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385.

For each element in a set of size 2n, an unbiased coin is tossed. The 2n coin tosses are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is: [2 marks]
(a) ²ⁿc_n/4ⁿ
(b) ²ⁿc_n/2ⁿ
(c) 1/(²ⁿc_n)
(d) 1/2

asked in Computer Science And Engineering, 2006

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386.

Consider the following log sequence of two transactions on a bank account, with initial balance 12000, that transfer 2000 to a mortgage payment and then apply a 5% interest.
1. T1 start
2. T1 B old=1200 new=10000
3. T1 M old=0 new=2000
4. T1 commit
5. T2 start
6. T2 B old=10000 new=10500
7. T2 commit
Suppose the database system crashes just before log record 7 is written. When the system is restarted, which one statement is true of the recovery procedure?
[1 mark]
(A) We must redo log record 6 to set B to 10500
(B) We must undo log record 6 to set B to 10000 and then redo log records 2 and 3
(C) We need not redo log records 2 and 3 because transaction T1 has committed
(D) We can apply redo and undo operations in arbitrary order because they are idempotent.

asked in Computer Science And Engineering, 2006

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387.

Let L₁ = {0^n+m1ⁿ0^m | n,m ≥ 0}, L₂ = {0^n+m1^n+m0^m | n,m≥0}, and
L3 = {0^n+m1^n+m0^n+m | n,m≥0}. Which of these languages are NOT context free?
[1 mark]
(A) L₁ only
(B) L₃ only
(C) L₁ and L₂
(D) L₂ and L₃

asked in Computer Science And Engineering, 2006

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388.

We are given a set X = {x₁, ........x_n}, where x_i = 2ⁱ. A sample S⊆ X is drawn by selecting each x_i independently with probability P_i= 1/2. The expected value of the smallest number in sample S is: [1 mark]
(a) 1/n
(b) 2
(c) √n
(d) n

asked in Computer Science And Engineering, 2006

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389.

An element in an array X is called a leader if it is greater than all elements to the right of it in X. The best algorithm to find all leaders in an array [1 mark]
(A) Solves it in linear time using a left to right pass of the array
(B) Solves it in linear time using a right to left pass of the array
(C) Solves it using divide and conquer in time θ (nlogn)
(D) Solves it in time θ(n²).

asked in Computer Science And Engineering, 2006

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390.

Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of the following statements is true? [1 mark]
(A) R is NP-complete
(B) R is NP-hard
(C) Q is NP-complete
(D) Q is NP-hard

asked in Computer Science And Engineering, 2006

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