Exam Details
| Subject | ||
| Paper | ||
| Exam / Course | mca | |
| Department | ||
| Organization | central university | |
| Position | ||
| Exam Date | 2012 | |
| City, State | telangana, hyderabad |
Question Paper
Booklet Code A
Entrance Examination (June 2012)
Master of Computer Applications
Time: 2 Hours
Max. Marks: 100
Hall Ticket Number: I
1. The numbers 1 to 100 are written in a 10 x 10 grid. The multiples for each of the first few odd numbers 11 and 13 -are coloured gray. The multiples of which number form a continuous line at 1350 in the grid? Angles are measured in the conventional anti-clockwise way from the horizontal line given by the bottom row of the grid.
A. 13
B. 5
C. 9
D. 11
2. There is a vertical stack of books marked and 3 on Table with 1 at the bottom and 3 on top. These are to be placed vertically on Table B with 1 at the bottom and 2 on the top, by making a series of moves from one table to the other. During a move, the topmost book, or the topmost two books, or all the three, can be moved from one of the tables to the other. If there are any books on the other table, the stack being transferred should be placed on top of the existing books, without changing the order of books in the stack that is being moved in that move. If there are no books on the other table, the stack is simply placed on the other table without disturbing the order of books in it. What is the minimum number of moves in which the above task can be accomplished?
A. One
B. Two
C. Three
D. Four
3. A clock loses time during the first week and then gains time during the next one week. If the clock was set right at 12 noon on a Sunday, what will be the time that the clock will show exactly 14 days from the time it was set right?
A. 1 36 48
B. 1 40 48
C. 1 41 24
D. 10 19 12
4. A part of the divisibility test for 11 is: sum up alternate digits (starting from units place) and if the difference between them is the number is divisible by 11. E.g., 1047673 gives 3 6 4 1 and 7 7 and therefore is divisible by 11. Now, sum up alternate pairs of digits (starting from units place) and if the difference between them is then the number is divisible by X. E.g., 46662 gives 62 04 and 66, and therefore is divisible by X. What is
A. 101
B. 11
C. 21
D. 22
5. In any year, if April 1 is a Wednesday, then so is
A. January 1
B. July 1
C. October 1
D. December 1
6. is an integer, which of the following CANNOT be the value of
A. 15
B. 21
C. 28
D. 50
7. There are two cubes on a table in which the volume of the second is half that of the first. If the first cube occupies a certain area on the table, how much area (approximately) does the second occupy?
A. Y/3 root2
B. Y/2
C. Y/3 root4
D. Y/root2
8. The age of a grandfather in years is the same as that of his grand-daughter's in months. If their ages differ by 55 years, the age of the grand-daughter is
A. 5 1/2 yrs
B. 5 1/2 months
C. 5 years
D. None of the above
9. Paper sizes are given by A0, A1, A2, etc. such that AO is two times larger (in area) than A0, Al is two times larger than A2 and so on. The longer dimension of each smaller size is equal to the shorter dimension of the larger size. For example, the longer dimension of A2 is the same as the shorter dimension of AI. In this scheme if A4 is 210 mm x 297 mm in size, what are the dimensions of A0 in mm?
A. 840x594
B. 420x594
C. 840x1188
D. None of the above
10. If a,b not equal to
then x
A. 7/2
B. 2
C. 1
D. 1/2
11. In a country with three major scooter manufacturers, Brand C sells three times as many as Brand A while Brand A sells half as many as Brand B. It implies that Brand C holds a market share of about
A. 50%
B. 33%
C. 66%
D. None of the above
12. On Planet a year has 400 days with a leap year of 401 days every4 years. Also, a year ending in is a leap year only if the year is divisible by 400, e.g. 2000 is a leap year but 3000 is not. Such a calendar is exact and needs no more corrections.
The length of the year on Planet X is
A. 400.2425 days
B. 400.2475 days
C. 400.25 days
D. None of the above
13. A gives B a start of 10 metres in a 100 metre race and still beats him by 1.25 seconds. How long does B take to complete the 100 metre race if A runs at the rate of 10m/sec?
