Computer Science  Mathematical Foundation of Computer Science
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 Answered
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Question 1 of 212
1. Question
A class of 30 students occupy a classroom containing 5 rows of seats, with 8 seats in each row. IF the students seat themselves at random, the probability that the sixth seat in the fifth row will be empty is
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Question 2 of 212
2. Question
The probability that a number selected at random between 100 and 999 (both inclusive) will not contain the digit 7 is
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Question 3 of 212
3. Question
0.152525252….. us sane as
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Question 4 of 212
4. Question
A class is composed of 2 brothers and 6 other boys. In how many ways can all the boys be seated at a round table so that the two brothers are not seated together?
Correct
Incorrect

Question 5 of 212
5. Question
The
n^{th}
order difference of a polynomial of degree n is
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Question 6 of 212
6. Question
Each coefficient in the equation
ax^{2}
+ bx + c = 0 is determined by throwing an ordinary die.
The probability that the equation will have real roots isCorrect
Incorrect

Question 7 of 212
7. Question
The sum of all numbers greater than 10,000 formed by using the digits 0, 2, 4, 6, 8, no digit being repeated in any number is
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Question 8 of 212
8. Question
For a game in which 2 partners oppose 2 other partners, six men are available. If every possible pair must play against every other pair, the number of games to be played is
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Question 9 of 212
9. Question
Let the elements g, h belong to a group G. If O(h) is 2, then O
(ghg1^{1})
is
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Question 10 of 212
10. Question
At any time, the total number of persons on earth who have shaken hands an odd number of times has to be
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Question 11 of 212
11. Question
Which of the following are irrational number?
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Question 12 of 212
12. Question
The function f(x) = 1 x/(x+1) 
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Question 13 of 212
13. Question
The domain of the function log (log sin (x)) is
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Question 14 of 212
14. Question
The system of equation
x + 2y + 3z = 4
x + λy + 2z = 3
x + 4y + µz = 3
has infinite number of solutions if
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Question 15 of 212
15. Question
Let R be a symmetric and transitive relation on a set A. Then
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Question 16 of 212
16. Question
The number of elements in the power set of the set
{{{}}, 1, {2, {2,3}} isCorrect
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Question 17 of 212
17. Question
If 4(log_{9}3) + (9(log_{2}4) = 10(log_{x}81), then x is
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Question 18 of 212
18. Question
The length of the longest pole that can be made inside a hall of length 18m, breadth 6m, and height 4.5m is
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Question 19 of 212
19. Question
Six x’s have to be placed in the squares in the adjacent figure, such that each row contains at least one x. This can be done in
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Question 20 of 212
20. Question
Out of 100 students, 10 students used to drink milk(M), coffee(C) and tea(T): 20 M and C: 30 C and T:25 M and T: 12 M only: 5 C only and 8 T only. The number of students who did not drink any of these is
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Question 21 of 212
21. Question
Given the relation R = {(1,2). (2.3)}. The minimum number of ordered pairs that must be added to this set so that the enlarged relation is reflexive, symmetric and transitive is
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Question 22 of 212
22. Question
A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept beside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence 2 black, 4 white, and 3 red is
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Question 23 of 212
23. Question
The range of the function f(X) =
x^{2}
/ (1+
x^{2}
) is
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Question 24 of 212
24. Question
In calculating the mean and variance of 10 readings, a student wrongly used 52 instead of the correct figure 25. If the mean be obtained was 45, then the correct mean is
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Question 25 of 212
25. Question
Refer Qn. 24. If the variance he obtained was 16, then the correct variance is
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Question 26 of 212
26. Question
If ^{n}C_{r1} = 36: ^{n}C_{r }= 84 and ^{n}C_{r + 1 }=126, then the value of ‘r’ is
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Question 27 of 212
27. Question
In the interval [0,∏], the equation x=cos(x) has
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Question 28 of 212
28. Question
Ten different letters are given.Five letter words are formed from these given letters. The number of words having at least repeated is
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Question 29 of 212
29. Question
The value of the expression
^{47}C_{4} + ^{5}∑_{j=1 }^{(52j)}C_{3 }is equal to
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Question 30 of 212
30. Question
The rank of the following (n+1)x(n+1) matrix, where a is a real number is
[1 a a^{2 }. . . . a^{n]}
[1 a a^{2 }. . . . a^{n]}
[. . .]
[. . .]
