65. Consider the following statements :

?'- (i) The inverse of a lower triangular matrix is lower triapgular.

(ii) The triangular factorization of an invertible matrix need not be unique.

(iii) Let A be a triangular matrix so that it can be factored as A = LU, where L is lower triangular and U is upper triangular. Then both L and U are also tridiagonal.

Which of the following options is correct for the above statements?

(a) Only (i) and (ii) are true

(b) Only (ii) and (iii) are true

(c) Only (i) and (iii) are true

(d) All (i), (ii) and (iii) are true

66. The average of 9 numbers is 61. If the average of first 5 numbers is 58 and that of last

\~ \ 5 numbers is 63, what is the fifth number?

(a) 66

(b) 61

(c) 56

(d) 53

67. The number of clock cycles needed for execution of the 'instruction LXI H, 2500H"using ~ microprocessor 8085 will be ·

(a) 7

(b) 10

(c) 14

(d) dependent. on the clock frequency of the ,processor

18/2~

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~ .

~

' .

68.

It I

69.

' I \

. .

Suppose_ P and Q ar'e two n x n matrices such that PQ = Q2 P. Then (PQ) 2 equals

. (a) Q2p2

(b) Q4p2

(c) Q6p2

(d) p2Q2

Divide 50 in two parts such that the sum of the reciprocals is -1

. What fl.re the 12

numbers?

{a) 20, 30

(b) 24, 26

(c) 28, 22

(d} 36,_ 14

. I

70. If 4 + 7 + 3 = 281294) 8 + 6 + 3 = 482466, 3 + 9 + 5 = 271527 and 7 + 2 + 5 = 143542, then ~v\' what is 9 + 5 + 4?

I

· {a) 364516

(b} 453661

{c) 453656

(d) 563672

71. Which of the following is true for the function f : R ~ R defined by f(x) = x ? \A x 2 + 1

(a) Only one-one

(b) Only onto

{c) One-one and onto

(d) Neither one-one nor onto

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/2. The probability that a squirrel passes the road safely without getting run over is 1/ 4. · The probability of the squirrel passing the road safely and a bird falling off her nest is

73. ( ./

74.

1 /6. What is the probability that the bird falls off her nest? · ·

(a) 1/24

(b) 2/3

(c) 2/5

(d) 1/3

An incorrect step, process, or data definition in a computer program is a

(a) failure

(b) mistake

(c) fault

(d) consequence

Five jobs. are to be processed on three machines A, Band C in the order A-B- C. The timings of the five jobs J 1 , J 2 , J 3 , J 4 and J 5 in machines A, Band C respectively are known to be (30, 40, 70), (80, 50, 90), (70, 10, 50), (50, 20, 60) a nd (40 30, 100) . The optimal sequence would be

75. In how many ways can 7 persons be seated as Adi would not sit on the middle seat or on either ends?

(a) 720

(b) 2160

(c) 2720

(d) 2880

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76.

( I

A code word 0010001 is received at the receiver . The receiver does not know what was transmitted. If even parity is used and only one bit is assumed to be in error, the bit position of the erroneous bit using Hamming code error detection method is

(a) l

(b) 2

(c} 4

(d) 7

77. If A and Bare symmetric matrices of the same order, then (ABT - BA-T ) is a

\~ (a) null matrix

(b) skew-symmetric matrix

(c) symmetric matrix

(d) None of the above

78. Which of the following is the correct declaration for "A pointer to a function which receives an int pointer and returns float pointer"?

(a) float*(ptr)*iht; .

(b) float*(*ptr) (int)

(c) floa t*(*ptr)(in t *)

(d) float(*ptr)(int)

79. Consider dy = ~-2Y· dx '

when x = 5, y = 0. When y = 3, the value of ·X is

(a) e 6 + 1

(b) e 6 +4

(c) e 6 + 9

2

(d) es

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80. Address resolution protocol (ARP) is

(a) a protocol used to monitor computers

(b) a protocol "that handles error and control messages

(c) a TCP / IP protocol used to dynamically bind a high-level IP address to a low-level physical hardware address

(d) a TCP /IP high-level protocol for transferring files from one machine to ano'ther

81. If y = 2· 6+ O· 7x is the least-squares l_ine for the data points (0 , 3), (1 , 3), (-1, 2), (2, 4) and (x5, 1), then the value of x ·5 is

82.

~\ I

83.

. ~

(a) 2·28

(b) _'.2·28

(c) 2

(d) -2 ;..

. In a departmental store prize box, 40% of the slips give the ~inner a dreamy vacation; the other slips are blank. What is the approximate probability t hat 3 out of ·5 people that draw the s lips one after the other, and immediately return the slips into the box get the dreamy vacation?

(a) 0·23

(b) 0·35

(c) 0-45

(d) · 0·65

1 y(x) 7t n The formula J dx = - L y(x .) is

- 1~l-x2 . n i= l i

{a) Simpson's formula

(b) Gauss-Hermit formula

(c) Gauss-Laguerre formula

(d) Gauss-Chebyshev formula

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..