A. 8 seconds
B. 10 seconds
C. 16.67 seconds
D. 12.5 seconds
14. A large number of people die every year due to drinking polluted water during the summer.
Given the two courses of action below, which of the answers A... D is APPROPRIATE?
I The government should make adequate arrangements to provide safe drinking water to all its citizens
II The people should be educated about the dangers of drinking polluted water.
A. Both I and II follow
B. Only I follows
C. Only II follows
D. Neither I nor II follows
15. Given that D is younger than F and older than G. A is younger than I and older than C. I is younger than G and older than J. J is younger than C and older than E. F is younger than Band older than H. H is older than D. The youngest of all of the above is
A. E
B. D
C. A
D. C
16. A military general needs to take his troop of 100 soldiers across a river from the bank A to bank B. He engages a boat with two boys, both of whom can row, at the bank A. But the boat can take only up to two boys or only one soldier. What is the minimum number of round trips that the boat has to make, to transfer all the 100 soldiers and the general to bank B and come back to bank
A. 404
B. 200
C. 202
D. 403
17. Mr.X lies only on Saturday, Sunday and Tuesday and speaks only truth on the remaining days. On a particular day he said, "Today being a Sunday, it is a rest day and tomorrow being a Wednesday I will go to the market" . What is the day on which this was spoken by Mr.X?
A. Monday
B. Tuesday
C. Friday
D. Saturday
18. Consider a number 23571113... made by placing in ascending order, all the prime numbers between 2 and 30. If this number were divided by 16, the remainder would be:
A. 1
Q:P is telling a lie
R:I saw P stealing
S:I am not the thief
A. P
B. Q
C. R
D. S
26. Let x (2+root3)2012 and f =fractional part of x. Then is equal to
A. 1
B. 2
C. root3
D. 7
27. If the equation x-4x3+ax2+ 0 has four positive roots then a and b
A.
B.
C. 6,4
D.
28. Find the point at which the line joining the points and intersects the XY-plane.
A.
B.
C.
D.
29. Suppose A B i-j k and C j where are unit vectors. Pick the odd one out among the following:
A. A.(B x
B. x B).C
C. A x C
D. A x B
30. Let alpha be an angle such that 0 alpha pie/2 and tan(alpha/2) is rational. Then which of the following is true?
A. Both sin(alpha/2) and cos(alpha/2) are rational
B. tan(alpha) is irrational
C. Both sin(alpha) and cos(alpha) are rational
D. None of the above
31. Suppose the land use pattern of an educational institution in the year 2000 was 30% for educational buildings, 20% for residential purposes and 50% left as wilderness. Then the usage pattern has changed according to the transition probabilities every 5-years as given below:
(Edu Res Wild
0.1 0.1 0.8
0.2 0.2 0.6
0.3 0.2 0.5)
Compute the land use pattern of educational buildings, residential purposes and wilderness in 2005 and then in 2010 respectively as percentages.
A. (21.9,17.6,60.5)
B. (21,17,62);(21.9,17.6,60.5)
C. (21,17,62);(23.9,17.8,58.3)
D. (23.9,17.8,58.3)
32. Consider the following equalities formed for any three vectors B and C.
I. (A.B)C A(B.C)
II. x x C A x x
III. A.(B x x B).C
IV.
A. Only I is true
B. III and IV are true
C. Only I and IV are true
D. All are true
33. A particle moves on a coordinate axis with a velocity of t2-2t m/sec at time t. The distance (in travelled by the particle in 3 seconds if it has started from rest is
A. 3
B. 0
C. 8/3
D. 4
34. If 5pie/4: alpha 3pie/2, then <img src='./qimages/1989-34.jpg'> is equal to
A. 1+cot alpha
B. 1-cot alpha
C. -1-cot alpha
D. cot alpha
35. The solution of the differential equation
<img src='./qimages/1989-35.jpg'>
A. x3 C1ex C2e2x C3e2x
B. x2 C1ex C2e2x C3e2x
C. x2 c1ex++ C2ex C3e2x
D. x3 c1ex C2ex C3e2x
36. Find the equation of the graph xy 1 after a rotation of the axes by 45 degrees anti-clockwise in the new coordinate system
A. x2-y2 1
B.
