MCA (Hyderabad University) PAPER 2009

Pratap Bhawan, Behind Leela Cinema, Hazrat Ganj, Lucknow PH.(0522) 4026913,9838162263; Web. www.inpsmcalucknow.com

1. A teacher when giving an assignment, instructed the students that a students can exchange notes but only with those who are taller than him/her. In a class of 40 students, how many exchanges are possible ?

(a) 780 (b) 40 (c) 39 (d) 0

2. Seven digits from 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 represented by a different letter in the figure below. The products A × B × C, B × G × E and D × E × F are equal. What digit does G represent ?

A D B G E C F (a) 4 (b) 2 (c) 8 (d) 1

3. Two objects are weighted using a faulty balance that either over - or under-weights every object by a constant amount. The first object weighted 50 kg and the second weighted 25 kg on such a balance. When they both are weighted together they weighted 77 kg. What is the true weight of the first object ?

(a) 52 kg (b) 27 kg (c) 51 kg (d) 49 kg

4. Big Bazzar is celebrating its 10th anniversary by offering a 20% discount for the whole 1st week of April. On April 5, which is the date of inauguration, they offer an additional discount of 15% (on discounted price). What is the overall discount ?

(a) 35% (b) 32% (c) 5% (d) 23%

5. Three dozen lemons cost as many rupees as one can have lemons for Rs. 16. How much does a dozen lemons cost ?

(a) Rs. 8 (b) Rs. 16 (c) Rs. 1 (d) Rs. 24

6. 10 cards numbered 0 to 9 are arranged in a stack in such a way that : while saying out loud Z, E, R, we move the cards from the top to the bottom of the stack and when saying ‘O’ we turn the card face up and we get 0. We then remove this card from the stack. We now repeat the above procedure with O, N, E and get ‘I’ and so on. What is the top card ?

(a) 7 (b) 2

(c) 1 (d) 4

7. Rakesh will eat the orange if Roopa does not cook. Based only on the information above, which of the following must be TRUE ?

(a) Rakesh will not eat the orange if Roopa cooks. (b) If Rakesh did not eat the orange, Roopa did

cook. (c) If Rakesh eats the orange, then Roopa did not

cook. (d) If Roopa does not cook, then Roopa did not

cook.

8. A large steel ball is placed inside a cubic box such that its height equals the diameter of the ball. An identical box is then filled with 216 smaller steel balls (each with 1/6 the diameter of the large ball). Which of the following statements is TRUE ?

(a) The two boxes are of equal weight. (b) The second box is heavier. (c) The first box is heavier.

(d) Depends on the exact amounts of space left in the box.

9. Given a 5 × 5 grid, in how many ways can the cells be filled with the numbers 1, 2, 3, 4 and 5 in such a way that no number is repeated in any row or column ?

(a) 120 (b) 153 (c) 25 (d) 62

10. Find the total number of ways a child can be given at least one rupee from four 25 paise coins, three 50 paise coins and two one-rupee coins;

(a) 53 (b) 51 (c) 54 (d) 55

11. A sensitive instrument can measure lengths upto 10–10 metre. A square sheet of paper of side 1 metre is repeatedly folded into halves. What is the maximum number of folds that can be made such that the instrument can still successfully measure it ?

(a) 10 (b) 20 (c) 30 (d) 40 12. If (a1, a2, a3) = (100, 0, 1) and (b1, b2, b3) = (1, 100,

00) then find a sequence s1, s2,.......,sk of numbers from 1, 2, 3 such that

1 2 k 1 2 ks s s s s s

a , a ,,...., a , b , b ,,...., b ,

MCA (Hyderabad University) PAPER 2009

Pratap Bhawan, Behind Leela Cinema, Hazrat Ganj, Lucknow PH.(0522) 4026913,9838162263; Web. www.inpsmcalucknow.com

(For example 13 is not a solution as a1a3 = 1001 and b1b3 = 100)

