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 x

^{2}- 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 = {w

_{1}aw_{2}| w_{1}, w_{2}Ïµ {a, b}*, |w_{1}| = 2, |w_{2}| ≥ 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 L

_{1}and L_{2}caches are 1 and 8 clock cycles, respectively. The miss penalty from the L_{2}cache to main memory is 18 clock cycles. The miss rate of L_{1}cache is twice that of L_{2}. The average memory access time (AMAT) of this cache system is 2 cycles. The miss rates of L_{1}and L_{2}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 Î˜ notation is

(A) Î˜(Iog
log n)

(B) Î˜(log n)

(C) Î˜(√n)

(D) Î˜(n)

Answer: B

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