C. 1
D. 1
37. The number of points satisfying 3x -4y 25 and x2 y2<=25 is
A. 0
B. 1
C. 2
D. infinite
38. Let A be an n x n non-singular matrix over C where n 3 is an odd integer. Let a ER Then the equation
det(aA) a det(A)
holds for
A. All values of a
B. No value of a
C. Only two distinct values of a
D. Only three distinct values of a
39. For any two positive integers a and define a=b if is divisible by 7. Then (1526 128).(363).(645)
A. 0
B. 3
C. 4
D. 5
40. The number of in the binary representation of 3 is
A. 7
B. 10
c. 12
D. 11
41. The binary relation on the integers defined by R is
A. Reflexive only
B. Symmetric only
C. Reflexive and Symmetric
D. An equivalence relation
42. How many matrices of the form <img src='./qimages/1989-42.jpg'> are orthogonal, where s and t are real numbers.
A. 1
B. 2
C. 0
D. infinity
43. Let A be the set of all complex numbers that lie on the circle whose radius is 2 and centre lies at the origin. Then
B 5z|z E
describes
A. a circle of radius 5 centred at
B. a straight line
C. a circle of radius root5 with centre at
D. a circle of radius 10 centred at
44. Let ax2 bx c and -ax2 +bx where ac not equal to 0. Then for the polynomial
A. All its roots are real
B. None of its roots are real
C. At least two of its roots are real
D. Exactly two of its roots are real
45. A point P on the line 3x 5y 15 is equidistant from the coordinate axes. Then P can lie in
A. Quadrant I only
B. Quadrant I or Quadrant III only
C. Quadrant I or Quadrant II only
D. any Quadrant
46. A circle and a square have the same perimeter. Then
A. their areas are equal
B. the area of the circle is larger
C. the area of the square is larger
D. the area of the circle is 7r times the area of the square
47. Consider a set of real numbers defined as <img src='./qimages/1989-47.jpg'> This set is
A. an unbounded infinite set
B. an infinite bounded set
C. a finite set with
D. a finite set with
48. The value of cos 37° sin 37°/cos 37°-sin 37° is
A. tan2 74°
B. sec 37°/csc37°
C. cot 8°
D. tan 16°
49. All the coefficients of the equation ax2 bx c 0 are determined by throwing a six-sided un-biased dice. The probability that the equation has real roots is
A. 57/216
B. 27/216
C. 53/216
D. 43/216
50. If (123)5 then the number of possible pairs is
A. 2
B. 4
C. 3
D. 1
51. Suppose 4 vertical lines are drawn on a rectangular sheet of paper. We name the lines A1B1, A2B2,A3B3 and A4B4 respectively. Suppose two players A and B join two disjoint pairs of end points within Al to A4 and B1 to B4 respectively without seeing how the other is marking. What is the probability that the figure thus formed has disconnected loops?
A. 1/3
B. 2/3
C. 3/6
D. 1/6
52. In a village having 5000 people, 100 people suffer from the disease Hepatitis B. It is known that the accuracy of the medical test for Hepatitis B is 90%. Suppose the medical test result comes out to be positive for Anil who belongs to the village, then what is the probability that Anil is actually having the disease.
A. 0.02
B. 0.16
C. 0.18
D. 0.3
53. Let A be an n x n-skew symmetric matrix with a11,a22,....ann as diagonal entries. Then which of the following is correct?
