CS/IT Gate Yearwise 


CS and IT GATE 2019 Questions with Answer

Ques 40 Discrete Mathematics

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



Ques 41 Discrete Mathematics

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′)′



Ques 42 Mathematics

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



Ques 43 Mathematics

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 Operating System

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 Operating System

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 Operating System

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 Operating System

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}



Ques 48 Operating System

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



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