(a) 1322132 (b) 1322322 (c) 1311322 (d) 1312312

13. What is the value of the ten’s digit in the sum 1!+ 2!+ 3!+.......+ 2008!

(a) 0 (b) 1 (c) 9 (d) 4

14. A four digit number a3a2a1a0 is formed from digits 1......9 such that

r 1

ri 1 i 1

a2a ,

a aor

2 2

if ai+1 is even otherwise i = 0, 1, 2 |a| is the smallest integer larger than a and [a] is the largest integer smaller than ‘a’. The smallest value that a3 can have is;

(a) 5 (b) 7 (c) 9 (d) 1

15. How many 5-digit prime numbers can be formed using the digits 3, 5, 7, 2 and 1 once each ?

(a) 1 (b) 5! – 4! (c) 0 (d) 5!

16. Swarup takes 5 hrs 45 min in walking to a certain place and riding back. He would have gained 2 hrs by riding both ways. The time he would take to walk both ways is;

(a) 3 hrs 45 min (b) 7 hrs 45 min (c) 7 hrs 30 min (d) 11 hrs 45 min

17. A number when divided by 783, gives a remainder 48. What remainder would be obtained by dividing the same number by 29 ?

(a) 29 (b) 27 (c) 19 (d) none of these

18. Four students have to be chosen - 2 girls as captain and vice captain and 2 boys as captain and vice-captain. There are 15 eligible girls and 12 eligible boys. In how many ways can they be chosen if Sunitha is sure to be captain ?

(a) 114 (b) 1020 (c) 360 (d) 1848

19. If there are 20 possible lines connecting nonadjacent points of a polygon, how many sides does it have ?

(a) 12 (b) 10 (c) 8 (d) 9

20. From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball ?

(a) 60 (b) 3720 (c) 4096 (d) none of the above

21. From city A to B, there are 3 different roads. From B to C there are 5 and from C to D there are 2 different roads. Laxman has to go from A to D attending to some work in B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he does not take the exact same path while coming back ?

(a) 250 (b) 870 (c) 90 (d) 100

22. If the sum of the least and greatest of 55 consecutive integers is 154, then the average of the 55 consecutive integers is;

(a) 155 (b) 77 (c) 50 (d) 110

23. A 3-inch cube is colored red on all sides. The cube is cut into small 1 inch cubes. The number of cubes which have atleast two sides colored red is;

(a) 19 (b) 21 (c) 22 (d) 20

24. Whenever Anoop sings, Bobby gets a headache and Rohit groans. If Rohit is not groaning, which of the following statements must be TRUE ?

(a) Anoop is singing and Bobby has a headache. (b) Bobby has a headache but Anoop is not

necessarily singing. (c) Anoop is singing, but Bobby does not

necessarily have a headache. (d) Anoop is not singing

25. Find the probability that a leap year will contain either 53 Tuesdays or 53 Wednesdays.

(a) 1/5 (b) 2/5 (c) 2/3 (d) 3/7

PART – B

MCA (Hyderabad University) PAPER 2009

Pratap Bhawan, Behind Leela Cinema, Hazrat Ganj, Lucknow PH.(0522) 4026913,9838162263; Web. www.inpsmcalucknow.com

26. Let R be a relation on the set of positive integers defined as follows : aRb iff 4a + 5b is divisible by 9 then R is;

(a) Reflexive only. (b) Reflexive and symmetric but not transitive. (c) Reflexive and transitive but not symmetric. (d) An Equivalence relation.