[1 a a^{2} . . . . a^{n]}
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Question 31 of 212
31. Question
Let ‘S’ be the standard deviation of ‘n’ numbers. If each of the ‘n’ numbers is multiplied by a constant C, then the new standard deviation will be
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Question 32 of 212
32. Question
Let A be a finite set of Size ‘n’. The number of elements in the power set of A x A is
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Question 33 of 212
33. Question
Probability of an event A happening is 0.4. Probability that in 3 independent trials. event A happens at least once is
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Question 34 of 212
34. Question
If x, y are two real numbers such that x > 0 and xy = 1, then x + y can’t be less than
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Question 35 of 212
35. Question
Let f(x+y) = f(x) + f(y), for all x,y. If f(x) is continuous at x = 0, then
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Question 36 of 212
36. Question
Let f(x+y)=f(x) + f(y), for all x, y. If f(5) = 2 and f'(0) =3, then f'(5) is equal to
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Question 37 of 212
37. Question
In numerical methods, accuracy refers to the
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Question 38 of 212
38. Question
Suppose A_{1 }A_{2}, . . . A_{30} are 30 sets, each with 5 elements, and B_{1 ,}B_{2 }. . . B_{n }are ‘n’ sets. each with 3 elements.
Let ^{30}U_{i=2} A_{i }= ^{n}U_{j=1} B_{j} = S.
Each element of S, belongs to exactly 10 of the A_{i }‘s and to exactly 9 of the B’S. then ‘n’ is
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Question 39 of 212
39. Question
Which of the following remarks about an illconditioned system of equations are true?
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Question 40 of 212
40. Question
If the cube roots of unity are 1, Co, Co^{2}, then the roots of the equation (x 1)^{3} + 8 = 0, are
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Question 41 of 212
41. Question
f(x) and g(x) are two functions differentiable in [0,1] such that f(0) = 2; g (0) = 0;f(1) = 6; and g(1) = 2. Then there must exist a constant C in
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Question 42 of 212
42. Question
Let f be a onetoone function with domain {x,y,z} and range {1, 2, 3}. It is given that exactly one of the following statements is true and the remaining 2 are false:
f(x) = 1
f(y) ‡ 1f(z) ‡ 2
Then f^{1} (1) equals
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Question 43 of 212
43. Question
Let f be a twice differentiable function such that
f”(x) = f(x) and f'(x) = g(x). Let h(x) = (f(x))^{2} + (g(x))^{2}. If h(5) = 11, the h(10) is
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Question 44 of 212
44. Question
i^{i}, where i is √1, is
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Question 45 of 212
45. Question
If p, q, r are three real numbers, then
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Question 46 of 212
46. Question
The number of 1’s in the binary representation of (3 x 4096 + 15 x 256 + 5 x 16 + 3) is
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Question 47 of 212
47. Question
A determinant is chosen at random from the set of all determinants of order 2 with each element either 0 or 1 only. the probability that the value of the chosen determinant is positive is
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Question 48 of 212
48. Question
The number of permutations of ‘n’ different things taken not more than ‘r’ at a time, with repetitions being allowed, is
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Question 49 of 212
49. Question
A relation R is defined in N x N, such that (a,b) R (c,d)iff a + d = b + c. The relation R is
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Question 50 of 212
50. Question
If log_{5} 10 = log_{7} x(log_{n}m), then the values of x, m, n are
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Question 51 of 212
51. Question
If √5 + √7 + i, is one of the roots of the equation f(x) = 0 with national coefficients, then the degree of the given equation can’t be less than
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Question 52 of 212
52. Question
Consider the equation x^{7 }2x^{5} + 7x^{4} + x^{3} – 9 = 0. The numbe of imaginary roots will be at least
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Question 53 of 212
53. Question
If f(a) and f(b) are of the same sign, then the equation f(x) = 0
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Question 54 of 212
54. Question
The equation x^{5 }+ x^{3} – 8x – 5 = 0 has
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Question 55 of 212
55. Question
Any polynomial of even degree in which the last term is negative and the coefficient of the highest power is positive, has at least
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Question 56 of 212
56. Question
When the polynomial f(x) is divided by (xa) (xβ), a≠β then the remainder is given by
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Question 57 of 212
57. Question
Log 0 is
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Question 58 of 212
58. Question
If a_{1}, . . . a_{n} are the roots of the equation x^{n} + nax – b = 0 then (a_{1} – a_{2})(a_{1} – a_{3}) . . . (a_{1} – a) equals
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Question 59 of 212
59. Question
The set of all natural numbers is not closed with respect to
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Question 60 of 212
60. Question
If a – b\ < n and \b  c < m, then a  c is
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Question 61 of 212
61. Question
The domain of the function 1/ √(1x)(x2) is
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Question 62 of 212
