# GATE Computer Science Solved Paper 2017 Session II - Part 4

31.       For any discrete random variable X, with probability mass function
define the polyiona1 function
For a certain discrete random variable Y, there exists a scalar β ϵ [0, 1] such that
gY(z) = (1 - β + βz)N. The expectation of Y is
(A) Nβ(1 - β)
(B) Nβ
(C) N(1 - β)
(D) Not expressible in terms of N and β alone
32.       Consider the following expression grammar G:
E -> E - T | T
T -> T + F | F
F -> (E) | id
Which of the following grammars is not left recursive, but is equivalent to G?
(A) E -> E - T | T
T -> T + F | F
F -> (E) | id
(B) E -> TE’
E’ -> -TE’ | ϵ
T -> T + F | F
F -> (E) | id
(C) E -> TX
X -> -TX | ϵ
T -> FY
Y -> +FY | ϵ
F -> (E) | id
(D) E -> TX | (TX)
X -> -TX | +TX | ϵ
T -> id
33.       A system shares 9 tape drives. The current allocation and maximum requirement of tape drives for three processes are shown below:
Which of the following best describes current state of the system?
34.       Consider a binary code that consists of only four valid codewords as given below:
00000,01011,10101,11110
Let the minimum Hamming distance of the code be p and the maximum number of erroneous bits that can be corrected by the code be q. Then the values of p and q are
(A) p = 3 and q = l
(B) p = 3 and q = 2
(C) p = 4 and q = 1
(D) p = 4 and q = 2
35.       Consider two hosts X and Y, connected by a single direct link of rate 106 bits/sec. The distance between the two hosts is 10,000 km and the propagation speed along the link is 2 x 108 m/sec. Host X sends a file of 50,000 bytes as one large message to host Y continuously. Let the transmission and propagation delays be p milliseconds and q milliseconds, respectively.
Then the values of p and q are
(A) p = 50 and q = 100
(B) p = 50 and q = 400
(C) p = 100 and q = 50
(D) p = 400 and q = 50

36.       The pre-order traversal of a binary search tree is given by 12, 8, 6, 2, 7, 9, 10, 16, 15, 19, 17, 20.
Then the post-order traversal of this tree is:
(A) 2,6,7,8,9,10,12,15,16,17,19,20
(B) 2,7,6,10,9,8,15,17,20,19,16,12
(C) 7,2,6,8,9,10,20,17,19,15,16,12
(D) 7,6,2,10,9,8,15,16,17,20,19,12
37.       Consider the C program fragment below which is meant to divide x by y using repeated
subtractions. The variables x, y, q and r are all unsigned int.
while (r >= y) {
r = r - y;
q=q + 1;
}
Which of the following conditions on the variables x, y, q and r before the execution of the fragment will ensure that the loop terminates in a state satisfying the condition
x == (y*q + r)?
(A) (q == r) && (r == 0)
(B) (x > 0) && (r == x) && (y > 0)
(C) (q == 0) && (r == x) && (y > 0)
(D) (q == 0) && (y > 0)
38.       Consider the following C function.
int fun(int n) {
int i, j;
for(i = 1; i <= n; i++) {
for(j = 1; j < n; j += i) {
printf(“%d %d”,i,j);
}
}
}
Time complexity of fun in terms of Θ notation is
(A) Θ(n√n)
(B) Θ(n2)
(C) Θ(n logn)
(D) Θ(n2 logn)
39.       Let δ denote the transition function and δ^ denote the extended transition function of the ϵ-NFA whose transition table is given below:
Then δ^(q2, aba) is
(A) Φ
(B) {q0, q1, q3}
(C) {q0, q1, q2}
(D) {q0, q2, q3}
40.    Consider the following languages.
L1 = {ap | p is a prime number}
L2 = {anbmc2m | n≥0, m≥0)
L3 = {anbnc2n | n≥0)
L4 = {anbn | n≥1)
Which of the following are CORRECT?
I. L1 is context-free but not regular.
II. L2 is not context-free.
III. L3 is not context-free but recursive.
IV. L4 is deterministic context-free.
(A) I, II and IV only
(B) II and III only
(C) I and IV only
(D) III and IV only