A. a11a22...ann a11+a22+...+ann
B. a11a22...ann (a11+a22 ann)2
C. a11+a22 +... +ann (a11+a22+...+ ann)3
D. All of the above
54. Find the statement that is NOT true about the graph of the equation asin2theta, where a 0.
A. The graph is symmetric about both x-and y-axes
B. The graph of this equation is like a flower with four petals
C. Maximum value is obtained at theta
D. The maximum value is a
55. If 0 and x3+y3+z3-kxyz then only one of the following is true. Which one is it?
A. k 3 whatever be y and z.
B. k 0 whatever be y and z.
C. k or or 0
D. If none of is zero, then k=3
56. The value of the power series
<img src='./qimages/1989-56.jpg'>
at x 3 is closest to
A. cos 3 (in radians)
B. log(1 32)
C. 1/e power9
D. sec 9 (in radians)
57. <img src='./qimages/1989-57.jpg'>
A. 17/3
B. 14/3
C. 1
D. 16/3
58. The distance between two binary strings of equal length is defined as the number of positions where the bits differ. The distance of a set of binary strings is the minimum distance of all pairs of binary strings in that set. Then, what is the distance of the following set?
{00011000, 11000111,01010010, 11111111}
A. 5
B. 4
C. 2
D. 3
59. Consider the system of equations
8x+7y+z=11
x+6y+7z=27
13x4y19z=-20
How many solutions does this system have?
A. Single
B. Finite
C. Zero
D. Infinite
60. Determine which sum of min-terms corresponding to the following boolean function:
<img src='./qimages/1989-60.jpg'>
A. z y x
B. xyz' xy'z x'yz
C.
D. xyz' xy'z
61. A decimal number N has 30 digits. Approximately, how many digits would the binary representation of N have?
A. 30
B. 60
C. 90
D. 120
62. Let E be a shifting operation applied to a function such that f(x for some h in IR. Then, for non-zero real numbers alpha and beta,
A. E(alpha f alphaE(f) betaE(g)
B. E(alpha f beta (alpha
C. E(alpha f beta alphabetaE(f+g)
D. None of the above
63. When a parabola represented by the equation y-2x2 8x is translated 3 units to the left and 2 units up, the new parabola has its vertex at
A.
B.
C.
D.
64. Out of 300 candidates interviewed in a company, 150 have a two-wheeler, 100 have a credit card and 150 possess a mobile phone. Further, 60 of them were found to have both a twowheeler and a credit card, 50 had both a credit card and a mobile phone and 50 had both a two-wheeler and a mobile phone and 20 had all the three. How many candidates had at least one of those?
A. 40
B. 260
C. 280
D. 140
65. A man can hit a target once in 5 shots. If he fires 5 shots in succession, what is the probability that he will hit his target?
A. 1
B. 1/5pow5
C. 1024/3125
D. 2101/3125
The Questions 66-69 are based on the Bow-chart given below.
Assume that the input is for all the questions. The symbol stands for interchange of values, the division operation is integer division
<img src='./qimages/1989-66.jpg'>
66. What is the output sequence?
A.
B.
C.
D. None of the above
67. How many times does the interchange of with occur?
A. 0
B. 1
C. 2
D. 3
68. What will be the output if we change the comparison statement from to
A.
B.
C.
D.
69. What will be the output if is replaced by in the flow-chart?
A.
B.
C.
D.
70. Angle made by any tangent of the curve y x5 8x 1 with x-axis is
A. always acute
B. always obtuse
C. can be either, depending on x
D. None of the above
71. <img src='./qimages/1989-71.jpg'>
A. 1
B. 1/2
C. 3/4
D. 0
72. Let be a continuous function. The equation f x
A. may not have any solution
B. must have exactly one solution
C. must have at least one solution
D. must have at least two solutions
73. The rational function has the inverse function Then find a+b.
A. 0
B.
C.