62. Question
A and B play a coin tossing game. They toss a coin alternately. The first one to get a head wins. If A starts, the probability of A winning is
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Question 63 of 212
63. Question
The number of trailing zeroes in 200!(i.e., factorial of 200) is
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Question 64 of 212
64. Question
The determinant of a matrix has 720 terms (in the unsimplified form), The order of the matrix is
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Question 65 of 212
65. Question
The error in using Simpson’s rule is of the order
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Question 66 of 212
66. Question
The domain of the function 1/√xx is
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Question 67 of 212
67. Question
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession. The probability that one of them is black and the other white is
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Question 68 of 212
68. Question
The iteration formula to find the square root of a positive real number b, using the Newton Rephson method is
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Question 69 of 212
69. Question
If x – 1 + x – 2 + x – 3 ≥ 6, then
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Question 70 of 212
70. Question
The number of real roots of the equation x^{2} – 3x + 2 = 0 is
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Question 71 of 212
71. Question
20√√20√. . . equals
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Question 72 of 212
72. Question
Two events A and B have probabilities 0.25 and 0.5 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is
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Question 73 of 212
73. Question
A function f(x) differentiable in the interval 0 ≤ x ≤ 5, is such that f(0) = 4 and f(5) = 1
If g(x) = f(x) / (x + 1), then there exists some constant C, 0 < C < 5 such that g'(C) equalsCorrect
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Question 74 of 212
74. Question
Let A and B be sets with cardinalities ‘m’ and ‘n’ respectively. The number of possible one to one mappings (injections) from A to B, when m < n, is
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Question 75 of 212
75. Question
Choose the correct option,
Let A = {1. 2, 3} is equal toCorrect
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Question 76 of 212
76. Question
Let A = {1. {2}, 3}
Choose the correct option.Correct
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Question 77 of 212
77. Question
In the set of integers, a relation R is defined as aRb, if and only if b = a. This realion is
Correct
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Question 78 of 212
78. Question
Let S = {1, 2, 3, 4} A relation R defined in S as, R = {(1, 2), (4, 3), (2, 2), (2, 1), (3, 1)} is
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Question 79 of 212
79. Question
Let A = {(1, 2, 3}. Which of the following relations are functions (mappings)?
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Question 80 of 212
80. Question
Consider the mapping f:x → Y. f is a bijection if and only if
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Question 81 of 212
81. Question
For a function to be invertible, it has to be
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Question 82 of 212
82. Question
The advantages of partial pivoting in the solution of a system of equations are
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Question 83 of 212
83. Question
Choose the correct statements.
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Question 84 of 212
84. Question
Choose the correct statements.
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Question 85 of 212
85. Question
In any undirected graph, the sum of degrees of all the nodes
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Question 86 of 212
86. Question
(PVQ) Λ (P→R) Λ (Q→S) is equivalent to
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Question 87 of 212
87. Question
Which of the following are tautologies?
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Question 88 of 212
88. Question
Identify the valid conclusion from the premises P V Q, Q → R, P → M, ˜M
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Question 89 of 212
89. Question
T is a graph with ‘n’ vertices. If T is connected and has exactly n1 edges, then
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Question 90 of 212
90. Question
If one has to obtain the roots of x^{2} – 2x + log 2 = 0 to four decimal places, log 2 should be given to the accuracy of approximately
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Question 91 of 212
91. Question
Choose the incorrect statement(s).
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Question 92 of 212
92. Question
M is a square matrix of order ‘n’ and its determinant value is 5. If all the elements of M are multiplied by 2, its determinant value becomes 40. The value of ‘n’ is
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Question 93 of 212
93. Question
in a computer an ndigit integer a_{n} a_{n} – 1 . . . a_{1} is represented as a_{n} a_{n} – 1 . . . a_{r + 1} 00 . . .0. The error e is
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Question 94 of 212
94. Question
1 – x^{2}/2! + x^{4}/4! – . . . . + (1)^{n} x^{2n}/2n! + . . . is the expansion of
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Question 95 of 212
95. Question
In the previous question, for 5digit accuracy, if x<∏/2, the number of terms in the series that should be considererd is
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Question 96 of 212
96. Question
Which of the following methods gives the least error when e^{x} is integrated from 0 to 0.4?