27. If f(x) = a loge|x|+ bx2 + x has the extreme at x = 1 and x = 3 then;

(a) a = 3/4, b = –1/8 (b) a = –3/4, b = 1/8 (c) a = –3/4, b = –1/8 (d) none of the above

28. The number of even proper factors of 1008 is; (a) 24 (b) 22 (c) 23 (d) 25

29. If 21/ xf(x) e , x 0 and f(0) = 0 then f '(0) is;

(a) 0 (b) 1 (c) e (d) none of the above

30. It is given that square matrix A is orthogonal and also that det A is not equal to 1. Then;

(a) |A| is zero (b) |A| > 1 (c) |A| cannot be determined (d) none of the above

31. Which of the following numbers has the largest number of ‘1’ when represented in binary;

(a) 8192 (b) 4099 (c) 1031 (d) 63

32. Suppose x and y are sides of a right angled triangle and ‘x’ is increased by dx, ‘y’ is decreased by dy, then the hypotenuse h of the triangle is changed by dh =

(a) 2 2

xdx ydy

x y

(b)

2 2

xdx ydy

x y

(c) 2 2

xdx ydy

2 x y

(d)

2 2

xdx ydy

2 x y

33. Let S be a set of strings with length ‘n’ (‘n’ is odd) using symbols 0, 1, 2. Define an equivalence relation R on S such that two elements of S are related to each other if they have the same central element. The size of equivalence class induced by R of elements having central element 1 is;

(a) 3n (b) n3/3 (c) 3n/3 (d) 3n–1

34. The probability that atleast one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') P(B ') is;

(a) 0.9 (b) 1.15 (c) 1.1 (d) 2

35. If 2 2 2 2n1 1 1 1s Lim ....1 2 3 n

then;

(a) unbounded (b) lies between 1 and 3/2 (c) 0 (d) lies between 3/2 and 7/4

36. The sum of two positive real numbers is 2a. The probability that product of these two numbers is not less than 3/4 times the greatest possible product is;

(a) 1/2 (b) 1/3 (c) 1/4 (d) 9/16

37. If 2f(0) f '(0) 0 and f ''(x) tan x then f(x) is;

(a) 21log sec(x) x2

(b) 21log sec(x) x2

(c) 21log cos(x) x2

(d) none of the above

38. If set A has 6 elements, B has 4 elements and C has 8 elements, the maximum number of elements in (B C) (A B) C is;

(a) 18 (b) 12 (c) 16 (d) 24

39. Let , be the roots of the equation(x – a) (x – b) = c, c 0, then the roots of the equation (x )(x ) c 0 are;

(a) a, –b (b) –a, b (c) –a, –b (d) a, b

40. The set having only one subset is; (a) { } (b) {0} (c) { {} } (d) none of the above 41. A cubic f(x) vanishes at x = –2 and has relative

minimum/maximum at x = –1 and x = –1/3. If 11f f(x)dx 14 / 3, then cubic f(x) is;

(a) x3 + x2 + x + 6 (b) x3 – x2 – x + 6 (c) x3 + x2 + x + 2 (d) x3 + x2 – x + 2

MCA (Hyderabad University) PAPER 2009

Pratap Bhawan, Behind Leela Cinema, Hazrat Ganj, Lucknow PH.(0522) 4026913,9838162263; Web. www.inpsmcalucknow.com

42. Let x y f(x) f(y)f2 2

for all real ‘x’ and ‘y’. If

f '(0) exists and equals –1 and f(0) = 1, then f(2) is;

(a) –1 (b) 2 (c) 0 (d) 1

43. The sides of the rectangle of the greatest area that can be inscribed in the ellise x2 + 2y2 = 8, are given by;

(a) 2, 2 (b) 4, 2 2 (c) 2 2 , 2 (d) 4 2 , 4

44. Find the base in which the number seven thousand, six hundred and forty two is represented by the symbol 1234;

(a) 19 (b) 18 (c) 17 (d) 20

45. Which measure is used for determining the average annual percent increase in sales from one period to another;

(a) Arithmetic mean (b) Harmonic mean (c) Mode (d) Geometric mean

46. If f(x) sin(log x), then the value of f(xy) f(x / y) 2f(x)cos log(y) is ; (a) 0 (b) –1 (c) 1 (d) –2

47. Consider the function f(x) sin 2x on R.3

Let

x1 and x2 be two real values such that 1 2f(x ) f(x ). Then x1 – x2 is always of the form

(a) n : n Z (b) 2n : n Z

(c) 2n : n Z3

(d) n : n Z3

48. Value of n

i n i

i 0

nsin A(1 sin A)

i

(for ‘n’ a poisitive

integer) depends on; (a) Values of A (b) Value of n (c) neither A nor n (d) both A and n

49. Two persons are standing at different floors of a tall building and are looking ata statue that is 100 metres far from the building. Angle of inclination of the person at higher floor is 600 and that of the

person at lower floor is 450. What is the distance between the two persons ?

