CS/IT Gate Yearwise 


CS and IT Gate 2019 Questions with Answer

Ques 40 Gate 2019

Consider the first order predicate formula:
∀x [( ∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w(w > x) ∧ (∀z z⏐w ⇒ ((w = z) ∨ (z = 1)))]
Here ‘a⏐b’ denotes that ‘a divides b’, where a and b are integers.
Consider the following sets:

S1: {1, 2, 3, ..., 100}
S2: Set of all positive integers
S3: Set of all integers


Which of the above sets satisfy φ ?

A

S1 and S3

B

S2 and S3

C

S1 and S2

D

S1, S2 and S3


(b) is the correct answer.

Ques 41 Gate 2019

Which one of the following is NOT a valid identity?

A

(x⊕y) ⊕z = x⊕(y ⊕ z)

B

(x + y) ⊕z = x ⊕ (y + z)

C

x ⊕ y = x + y, if xy = 0

D

x ⊕ y = (xy + x′y′)′


(b) is the correct answer.

Ques 42 Gate 2019

Let X be a square matrix. Consider the following two statements on X.

I. X is invertible
II. Determinant of X is non-zero


Which one of the following is TRUE?

A

I implies II; II does not imply I

B

II implies I; I does not imply II

C

I does not imply II; II does not imply I

D

I and II are equivalent statements


(d) is the correct answer.

Ques 43 Gate 2019

Suppose Y is distributed uniformly in the open interval (1, 6). The probability that the polynomial 3x2 + 6xY + 3Y + 6 has only real roots is (rounded off to 1 decimal place) _________.


(0.80) is the correct answer.

Ques 44 Gate 2019

A certain processor deploys a single-level cache. The cache block size is 8 words and the word size is 4 bytes. The memory system uses a 60 MHz clock. To service a cache-miss, the memory controller first takes 1 cycle to accept the starting address of the block, it then takes 3 cycles to fetch all the eight words of the block, and finally transmits the words of the requested block at the rate of 1 word per cycle. The maximum bandwidth for the memory system when the program running on the processor issues a series of read operations is _________ × 106 bytes/sec.


(160) is the correct answer.

Ques 45 Gate 2019

The index node (inode) of a Unix-like file system has 12 direct, one single-indirect and one double-indirect pointer The disk block size is 4 kB and the disk block addresses 32-bits long. The maximum possible file size is (rounded off to 1 decimal place) __________ GB.


(4) is the correct answer.

Ques 46 Gate 2019

The following C program is executed on a Unix / Linux system:
 

#include<unistd.h>
int main() {
    int i;
    for (i = 0; i < 10; i++)
    if (i % 2 == 0)
        fork();
    return 0;
}
The total number of child process created is __________


(a) is the correct answer.

Ques 47 Gate 2019

Consider the following snapshot of a system running n concurrent processes. Process i is holding Xi instances of a resource R, 1 ≤ i ≤ n. Assume that all instances of R arecurrently in use. Further, for all i, process i can place a request for at most Yi additional instances of R while holding the Xt instances it already has. Of the n processes, there are exactly two processes p and q such that Yp = Yq = 0. Which one of the following conditions guarantees that no other process apart from p and q can complete execution?

A

Xp + Xq < Min {Yk ⏐ 1 ≤ k ≤ n, k ≠ p, k ≠ q}

B

Xp + Xq < Min {Yk ⏐ 1 ≤ k ≤ n, k ≠ p, k ≠ q}

C

Min (Xp , Xq ) ≤ Max {Yk ⏐ 1 ≤ k ≤ n, k ≠ p, k ≠ q}

D

Min (Xp , Xq ) ≤ Max {Yk ⏐ 1 ≤ k ≤ n, k ≠ p, k ≠ q}


(a) is the correct answer.

Ques 48 Gate 2019

Assume that in a certain computer, the virtual addresses are 64 bits long and the physical addresses are 48 bits long. The memory is word addressable. The page size is 8k Band the word size is 4 bytes. The Translation Look-aside Buffer (TLB) in the address translation path has 128 valid entries. At most how many distinct virtual addresses can be translated without any TLB miss?

A

16 x 210

B

8 x 220

C

4 x 220

D

256 x 210


(d) is the correct answer.

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