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Question 97 of 212
97. Question
Which of the following laws doesn’t hold good in finite precision floating point arithmetic?
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Question 98 of 212
98. Question
Surplus variables are usually introduced in an LPP model
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Question 99 of 212
99. Question
In an LPP model in its standard form, three of the constraints are
x_{1} + x_{2} ≤ 2
2x_{1} + 2x_{2} ≤ 3
3x_{1} + 3x_{2} ≤ 8
Removal of which of the constraints will not affect the optimality?
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Question 100 of 212
100. Question
An LPP having 2 optimal solutions must have
Correct
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Question 101 of 212
101. Question
The number of iterations taken by simplex method for solving an LPP in its standard form with ‘m’ equations and ‘n’ unknowns (m < n) can't exceed
Correct
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Question 102 of 212
102. Question
In the solution of an LPP using simplex method, the curreat cost of the objective function must
Correct
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Question 103 of 212
103. Question
If the cost of the objective function (of an LPP in its standard form) which corresponds to one of the corners of the convex region bound by the constraints, is greater than the cost corresponding to all its adjacent corners, then
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Question 104 of 212
104. Question
Revised simplex method
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Question 105 of 212
105. Question
The dual simplex method starts with a
Correct
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Question 106 of 212
106. Question
Which of the following simplex based techniques are ideal for sensitivity analysis?
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Question 107 of 212
107. Question
Choose the correct statements.
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Question 108 of 212
108. Question
Choose the correct statement(s)
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Question 109 of 212
109. Question
Changing the right hand side of the constraints and the coefficient of the cost function
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Question 110 of 212
110. Question
Let A be the set of all non singular matrices over real numbers and let * be the matrix multiplication operator. then
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Question 111 of 212
111. Question
NewtonRaphson method
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Question 112 of 212
112. Question
In the bisection method for finding the roots of an equation, the approximate relative error is always
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Question 113 of 212
113. Question
Trapezoidal rule gives the exact solution when the curve is
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Question 114 of 212
114. Question
If a function y’ = f(x) has an inverse function, then f(x) can’t be
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Question 115 of 212
115. Question
For what value of c, will the vector i + cj be orthogonal to 2i – j?
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Question 116 of 212
116. Question
The solution of the differential equation y” + 3y’ + 2y = 0, is of the form
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Question 117 of 212
117. Question
If the proposition P → Q is true, then the truth value of the proposition P V (P → Q), is
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Question 118 of 212
118. Question
The number of the divisors of 600 (including 1 and 600) is
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Question 119 of 212
119. Question
The determinant value of the matrix (1 2 3)
(4 5 6) is
(5 7 9)Correct
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Question 120 of 212
120. Question
Which of the following elementary operations may affect the rank of a matrix?
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Question 121 of 212
121. Question
Which of the following will not form an abelian group?
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Question 122 of 212
122. Question
A group has 11 elements. The number of proper Subgroups it can have is
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Question 123 of 212
123. Question
Let A and B be two n X n real symmetric matrices. Then
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Question 124 of 212
124. Question
Backward Euler method for solving the differential equation dy/dx =f(x,y), is specified by
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Question 125 of 212
125. Question
The rank of the matrix
[0 0 3]
[9 3 5] is
[3 1 1]Correct
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Question 126 of 212
126. Question
(G, *) is an abelian group, Then
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Question 127 of 212
127. Question
In a compact single dimensional array representation for lover triangular matrices (i.e. all the elements above the diagonal are zero). of size n X n, nonzero elements (i.e. elements of the lower triangle) of each row are stored one after the other, starting from the first row, The index of the (i,j)th element of the lower triangular matrix in this new representation is
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Question 128 of 212
128. Question
The number of substrings (of all lengths) that can be formed from a character string of length n is
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Question 129 of 212
129. Question
In the set of natural numbers, the binary operators that are not associative and not commutative are
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Question 130 of 212
130. Question
A relation R is defined as xRy, if x ≠ y, This relation R is
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Question 131 of 212
131. Question
The number of subsets of {1,2, . . .,n} of odd cardinality is
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Question 132 of 212
132. Question
The probability of an event B occurring is P. The probability that events A and B occur together is Q. The probability that A occurs, without B occurring, is R.Then the probability of A occurring is
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Question 133 of 212
133. Question
Let A, B, C be independent events with probabilities o.8, 0.5, 0.3. The probability of occurrence of at least one of these three is
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Question 134 of 212
134. Question
The subset of a countable set
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Question 135 of 212
135. Question
Every element of some ring (R, +,*) is such that a*a=a. This ring
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Question 136 of 212
136. Question
For the M/G/1 queuing system, the arrival pattern and service time follows
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Question 137 of 212
137. Question
Consider the set {1, 2, 3, 4, 6, 8, 12, 24}, together with the two binary operations LCM (Least Common Multiple) and GCD (Greatest Common Divisor).Which of the following does this algebraic structure represent?
