41.
Let L(R) be the language represented by
regular expression R. Let L(G) be the language generated by a context free
grammar G. Let L(M) be the language accepted by a Turing machine M.
Which of the
following decision problems are undecidable?
I. Given a
regular expression R and a string w, is w ϵ L(R)?
II. Given a
context-free grammar G, is L(G) = Φ?
III. Given a
context-free grammar G, is L(G) = ∑* for some alphabet ∑?
IV. Given a Turing
machine M and a string w, is w ϵ L(M)?
(A) I and IV
only
(B) II and
III only
(C) II, III
and IV only
(D) III and
IV only
Answer: D
42. The
next state table of a 2-bit saturating up-counter is given below.
The counter
is built as a synchronous sequential circuit using T flip-flops. The
expressions for T1 and T0 are
Answer: B
43. Consider
the following snippet of a C program. Assume that swap (& x, & y)
exchanges the contents of x and y.
int main() {
int
array[] = {3, 5, 1, 4, 6, 2);
int
done = 0;
int
i;
while
(done == 0) {
done = 1;
for
(i=0; i<=4; i++) {
if
(array[i] < array[i+1]) {
swap(&array[i], &array[i+1]);
done
= 0;
}
}
for
(i=5; i>=1; i--) {
if
(array[i] > array[i-1]) {
swap(&array[i], &array[i-1]);
done
= 0;
}
}
}
printf
(“%d”, array[3]);
}
The output
of the program is ...................
Answer: 3.0
44. Two
transactions T1 and T2 are given as
T1:
r1(X)w1(X)r1(Y)w1(Y)
T2:
r2(Y)w2(Y)r2(Z)w2(Z)
where ri(V)
denotes a read operation by transaction Ti on a variable V and wi(V)
denotes a write operation by transaction Ti on a variable V. The
total number of conflict serializable schedules that can be formed by T1
and T2 is ...............
Answer: 54.0
45. The
read access times and the hit ratios for different caches in a memory hierarchy
are as given below.
The read
access time of main memory is 90 nanoseconds. Assume that the caches use the referred-word-first
read policy and the write back policy. Assume that all the caches are direct
mapped caches. Assume that the dirty bit is always 0 for all the blocks in the
caches. In execution of a program, 60% of memory reads are for instruction fetch
and 40% are for memory operand fetch. The average read access time in
nanoseconds (up to 2 decimal places) is ..................
Answer: 4.72
46. Consider
the following database table named top_scorer.
Consider the
following SQL query:
SELECT
ta.player FROM top scorer AS ta
WHERE
ta.goals > ALL (SELECT tb.goals
FROM
top_scorer AS tb
WHERE
tb.country = ‘Spain’)
AND ta.goals
>ANY(SELECT tc.goals
FROM top_scorer AS tc
WHERE
tc.country = ‘Germany’)
The number
of tuples returned by the above SQL query is ...............
Answer: 7.0
47. If
the ordinary generating function of a sequence
then a3-a0
is equal to ....................
Answer: 15.0
48. If
a random variable X has a Poisson distribution with mean 5, then the
expectation E[(X+2)2] equals ................
Answer: 54.0
49. In
a B+ tree, if the search-key value is 8 bytes long, the block size is 512 bytes
and the block pointer size is 2 bytes, then the maximum order of the B+ tree is
...................
Answer: 52.0
50. A
message is made up entirely of characters from the set X={P,Q,R,S,T}. The table
of probabilities for each of the characters is shown below:
If a message
of 100 characters over X is encoded using Huffman coding, then the expected
length of the encoded message in bits is ..............
Answer: 225.0
51. Consider
the set of processes with arrival time (in milliseconds), CPU burst time (in
milliseconds), and priority (0 is the highest priority) shown below. None of
the processes have I/O burst time.
The average
waiting time (in milliseconds) of all the processes using preemptive priority scheduling
algorithm is ................
Answer: 29.0
52. If
the characteristic polynomial of a 3 x 3 matrix M over R (the set of real numbers)
is λ3-4λ2+aλ+30, a ϵ R, and one eigen value of M is 2,
then the largest among the absolute values of the eigen values of M is
.................
Answer: 5.0
53. Consider
a machine with a byte addressable main memory of 232 bytes divided
into blocks of size 32 bytes. Assume that a direct mapped cache having 512
cache lines is used with this machine. The size of the tag field in bits is
.............
Answer: 18.0
54. Consider
the following C Program.
#include<stdio.h>
int main() {
int
m = 10;
int
n, n1;
n
= ++m;
n1=m++;
n--;
--n1;
n-=n1;
printf(“%d”,
n);
return
0;
}
The output
of the program is ..................
Answer: 0
55. Consider
the following C Program.
#include<stdio.h>
#include<string.h>
int main() {
char*
c = “GATECSIT2017”;
char*
p = c;
printf(“%d”,
(int)strlen(c+2[p]-6[p]-1));
return
0;
}
The output
of the program is .................
Answer: 2.0
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