Indian Institute of Technology Madras (IIT-M) 2000 A.M.I.E.T.E Computer Science
Wednesday, 23 January 2013 04:25Web
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(c) k can take any value ranging from 0 and 1
(d) None of the above
2.2. E1 and E2 are events in a probability space satisfying the subsequent constraints:
• Pr(E1) = Pr(E2)
• Pr(E1uE2)=1
• E1 and E2 are independent
The value of Pr(E1), the probability of the event E1, is
(a) 0
(b)
(c)
(d) 1
2.3. Let S=ilog21 and
100
andT=f xlog2xdx
Which of the subsequent statements is true?
(a) S>T
(b) S=T
(c) S
(d) 2S < T
2.4. A polynomial p(x) satisfies the following:
p(1) = p(3) = p(5) = 1
p(2) = p(4) = -1
The minimum degree of such a polynomial is
(a) 1
(b) 2
(c) 3
(d) 4
2.5. A relation R is described on the set of integers as x Ry iff (x+y) is even. Which of
the subsequent statements is true?
(a) R is not an equivalence relation
(b) R is an equivalence relation having one equivalence class
(c) R is an equivalence relation having two equivalence classes
(d) R is an equivalence relation having three equivalence classes
2.6. Let P(S) denotes the powerset of set S. Which of the subsequent is always true?
(a) P(P(S))=P(S)
(b) P(S) nP(P(S)) = {Ø}
(c) P(S) nS = P(S)
(d) S P(S)
2.7. Let a, b, c, d be propositions. presume that the equivalence a -* (b V-b) and b -* c hold.
Then the truth-value of the formula (a A b) — (a A c) v d is always
(a) actual
(b) False
(c) identical as the truth-value of b
(d) identical as the truth-value of d
2.8. What can be stated about a regular language L over {a} whose minimal finite state
automation has 2 states?
(a) L must be {aIn is odd}
(b) L must be {aIn is even}
(c) L must be {aI0}
(d) Either L must be {aIn is odd}, or L must be {aI n is even}
2.9. Consider the subsequent decision problems:
(P1) Does a provided finite state machine accept a provided string
(P2) Does a provided situation free grammar generate an infinite number of stings
Which of the subsequent statements is true?
| Earning: Approval pending. |
