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439.

A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is: [2 marks]
(a) 1/2ⁿ
(b) 1 - 1/n
(c) 1/n!
(d) 1 - 1/2ⁿ

asked in Computer Science And Engineering, 2005

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440.

Box P has 2 red balls and 3 blue balls and box Q has 3 balls and 1 blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes P and Q are 1/3 and 2/3, respectively. Given that a ball selected in the above process is a red ball, the probability that it came from the box P is: [2 marks]
(a) 4/19
(b) 5/19
(c) 2/9
(d) 19/30

asked in Computer Science And Engineering, 2005

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441.

[2 marks]
(a) i
(b) i+1
(c) 2i
(d) 2ⁱ

asked in Computer Science And Engineering, 2005

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442.

What are the eigen values of the following 2 × 2 matrix? [2 marks]

(a) -1 and 1
(b) 1 and 6
(c) 2 and 5
(d) 4 and -1

asked in Computer Science And Engineering, 2005

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443.

Consider the following system of equations in three real variables x₁, x₂ and x₃ :
[2 marks]
2x₁ - x₂ + 3x₃ = 1
3x₁ + 2x₂ + 5x₃ = 2
-x₁ + 4x₂ + x₃ = 3
The system of equations has [2 marks]
(a) no solution
(b) a unique solution
(c) more than one but a finite number of solutions
(d) an infinite number of solutions

asked in Computer Science And Engineering, 2005

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444.

Which one of the following graphs is NOT planar? [2 marks]

asked in Computer Science And Engineering, 2005

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