21.
Consider the Karnaugh map given below, where
X represents “don’t care” and blank represents 0.
Assume for
all inputs (a, b, c, d), the respective complements (a’, b’, c’, d’) are also
available. The above logic is implemented using 2-input NOR gates only. The
minimum number of gates required is....................
Answer: 1.0
22. Consider
the language L given by the regular expression (a + b)*b(a + b) over the
alphabet {a, b}. The smallest number of states needed in a deterministic
finite-state automaton (DFA) accepting L is ..............
Answer: 4.0
23. Consider
a database that has the relation schema EMP (EmpId, EmpName, and DeptName). An instance
of the schema EMP and a SQL query on it are given below.
The output
of executing the SQL query is ...............
Answer: 2.6
24. Consider
the following CPU processes with arrival times (in milliseconds) and length of
CPU bursts (in milliseconds) as given below:
If the pre-emptive
shortest remaining time first scheduling algorithm is used to schedule the processes,
then the average waiting time across all processes is ................... milliseconds.
Answer: 3.0
25. Consider
a two-level cache hierarchy with L1 and L2 caches. An application incurs 1.4
memory accesses per instruction on average. For this application, the miss rate
of L1 cache is 0.1; the L2 cache experiences, on average, 7 misses per 1000
instructions. The miss rate of L2 expressed correct to two decimal places is ................
Answer: 0.05
26. Let
G = (V, E) be any connected undirected edge-weighted graph. The weights of the
edges in E are positive and distinct. Consider the following statements:
(I) Minimum
Spanning Tree of G is always unique.
(II)
Shortest path between any two vertices of G is always unique.
Which of the
above statements is/are necessarily true?
(A) (I) only
(B) (II)
only
(C) both (I)
and (II)
(D) neither
(I) nor (II)
Answer: A
27. A
multithreaded program P executes with x number of threads and uses v number of
locks for ensuring mutual exclusion while operating on shared memory locations.
All locks in the program are non-reentrant. i.e., if a thread holds a lock l,
then it cannot re-acquire lock I without releasing it. If a thread is unable to
acquire a lock, it blocks until the lock becomes available. The minimum value
of x and the minimum value of y together for which execution of P can result in
a deadlock are:
(A) x=1, y=2
(B) x=2, y=1
(C) x=2, y=2
(D) x=1, y=1
Answer: D
28. The
value of
(A) is 0
(B) is -1
(C) is 1
(D) does not
exist
Answer: C
29. Let
p, q, and r be propositions and the expression (p→q)→r be a contradiction. Then,
the expression (r→p)→q is
(A) a tautology
(B) a
contradiction.
(C) always
TRUE when p is FALSE.
(D) always
TRUE when q is TRUE.
Answer: D
30. Let
u and v be two vectors in R2 whose Euclidean norms satisfy ||u||
= 2||v||. What is the value of α such that w = u + αv bisects the angle between
u and v?
(A) 2
(B) 1/2
(C) 1
(D) -1/2
Answer: A
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