D. 1/2
74. Suppose a random variable X follows a binomial distribution with parameters n=6 and p. If
9Pr(X Pr(X
then
A. 2/3
B. 1/4
C. 1/3
D. 3/4
75. In solving a system of linear equations Ax b by LU decomposition; the L and U matrices of the matrix
<img src='./qimages/1989-75.jpg'>
<img src='./qimages/1989-75-1.jpg'>
Entrance Examination (June 2012)
Master of Computer Applications
Time: 2 Hours
Max. Marks: 100
Hall Ticket Number: I
1. The numbers 1 to 100 are written in a 10 x 10 grid. The multiples for each of the first few odd numbers 11 and 13 -are coloured gray. The multiples of which number form a continuous line at 1350 in the grid? Angles are measured in the conventional anti-clockwise way from the horizontal line given by the bottom row of the grid.
A. 13
B. 5
C. 9
D. 11
2. There is a vertical stack of books marked and 3 on Table with 1 at the bottom and 3 on top. These are to be placed vertically on Table B with 1 at the bottom and 2 on the top, by making a series of moves from one table to the other. During a move, the topmost book, or the topmost two books, or all the three, can be moved from one of the tables to the other. If there are any books on the other table, the stack being transferred should be placed on top of the existing books, without changing the order of books in the stack that is being moved in that move. If there are no books on the other table, the stack is simply placed on the other table without disturbing the order of books in it. What is the minimum number of moves in which the above task can be accomplished?
A. One
B. Two
C. Three
D. Four
3. A clock loses time during the first week and then gains time during the next one week. If the clock was set right at 12 noon on a Sunday, what will be the time that the clock will show exactly 14 days from the time it was set right?
A. 1 36 48
B. 1 40 48
C. 1 41 24
D. 10 19 12
4. A part of the divisibility test for 11 is: sum up alternate digits (starting from units place) and if the difference between them is the number is divisible by 11. E.g., 1047673 gives 3 6 4 1 and 7 7 and therefore is divisible by 11. Now, sum up alternate pairs of digits (starting from units place) and if the difference between them is then the number is divisible by X. E.g., 46662 gives 62 04 and 66, and therefore is divisible by X. What is
A. 101
B. 11
C. 21
D. 22
5. In any year, if April 1 is a Wednesday, then so is
A. January 1
B. July 1
C. October 1
D. December 1
6. is an integer, which of the following CANNOT be the value of
A. 15
B. 21
C. 28
D. 50
7. There are two cubes on a table in which the volume of the second is half that of the first. If the first cube occupies a certain area on the table, how much area (approximately) does the second occupy?
A. Y/3 root2
B. Y/2
C. Y/3 root4
D. Y/root2
8. The age of a grandfather in years is the same as that of his grand-daughter's in months. If their ages differ by 55 years, the age of the grand-daughter is
A. 5 1/2 yrs
B. 5 1/2 months
C. 5 years
D. None of the above
9. Paper sizes are given by A0, A1, A2, etc. such that AO is two times larger (in area) than A0, Al is two times larger than A2 and so on. The longer dimension of each smaller size is equal to the shorter dimension of the larger size. For example, the longer dimension of A2 is the same as the shorter dimension of AI. In this scheme if A4 is 210 mm x 297 mm in size, what are the dimensions of A0 in mm?
A. 840x594
B. 420x594
C. 840x1188
D. None of the above
10. If a,b not equal to
then x
A. 7/2
B. 2
C. 1
D. 1/2
11. In a country with three major scooter manufacturers, Brand C sells three times as many as Brand A while Brand A sells half as many as Brand B. It implies that Brand C holds a market share of about
A. 50%
B. 33%
C. 66%
D. None of the above
12. On Planet a year has 400 days with a leap year of 401 days every4 years. Also, a year ending in is a leap year only if the year is divisible by 400, e.g. 2000 is a leap year but 3000 is not. Such a calendar is exact and needs no more corrections.
The length of the year on Planet X is
A. 400.2425 days
B. 400.2475 days
C. 400.25 days
D. None of the above
13. A gives B a start of 10 metres in a 100 metre race and still beats him by 1.25 seconds. How long does B take to complete the 100 metre race if A runs at the rate of 10m/sec?
