21.
Consider the set X = {a,b,c,d,e} under the
partial ordering
R = {(a, a),
(a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d),
(d, e), (e, e)}.
The Hasse
diagram of the partial order (X, R) is shown below.
The minimum number
of ordered pairs that need to be added to R to make (X, R) a lattice is
..................
Answer: -0.01 to
0.01
22. Let
be two matrices.
Then the rank
of P + Q is ..................
Answer: 2.0
23. G
is an undirected graph with n vertices and 25 edges such that each vertex of G
has degree at least 3. Then the maximum possible value of n is ...............
Answer: 16.0
24. Consider
a quadratic equation x2 - 13x + 36 = 0 with coefficients in a base
b. The solutions of this equation in the same base b are x = 5 and x = 6. Then
b = ...................
Answer: 8.0
25. The
minimum possible number of states of a deterministic finite automaton that
accepts the regular language L = {w1aw2 | w1,
w2 ϵ {a, b}*, |w1| = 2, |w2| ≥ 3} is ................
Answer: 8.0
26. P
and Q are considering to apply for a job. The probability that P applies for
the job is ¼, the probability that P applies for the job given that Q applies
for the job is ½, and the probability that Q applies for the job given that P
applies for the job is 1/3. Then the probability that P does not apply for the
job given that Q does not apply for the job is
(A) 4/5
(B) 5/6
(C) 7/8
(D) 11/12
Answer: A
27. If
w, x, y, z are Boolean variables, then which one of the following is INCORREC’T?
Answer: C
28. Given
f(w,x,y,z) = ∑m(0,1,2,3,7,8,10) + ∑d(5,6,11,15), where d
represents the don’t-care condition in Karnaugh maps. Which of the
following is a minimum product-of-sums (POS) form of f(w, x, y, z)?
(A) f = (w’
+ z’)(x’ + z)
(B) f = (w’
+ z)(x + z)
(C) f = (w +
z)(x’ + z)
(D) f = (w +
z’)(x’ + z)
Answer: A
29. In
a two-level cache system, the access times of L1 and L2 caches
are 1 and 8 clock cycles, respectively. The miss penalty from the L2
cache to main memory is 18 clock cycles. The miss rate of L1 cache
is twice that of L2. The average memory access time (AMAT) of this
cache system is 2 cycles. The miss rates of L1 and L2
respectively are:
(A) 0.111
and 0.056
(B) 0.056
and 0.111
(C) 0.0892
and 0.1784
(D) 0.1784 and
0.0892
Answer: A
30. Consider
the recurrence function
Then T(n) in
terms of Θ notation is
(A) Θ(Iog
log n)
(B) Θ(log n)
(C) Θ(√n)
(D) Θ(n)
Answer: B
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