(a) ( 3 1 )100 (b) ( 3 1 )100 (c) 3 100 (d) 100 / 3

50. If R and S are equivalence relations on a set A, then;

(a) R S is an equivalence relation (b) RS is an equivalence relation (c) Both A and B are true (d) Neither A nor B is true

51. Let A and B be sets and the cardinality of B is 6. The number of one-to-one functions from A to B is 360. Then the cardinality of A is;

(a) 5 (b) 6 (c) 4 (d) can’t be determined

52. The equation of the circle having the chord x– y=

1 of the circle 2 225x y x 3y 02

as a

diameter is;

(a) 2 2 21x y 3x y 02

(b) 2 225x y 3x y 02

(c) 2 225x y x 3y 02

(d) 2 221x y 3x y 02

53. Let A be a set with 10 elements. The total number of relations that can be defined on A that are both reflexive and asymmetric is;

(a) 245 (b) 255

(c) 102

(d) none of the above

54. If i i 1 1

A and Bi i 1 1

then A8 equals

to; (a) 64 B (b) 128 B (c) –128 B (d) –64 B

55. If A is a 3 × 3 matrix and AtA = I and |A| = 1 then the value of |(A – 1)| =

(a) 1 (b) –1 (c) 0 (d) none of the above

MCA (Hyderabad University) PAPER 2009

Pratap Bhawan, Behind Leela Cinema, Hazrat Ganj, Lucknow PH.(0522) 4026913,9838162263; Web. www.inpsmcalucknow.com

56. If a, b, c are the roots of x3 + px2 + q = 0, then a b cb c ac b b

(a) p (b) p2 (c) p3 (d) q

57. If 1d (a b) (b c) v(c a), a.(b c)3

and

d.(a b c) 3

then v is; (a) 6 (b) 9 (c) 1 (d) 0

58. The eigen vectors of a real symmetric matrix corresponding to different eigen values are;

(a) Singular (b) Orthogonal (c) Non-singular (d) none of the above The questions 59 - 61 are based on the flow

chart given here.

59. If the sequence of numbers read is 1, 5, 7, 9, 17,

23, 45, 56, 63, 99, 101, 109, 121, 130, 142, 146, 150, how many times is the comparison I J done before the key 130 is found;

(a) 3 (b) 4 (c) 2 (d) 5

60. For the same sequence of numbers as above, if the key being searched is 17, the final values of (I, J) are;

(a) 3, 7 (b) 4, 8 (c) 5, 5 (d) 3, 8

61. If 8192 numbers are read and they key is a number that is not present in the sequence read, how many time is the comparison I J done before it prints KEY NOT FOUND ?

MCA (Hyderabad University) PAPER 2009

Pratap Bhawan, Behind Leela Cinema, Hazrat Ganj, Lucknow PH.(0522) 4026913,9838162263; Web. www.inpsmcalucknow.com

(a) 4096 (b) 8192 (c) 13 (d) 8191

62. Equation of a circle passing through (3, 2) and (9, 10) with a radius of 5 is ;

(a) x2 + y2 + 46x – 55y – 39 = 0 (b) x2 + y2 = 44x – 54y – 37 = 0 (c) x2 + y2 – 12x – 12y + 47 = 0 (d) x2 = y2 + 12x + 12y + 47 = 0

63. The value of ‘x’ for which the volume of parallelepiped formed by the vectors i + xj + k, j + xk and xi + k is minimum is;