A. 8 seconds
B. 10 seconds
C. 16.67 seconds
D. 12.5 seconds
14. A large number of people die every year due to drinking polluted water during the summer.
Given the two courses of action below, which of the answers A... D is APPROPRIATE?
I The government should make adequate arrangements to provide safe drinking water to all its citizens
II The people should be educated about the dangers of drinking polluted water.
A. Both I and II follow
B. Only I follows
C. Only II follows
D. Neither I nor II follows
15. Given that D is younger than F and older than G. A is younger than I and older than C. I is younger than G and older than J. J is younger than C and older than E. F is younger than Band older than H. H is older than D. The youngest of all of the above is
A. E
B. D
C. A
D. C
16. A military general needs to take his troop of 100 soldiers across a river from the bank A to bank B. He engages a boat with two boys, both of whom can row, at the bank A. But the boat can take only up to two boys or only one soldier. What is the minimum number of round trips that the boat has to make, to transfer all the 100 soldiers and the general to bank B and come back to bank
A. 404
B. 200
C. 202
D. 403
17. Mr.X lies only on Saturday, Sunday and Tuesday and speaks only truth on the remaining days. On a particular day he said, "Today being a Sunday, it is a rest day and tomorrow being a Wednesday I will go to the market" . What is the day on which this was spoken by Mr.X?
A. Monday
B. Tuesday
C. Friday
D. Saturday
18. Consider a number 23571113... made by placing in ascending order, all the prime numbers between 2 and 30. If this number were divided by 16, the remainder would be:
A. 1
Q:P is telling a lie
R:I saw P stealing
S:I am not the thief
A. P
B. Q
C. R
D. S
26. Let x (2+root3)2012 and f =fractional part of x. Then is equal to
A. 1
B. 2
C. root3
D. 7
27. If the equation x-4x3+ax2+ 0 has four positive roots then a and b
A.
B.
C. 6,4
D.
28. Find the point at which the line joining the points and intersects the XY-plane.
A.
B.
C.
D.
29. Suppose A B i-j k and C j where are unit vectors. Pick the odd one out among the following:
A. A.(B x
B. x B).C
C. A x C
D. A x B
30. Let alpha be an angle such that 0 alpha pie/2 and tan(alpha/2) is rational. Then which of the following is true?
A. Both sin(alpha/2) and cos(alpha/2) are rational
B. tan(alpha) is irrational
C. Both sin(alpha) and cos(alpha) are rational
D. None of the above
31. Suppose the land use pattern of an educational institution in the year 2000 was 30% for educational buildings, 20% for residential purposes and 50% left as wilderness. Then the usage pattern has changed according to the transition probabilities every 5-years as given below:
(Edu Res Wild
0.1 0.1 0.8
0.2 0.2 0.6
0.3 0.2 0.5)
Compute the land use pattern of educational buildings, residential purposes and wilderness in 2005 and then in 2010 respectively as percentages.
A. (21.9,17.6,60.5)
B. (21,17,62);(21.9,17.6,60.5)
C. (21,17,62);(23.9,17.8,58.3)
D. (23.9,17.8,58.3)
32. Consider the following equalities formed for any three vectors B and C.
I. (A.B)C A(B.C)
II. x x C A x x
III. A.(B x x B).C
IV.
A. Only I is true
B. III and IV are true
C. Only I and IV are true
D. All are true
33. A particle moves on a coordinate axis with a velocity of t2-2t m/sec at time t. The distance (in travelled by the particle in 3 seconds if it has started from rest is
A. 3
B. 0
C. 8/3
D. 4
34. If 5pie/4: alpha 3pie/2, then <img src='./qimages/1989-34.jpg'> is equal to
A. 1+cot alpha
B. 1-cot alpha
C. -1-cot alpha
D. cot alpha
35. The solution of the differential equation
<img src='./qimages/1989-35.jpg'>
A. x3 C1ex C2e2x C3e2x
B. x2 C1ex C2e2x C3e2x
C. x2 c1ex++ C2ex C3e2x
D. x3 c1ex C2ex C3e2x
36. Find the equation of the graph xy 1 after a rotation of the axes by 45 degrees anti-clockwise in the new coordinate system
A. x2-y2 1
B.