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Question 138 of 212
138. Question
The set {1, 2, 3, 4, 6, 8, 12, 24}, together with LCM as the binary operation is not a group because
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Question 139 of 212
139. Question
The set {1, 2, 3, 4, 6, 8, 12, 24}, together with GCD as the binary operation is not a group because
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Question 140 of 212
140. Question
The following set
(a) Q(x) → P(x) V˜R(a) (b) R(a) V˜Q(a)
(c) Q(a) (d) ˜P(y)
Where x and y are universally quantified variables, a is a constant and P, Q, R are monodic Predicates, isCorrect
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Question 141 of 212
141. Question
Let x and y be sets with cardinalities m and n receptively. If the number of possible functions that can be defined with domain X and codomain Y is exactly 10, then
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Question 142 of 212
142. Question
Let F: R^{2} → R^{2} be the mapping defined by F(x,y) = (x/3,y/4). What will be the image of X^{2}/9 + y^{2}/16 = 1 under F?
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Question 143 of 212
143. Question
A function g is defined as g(x) = f(x)[f(x)+f(x)]. Which of the following remarks about the function g is right?
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Question 144 of 212
144. Question
What is the total number of equivalent relations that can be defined on the set {1, 2, 3}?
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Question 145 of 212
145. Question
Cube roots of unity form a cyclic group under multiplication. For this group,
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Question 146 of 212
146. Question
The value of_{ }lim_{x→0 }x log x is
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Question 147 of 212
147. Question
If x ε [0, 1], and f(x) and g(x) are defined as f(x) = sin (cos(x∏/4)) and g(x) =cos (sin (x∏/4)), then
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Question 148 of 212
148. Question
The function f(x) is continuous in [0, 1] such that f(0) = 1, f(1/2) = 1 and f(1) = 1, We can conclude that
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Question 149 of 212
149. Question
The sum of the infinite series ∑kx^{k}, Where 1 < x < 1, is
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Question 150 of 212
150. Question
Which of the following is not a linear transformation?
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Question 151 of 212
151. Question
If the determinant of an n X n matrix A is zero, then
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Question 152 of 212
152. Question
A is 2 X 2 matrix with eigen values 2 and 3. The eigen values of the matrix A^{2}
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Question 153 of 212
153. Question
Among any n + 1 distinct positive integers less than or equal to 2n, we can always find
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Question 154 of 212
154. Question
Let X_{1} and X_{2} be any two unit vectors in R^{3} The angle between the two planes X_{1} . X = c and X_{2} . X = 2c, where c is a constant is given by
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Question 155 of 212
155. Question
If (x_{1}, x_{2}, x_{3}) x (1, 3, 1) = (2, 1, 6), where x denotes the vector product, then (x_{1}, x_{2}, x_{3}) is given by
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Question 156 of 212
156. Question
Which of the following is a cube root of the complex number 27i?
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Question 157 of 212
157. Question
Suppose a system has been evolved by extraterrestrial creatures having only 3 fingers. They use the figures 0, 1, 2 with 2 > 1 > 0. What will be the binary equivalent of 222 in this system?
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Question 158 of 212
158. Question
If you want to retain the first 4 bits of given string of 8 bits and complement the last 4 bits then the correct mask and the operation should be
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Question 159 of 212
159. Question
Which of the following logical operation almost resembles an arithmetic multiplication operation?
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Question 160 of 212
160. Question
To change lower case to upper case letters in ASCII. the correct mask and operation should be (ASCII value of character A is 65 and character a is 97)
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Question 161 of 212
161. Question
Consider the nested for loop
for I1 = 1 to N
for I2 = 1 to I1
for I3 = 1 to I2
.
.
for Ik = 1 to I (k1)
PRINT I1, I2, I3, . . . Ik
How many times is the PRINT statements executed ?Correct
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Question 162 of 212
162. Question
Which of the following remark(s) will be true for any x?
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Question 163 of 212
163. Question
Which of the following, lists f(x),g(x),x,x1 and x+1 in a nondecreasing sequence?