84. Using IEEE 754 single precision representation for - 0 · 75, the bit values in the bits representing the exponent reads

85.

86. •

'

(a) 01111110

(b) 00000001

(c) 11110001

(d) 11111111

The solution to the minimization problem

Minimize xf + x~

subject to

will be

(a) (1, 0)

(b) (0, -1)

x 2 - x1 -2 ~ 0

x{ - x2 -4 ~ 0

(c) Solution does not exist

(d) None of the above·

If n is the number of vertices, e the edges and r the faces in a graph, then which of the follo_w,ing holds true for a planar graph?

(a) n - e + r = 2

(b) n + e- r = 2

(c) e + r- n = 2

(d) None of the above

87. A binary tree is called full if every internal verdx has exactly two children. Then ~ determine the height of a full balanced binary tree with 4095 vertices .

(a) 10

(b) 11 .. (c) 12

(d) None of the above

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j ..

88.

v

89.

!;'!

Study the following C program code

#include<stdio.h> # include<stdlib.h>

int main() {

static char·*p=(char*)malloc(l O); return O;

Which one of the following options is_ true for the above C program code?

{a) Error : Lvalue required

(b) . Error : rva lue required

(c) Error : invalid *p declaration

{d) ' No· error

. II fx-.JXdx ( 0) Evaluate the mtegra = x > . . x + .JX

(a)

(b)

(c)

(d)

4 lr1:(.JX + 1) + c

x -4.JX + c

x - 4.JX + 4 ln ('.JX + 1) + c

')

x- -4x + 4ln Ix+ 11 + c

90. Consider a relation. Star (name, street, city, birthdate) with key underlined. The functional dependency name ~ birthdate holds for the relation. The normal form of Star is

(a) lNF

(b) 2NF

(c) 3NF

(d) Cannot oe determined with the given information

91. Consider t!'1e set A containing n elements . Then the total m~m~er of injective functions from A onto itself is

(a ) 2n

(b) n 2

(c) n * (n - 1)

(d) n!

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•.

..

:::.

92. The minimum number of nodes in an AVL tree (height-balanced binary tree) of height 9 is

(a) 85

{b) 88

(c) 143

(d) 54

l mx + !, if 93. If f(x) :== .

if · s1nx + n ,

x<K . - ~ is continuous at x = ~, then which one of the following is

x>- 2 2 . t

true?

mrc (a) n=-

2

(b) 7t

m=n=-2

n 7t (c) m=-+1

2

(d) m = 1, n=O

94. Exponents in floating point number representation are biased to

95.

(a) enhance the range of representation

{b} enhance the precision in the representation

{c) to facilitate representation of zeros

(d) None of the above

The correct representation in first-order logic for the sentence "Everyone who loves all animals is loved by someone" is

{a.) 'd x (Vy Animal (y) 4 Loves (x, y) ! 4 [3y Loves (y, x) J

{b} V x ('t y Animal (y) 4 Loves (x, y) J 4 [3z Loves {y, z)]

(c) [VxVy·Animal (y) 4 Loves(x, y)] 4 _[3y Loves(y, x} ]

(d) None of the above

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96. The maximum value of X 12 + 2X~ + 4X 3 using dynamic programming is obtained as

97.

(aj" 64

(b) 46

(c) 32

(d) 8

Let A be a matrix of order 3 s u ch that its eigenvalues are 0, 1, 2. Then the eigenvalues of A(A - I) (A - 21) will become

(a) 0, 1, 2

(b) . Q, -1 , - 2

(c) 0, i , 2i

(d)_ None of the above .

':"h ere i is the complex numb~r in which i 2 = - 1.

98. Postfix expression fo r the infix 1expression [(A+ BJ* (C+ D- E) * F] is

"f (a) ABCDEF * - + * +

(b) AB+CDE-+F**

(c) AB+ CD+ EF * - *

(d) AB+ CD+ E-*F*

99. ' 1 r (x - µ) 2 1 .

The normal density func!ion is defined by f(x) = rrc expl- J, - oo < x < oo. Then' -v2n 2cr 2 .

J~ 00

x f(x) dx is

(a) 1

(J (b)

µ

(c) µ

(d) (J 2 +µ2

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100. What would be the sequence of nodes in postorder traversal of a binary tree whose inorder and preorder traversals are as under?

lnorder : A D E F C B

Preorder : A B C D E F

(a) FD EC BA

(b) FED CB A

(c) FED BC A

(d) DE F C BA

101. A collection of attributes which uniquely identify a tuple in a relation is called a

(a) primary key

(b) superkey

(c) candidate key

(d) unique key

102. · Let (X, d) be a metric space, where Xis 4 i1u11cmpty set a nd the metric d(., .) on Xis defined as

for x, ye X

{ 1 if x t y

d(x. y) = 0 if x = y

Then Xis

(a) a complete metric space

.(b) a compact metric space

(c) n either a complete nor a compact metric space .•

(d) None of the above

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103. What is the output of the following C program?

104.