C. 1
D. 1
37. The number of points satisfying 3x -4y 25 and x2 y2<=25 is
A. 0
B. 1
C. 2
D. infinite
38. Let A be an n x n non-singular matrix over C where n 3 is an odd integer. Let a ER Then the equation
det(aA) a det(A)
holds for
A. All values of a
B. No value of a
C. Only two distinct values of a
D. Only three distinct values of a
39. For any two positive integers a and define a=b if is divisible by 7. Then (1526 128).(363).(645)
A. 0
B. 3
C. 4
D. 5
40. The number of in the binary representation of 3 is
A. 7
B. 10
c. 12
D. 11
41. The binary relation on the integers defined by R is
A. Reflexive only
B. Symmetric only
C. Reflexive and Symmetric
D. An equivalence relation
42. How many matrices of the form <img src='./qimages/1989-42.jpg'> are orthogonal, where s and t are real numbers.
A. 1
B. 2
C. 0
D. infinity
43. Let A be the set of all complex numbers that lie on the circle whose radius is 2 and centre lies at the origin. Then
B 5z|z E
describes
A. a circle of radius 5 centred at
B. a straight line
C. a circle of radius root5 with centre at
D. a circle of radius 10 centred at
44. Let ax2 bx c and -ax2 +bx where ac not equal to 0. Then for the polynomial
A. All its roots are real
B. None of its roots are real
C. At least two of its roots are real
D. Exactly two of its roots are real
45. A point P on the line 3x 5y 15 is equidistant from the coordinate axes. Then P can lie in
A. Quadrant I only
B. Quadrant I or Quadrant III only
C. Quadrant I or Quadrant II only
D. any Quadrant
46. A circle and a square have the same perimeter. Then
A. their areas are equal
B. the area of the circle is larger
C. the area of the square is larger
D. the area of the circle is 7r times the area of the square
47. Consider a set of real numbers defined as <img src='./qimages/1989-47.jpg'> This set is
A. an unbounded infinite set
B. an infinite bounded set
C. a finite set with
D. a finite set with
48. The value of cos 37° sin 37°/cos 37°-sin 37° is
A. tan2 74°
B. sec 37°/csc37°
C. cot 8°
D. tan 16°
49. All the coefficients of the equation ax2 bx c 0 are determined by throwing a six-sided un-biased dice. The probability that the equation has real roots is
A. 57/216
B. 27/216
C. 53/216
D. 43/216
50. If (123)5 then the number of possible pairs is
A. 2
B. 4
C. 3
D. 1
51. Suppose 4 vertical lines are drawn on a rectangular sheet of paper. We name the lines A1B1, A2B2,A3B3 and A4B4 respectively. Suppose two players A and B join two disjoint pairs of end points within Al to A4 and B1 to B4 respectively without seeing how the other is marking. What is the probability that the figure thus formed has disconnected loops?
A. 1/3
B. 2/3
C. 3/6
D. 1/6
52. In a village having 5000 people, 100 people suffer from the disease Hepatitis B. It is known that the accuracy of the medical test for Hepatitis B is 90%. Suppose the medical test result comes out to be positive for Anil who belongs to the village, then what is the probability that Anil is actually having the disease.
A. 0.02
B. 0.16
C. 0.18
D. 0.3
53. Let A be an n x n-skew symmetric matrix with a11,a22,....ann as diagonal entries. Then which of the following is correct?
