61. The region of feasible solution of a linear programming problem has a _____ property in

geometry, provided the feasible solution of the problem exists.

(1) concavity

(2) convexity

(3) quadratic

(4) polyhedron

62. Consider the following statements :

(a) Revised simplex method requires lesser computations than the simplex method.

(b) Revised simplex method automatically generates the inverse of the current basis

matrix.

(c) Less number of entries are needed in each table of revised simplex method than

usual simplex method.

Which of these statements are correct ?

(1) (a) and (b) only

(2) (a) and (c) only

(3) (b) and (c) only

(4) (a), (b) and (c)

63. The following transportation problem :

A B C Supply

I 50 30 220 1

II 90 45 170 3

III 250 200 50 4

Demand 4 2 2

has a solution

A B C

I 1

II 3 0

III 2 2

The above solution of a given transportation problem is

(1) infeasible solution

(2) optimum solution

(3) non-optimum solution

(4) unbounded solution

64. Let R and S be two fuzzy relations defined as :

65. Compute the value of adding the following two fuzzy integers :

A = {(0.3, 1), (0.6, 2), (1, 3), (0.7, 4), (0.2, 5)}

B = {(0.5, 11), (1, 12), (0.5, 13)}

Where fuzzy addition is defined as

μA+B (z) = max

x + y = z

(min (μA(x), μB(x)))

Then, f (A + B) is equal to

(1) {(0.5, 12), (0.6, 13), (1, 14), (0.7, 15), (0.7, 16), (1, 17), (1, 18)}

(2) {(0.5, 12), (0.6, 13), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18)}

(3) {(0.3, 12), (0.5, 13), (0.5, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}

(4) {(0.3, 12), (0.5, 13), (0.6, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}

66. A perceptron has input weights W1 = – 3.9 and W2 = 1.1 with threshold value T = 0.3.

What output does it give for the input x1 = 1.3 and x2 = 2.2 ?

(1) – 2.65

(2) – 2.30

(3) 0

(4) 1

67. What is the function of following UNIX command ?

WC – l <a > b &

(1) It runs the word count program to count the number of lines in its input, a, writing

the result to b, as a foreground process.

(2) It runs the word count program to count the number of lines in its input, a, writing

the result to b, but does it in the background.

(3) It counts the errors during the execution of a process, a, and puts the result in

process b.

(4) It copies the ‘l’ numbers of lines of program from file, a, and stores in file b.

68. Which of the following statement is not correct with reference to cron daemon in UNIX

O.S. ?

(1) The cron daemon is the standard tool for running commands on a pre-determined

schedule.

(2) It starts when the system boots and runs as long as the system is up.

(3) Cron reads configuration files that contain list of command lines and the times at

which they invoked.

(4) Crontab for individual users are not stored.

69. In Unix, files can be protected by assigning each one a 9-bit mode called rights bits. Now,

consider the following two statements:

I. A mode of 641 (octal) means that the owner can read and write the file, other

members of the owner’s group can read it, and users can execute only.

II. A mode of 100 (octal) allows the owner to execute the file, but prohibits all other

access.

Which of the following options is correct with reference to above statements ?

(1) Only I is correct

. (2) Only II is correct.

(3) Both I and II are correct

. (4) Both I and II are incorrect.

70. Consider the statement,

“Either – 2 ≤ x ≤ – 1 or 1 ≤ x ≤2”.

The negation of this statement is

(1) x < – 2 or 2 < x or – 1 < x < 1 (2) x < – 2 or 2 < x

(3) – 1 < x < 1 (4) x ≤ – 2 or 2 < x or – 1 < x < 1

geometry, provided the feasible solution of the problem exists.

(1) concavity

(2) convexity

(3) quadratic

(4) polyhedron

62. Consider the following statements :

(a) Revised simplex method requires lesser computations than the simplex method.

(b) Revised simplex method automatically generates the inverse of the current basis

matrix.

(c) Less number of entries are needed in each table of revised simplex method than

usual simplex method.

Which of these statements are correct ?

(1) (a) and (b) only

(2) (a) and (c) only

(3) (b) and (c) only

(4) (a), (b) and (c)

63. The following transportation problem :

A B C Supply

I 50 30 220 1

II 90 45 170 3

III 250 200 50 4

Demand 4 2 2

has a solution

A B C

I 1

II 3 0

III 2 2

The above solution of a given transportation problem is

(1) infeasible solution

(2) optimum solution

(3) non-optimum solution

(4) unbounded solution

64. Let R and S be two fuzzy relations defined as :

65. Compute the value of adding the following two fuzzy integers :

A = {(0.3, 1), (0.6, 2), (1, 3), (0.7, 4), (0.2, 5)}

B = {(0.5, 11), (1, 12), (0.5, 13)}

Where fuzzy addition is defined as

μA+B (z) = max

x + y = z

(min (μA(x), μB(x)))

Then, f (A + B) is equal to

(1) {(0.5, 12), (0.6, 13), (1, 14), (0.7, 15), (0.7, 16), (1, 17), (1, 18)}

(2) {(0.5, 12), (0.6, 13), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18)}

(3) {(0.3, 12), (0.5, 13), (0.5, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}

(4) {(0.3, 12), (0.5, 13), (0.6, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}

66. A perceptron has input weights W1 = – 3.9 and W2 = 1.1 with threshold value T = 0.3.

What output does it give for the input x1 = 1.3 and x2 = 2.2 ?

(1) – 2.65

(2) – 2.30

(3) 0

(4) 1

67. What is the function of following UNIX command ?

WC – l <a > b &

(1) It runs the word count program to count the number of lines in its input, a, writing

the result to b, as a foreground process.

(2) It runs the word count program to count the number of lines in its input, a, writing

the result to b, but does it in the background.

(3) It counts the errors during the execution of a process, a, and puts the result in

process b.

(4) It copies the ‘l’ numbers of lines of program from file, a, and stores in file b.

68. Which of the following statement is not correct with reference to cron daemon in UNIX

O.S. ?

(1) The cron daemon is the standard tool for running commands on a pre-determined

schedule.

(2) It starts when the system boots and runs as long as the system is up.

(3) Cron reads configuration files that contain list of command lines and the times at

which they invoked.

(4) Crontab for individual users are not stored.

69. In Unix, files can be protected by assigning each one a 9-bit mode called rights bits. Now,

consider the following two statements:

I. A mode of 641 (octal) means that the owner can read and write the file, other

members of the owner’s group can read it, and users can execute only.

II. A mode of 100 (octal) allows the owner to execute the file, but prohibits all other

access.

Which of the following options is correct with reference to above statements ?

(1) Only I is correct

. (2) Only II is correct.

(3) Both I and II are correct

. (4) Both I and II are incorrect.

70. Consider the statement,

“Either – 2 ≤ x ≤ – 1 or 1 ≤ x ≤2”.

The negation of this statement is

(1) x < – 2 or 2 < x or – 1 < x < 1 (2) x < – 2 or 2 < x

(3) – 1 < x < 1 (4) x ≤ – 2 or 2 < x or – 1 < x < 1

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