(a) –3 (b) 1/ 3 (c) 3 (d) –1/ 3

64. Loci of a point equidistant to (2, 0) and x = –2 is; (a) y2 = 8x (b) y2 = 4x (c) x2 = 2y (d) x2 = 16y

65. Given two fixed points A(–3, 0) and B(3, 0) with AB = 6, the equation of the locus of point P which moves such that PA + PB = 8 is;

(a) x y 18 6 (b)

2 2x y 116 9

(c) x y 17 16 (d)

2 2x y 116 7

66. Let a, b and c

are three non-zero vectors, no two

of which are collinear. If a 2b

is collinear with c and b 3c

is collinear a, then a 2b 6c

is;

(a) 0

(b) parallel to a

(c) parallel to b

(d) parallel to c

67. The following system of equations 6x+ 5y + 4z = 0 3x + 2y + 2z = 0; 12x + 9y + 8z = 0;

(a) no solution (b) a unique solution (c) more than one but finite number of solution (d) infinite solutions

68. Which of the following functions cannot define a probability distribution;

(a) f (x) 14

for x = 3, 4, 5, 6

(b) 2xf(x)

25 for x = 0, 1, 2, 3, 4

(c) xf(x)

15 for x = 0, 1, 2, 3, 4, 5

(d) 25 xf(x)

6

for x = 0, 2

69. If ˆ ˆˆ ˆ ˆ ˆa i 2 j 3k, b 2i j k

and c

is a vector

satisfying a c a b and a.c 0 2then 3 | c |

(a) 0 (b)3/4

(c) 30/4 (d) 3 102

70. Let a b

Ac d

be a 2×2 matrix such that A3 = 0.

The sum of all the elements of A2 is; (a) 0 (b) a + b + c + d (d) a2 + b2 + c2 + d2 (d) a3 + b3 + c3 + d3

71. According to the IEEE standard, a 32-bit, single precession, floating point number N is defined to be N = (–1)s × 1 . F× 2E–127 where S is the sign bit, F the fractional mantissa and E the biased exponent. A floating point number is stored as S : E : F, where S, E and F are stored in 1 bit, 8 bits and 23 bits respectively. What is the decimal value of the floating point number C1E00000 in hexadecimal notation.

(a) 26 (b) –13 (c) –26 (d) –28

72. The number of positive real roots for the following polynomial 4 3 2P(x) x 5x 5x 5x 6 is;

(a) 0 (b) 1 (c) 2 (d) 3

73. Given a series of values of X as 1, 3.5, 4.5, 6, 7.5, 8, 9, 10.5, 12, what is the value of the sum of the deviations taken from the mean ?

(a) 16.5 (b) 6.5 (c) 7.5 (d) none of the above 74. (341)16 can be represented in base 7 as;

MCA (Hyderabad University) PAPER 2009

Pratap Bhawan, Behind Leela Cinema, Hazrat Ganj, Lucknow PH.(0522) 4026913,9838162263; Web. www.inpsmcalucknow.com

(a) 2311 (b) 2300 (c) 3200 (d) 2003

75. What does the above flowchart do ? (a) Computes Least Common Divisor (b) Computes Least Common Multiple (c) Computes Greatest Common Divisor (d) none of the above

*****

ANSWERS 01. a 02. b 03. a 04. b 05. a 06. a 07. b 08. a 09. a 10. c 11. 12. c 13. b 14. d 15. c 16. b 17. c 18. d 19. c 20. b 21. b 22. b 23. d 24. d 25. d 26. d 27. c 28. c 29. a 30. 31. d 32. a 33. d 34. c 35. d 36. a 37. a 38. b 39. c 40. a 41. d 42. a 43. b 44. a 45. b 46. a 47. a 48. c 49. a 50. b 51. c 52. d 53. d 54. b 55. c 56. c 57. b 58. b 59. b 60. c 61. c 62. c 63. b 64. a 65. d 66. a 67. d 68. b 69. d 70. a 71. d 72. b 73. d 74. b 75. c