A. a11a22...ann a11+a22+...+ann
B. a11a22...ann (a11+a22 ann)2
C. a11+a22 +... +ann (a11+a22+...+ ann)3
D. All of the above
54. Find the statement that is NOT true about the graph of the equation asin2theta, where a 0.
A. The graph is symmetric about both x-and y-axes
B. The graph of this equation is like a flower with four petals
C. Maximum value is obtained at theta
D. The maximum value is a
55. If 0 and x3+y3+z3-kxyz then only one of the following is true. Which one is it?
A. k 3 whatever be y and z.
B. k 0 whatever be y and z.
C. k or or 0
D. If none of is zero, then k=3
56. The value of the power series
<img src='./qimages/1989-56.jpg'>
at x 3 is closest to
A. cos 3 (in radians)
B. log(1 32)
C. 1/e power9
D. sec 9 (in radians)
57. <img src='./qimages/1989-57.jpg'>
A. 17/3
B. 14/3
C. 1
D. 16/3
58. The distance between two binary strings of equal length is defined as the number of positions where the bits differ. The distance of a set of binary strings is the minimum distance of all pairs of binary strings in that set. Then, what is the distance of the following set?
{00011000, 11000111,01010010, 11111111}
A. 5
B. 4
C. 2
D. 3
59. Consider the system of equations
8x+7y+z=11
x+6y+7z=27
13x4y19z=-20
How many solutions does this system have?
A. Single
B. Finite
C. Zero
D. Infinite
60. Determine which sum of min-terms corresponding to the following boolean function:
<img src='./qimages/1989-60.jpg'>
A. z y x
B. xyz' xy'z x'yz
C.
D. xyz' xy'z
61. A decimal number N has 30 digits. Approximately, how many digits would the binary representation of N have?
A. 30
B. 60
C. 90
D. 120
62. Let E be a shifting operation applied to a function such that f(x for some h in IR. Then, for non-zero real numbers alpha and beta,
A. E(alpha f alphaE(f) betaE(g)
B. E(alpha f beta (alpha
C. E(alpha f beta alphabetaE(f+g)
D. None of the above
63. When a parabola represented by the equation y-2x2 8x is translated 3 units to the left and 2 units up, the new parabola has its vertex at
A.
B.
C.
D.
64. Out of 300 candidates interviewed in a company, 150 have a two-wheeler, 100 have a credit card and 150 possess a mobile phone. Further, 60 of them were found to have both a twowheeler and a credit card, 50 had both a credit card and a mobile phone and 50 had both a two-wheeler and a mobile phone and 20 had all the three. How many candidates had at least one of those?
A. 40
B. 260
C. 280
D. 140
65. A man can hit a target once in 5 shots. If he fires 5 shots in succession, what is the probability that he will hit his target?
A. 1
B. 1/5pow5
C. 1024/3125
D. 2101/3125
The Questions 66-69 are based on the Bow-chart given below.
Assume that the input is for all the questions. The symbol stands for interchange of values, the division operation is integer division
<img src='./qimages/1989-66.jpg'>
66. What is the output sequence?
A.
B.
C.
D. None of the above
67. How many times does the interchange of with occur?
A. 0
B. 1
C. 2
D. 3
68. What will be the output if we change the comparison statement from to
A.
B.
C.
D.
69. What will be the output if is replaced by in the flow-chart?
A.
B.
C.
D.
70. Angle made by any tangent of the curve y x5 8x 1 with x-axis is
A. always acute
B. always obtuse
C. can be either, depending on x
D. None of the above
71. <img src='./qimages/1989-71.jpg'>
A. 1
B. 1/2
C. 3/4
D. 0
72. Let be a continuous function. The equation f x
A. may not have any solution
B. must have exactly one solution
C. must have at least one solution
D. must have at least two solutions
73. The rational function has the inverse function Then find a+b.
A. 0
B.
C.
D. 1/2
74. Suppose a random variable X follows a binomial distribution with parameters n=6 and p. If
9Pr(X Pr(X
then
A. 2/3
B. 1/4
C. 1/3
D. 3/4
75. In solving a system of linear equations Ax b by LU decomposition; the L and U matrices of the matrix
<img src='./qimages/1989-75.jpg'>
<img src='./qimages/1989-75-1.jpg'>