#include<stdio.h>

int main() {

struct s 1

char *z; int i;

struct s 1 *p;

f; static struct s 1 al]={ {"Nagpur", 1, a+ l},

{"Chennai", 2, a+2},

}

{"Bangalore", 3, a}}; struct s 1 *ptr = a; printf("%s, ", ++(ptr->z)); printf("%s, ", a[ (++ptr)->i] .z); printf("%s", a[--(ptr->p->i)J .z); return O;

(a) Nagpur, Chennai, Bangalore

(b) agpur, hennai, angalore

(c) agpur, Bangalore, Bangalore

(d) None of. the above

In a homogeneous system of equations AX= 0, where X = 0, which of the following ·is false for the square matrix A?

(a)

(b)

(c)

{d l

A is a nonsingular

Adj A=~ IAI

(AB)-1 = B- 1 A - l , where. B is a square matrix of order same a s that of A

105. The three states of a tristate output buffer are

(a) HIGH, LOW, High impedance

(b) HIGH, LOW, Low impedance

(c) HIGH, LOW, Ground

(d) . Right, Left, Center

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}06. The Hessian matrix of the function f(x1, x2

) = e(x1 -x2) +e(~-xi) is

'" (a) positive definite

(b) positive semi-definite only

(c) negative definlte

(d) indefinite

107. Given a context-free grammar G = (V, T, .P. S), which of the following statements does not hold trLie for a derivation tree for G?

(a) Every vertex is labelled by a E Vu M

• (b) !f the vertex is interior and has a label A, then A E V

(c) If n has a labe l A and vertices n, n 1, n2 , .. . , nk are the sons of vertex n, in order from left, with labels X1, X2, ... , Xk respectively, then A~ Xj X 2 ... Xk must be a production in P ·

(d) If a vertex n has . label · E, then n is a leaf and is the only child of its parent

108. Let n be the number of vertices, e the number of edges a~d k the number of

1• com ponents in a graph G, then nullity of G is

109.

(a) n-k

(b) e-k

(c) n-e+k

(d) n-(e+ k)

The ratio test is

(a) to derive a function f(n) = n c for the main term in the algorithm's running time. for

some constant c? c'.

(b) to derive a function f(n) = n c for the least term in the algorithm's running tfme for

some constant c;?: 0

(c) '

(d)

to plot r(n) = t(n) / f (n), where t(n) is the actual running time of the algorithm on a specific problem instance siz~ n, r(n) the ratio function and f(n) the polynomial to estimate the average running time

to plot r(n) = f (n) / t(n), where t(n) is the actual running time of the algorithm on a specific problem instance size n, r(n) the ratio function and f(n) the polynomial to estimate the average running time ·

29/26

110. Let f(x) = sin2x in [ 0, ~] . Which one of the· following statemer:ts is fals'e for Rolle's

theorem for f(x)?

111.

{Y'·

112.

(a) [ -7t2J f(x) is continuous in 0,

(b) /(0) = f(n)

(c) f is derivable in 0, ( -1t2)

(dJ The tangent at x = ~ is parallel to x-axis 4

The number of bits required for a direct-mapped cache with 16 KB of data and 4-word blocks, assuming a 32-bit address, is

(a) 100 Kbits

(b) 147 Kbits

(c) 256 Kbits

(d) 1123 Kbits

1 . . The value of f l2x - 11 dx, where I yl denotes the absolute value of y, is

(a)

(b)

(c)

(d)

. -1

2

-2

1 -2-

2

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113. Consider the following statements :

... '

114.

(i) The regular ~ets are closed under intersection.

(ii) The set of strings accepted by a finite automaton. M with n states is firiite if and only if the automaton accepts some string of length c·, n St" s 2rL

(iii) Moore machine is a finite automaton with output where the output is associated with the state.

Which of the above statements is/ are false?

(a) Only (i)

(b) Only (ii)

(c) Both (i) and (iii)

(d) . Both {ii) and (iii)

Arrivals to an airport are all directed to the same runway. At a certain time of the day, these arrivals are Poisson distributed at the rate of 30 per hour. The time to land an aircraft is a constant 90 seconds. The runway utilization is

(ar 3/4

(b) 2·25

(c) 3·75

(d). 1 /3

115. Of the following sorting algorithms, which has a running time that is least dependent on .p. the initial ordering of the input?

(a) Insertion sort

(b} Selecdon sort

(c) Shell sort

(d) Merge sort

116. Translator that performs macro-expansion is called

. I\ (a) assembler

(b) micro-preprocessor

(c) macro-processor

(d) macro-preprocessor

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117. Consider the matrix A ~ ( ~ ~} Then the norm of A will become

_<("- (a) 0

(b) 1

(c) 2

(d) 3

1 f8. pH q _is false , when

\l'I · (a) both p and q are false

(b) neither p nor q is false

(c) p is true and q is true or false

·(d) either p is false or q is false

119. The address lines required for a ·512K word memory are

(a) 10

(b) 15

(c) 19

(d) None of the above

120. Which one of the following statements is true about a fibre?

(a) It is a user-level thread

(b) .It is a kernel-level thread

(c) It is a process

(d) ~one of the above

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