GATE CS 2019

Question 51

Consider the following matrix:

The absolute value of the product of Eigenvalues of R is _________ .
Note: This was Numerical Type question.

• 12
• 145
• 125
• 4

Question 52

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.
Note: This was Numerical Type question.

• 160
• 128
• 256
• 320

Question 53

Let T be a full binary tree with 8 leaves. (A full binary tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) ___________ .
Note: This was Numerical Type question.

• 5.71 to 5.73
• 4.85 to 4.86
• 2.71 to 2.73
• 4.24 to 4.26

Question 54

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) _________.
Note: This was Numerical Type question.

• 0.80
• 0.17
• 0.20
• 1

Question 55

Let Σ be the set of all bijections from {1, ..., 5} to {1, ..., 5}, where id denotes the identity function, i.e. id(j) = j,∀j. Let ° denote composition on functions. For a string x = x₁x₂ ... x_n ∈ Σn, n ≥ 0, let π(x) = x₁°x₂° ... °x_n. Consider the language L = {x ∈ Σ* ⏐ π(x) = id}. The minimum number of states in any DFA accepting L is _________ .
Note: This was Numerical Type question.

• 120
• 125
• 210
• None of these

Question 56

Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do not have any separate up link ports. The minimum number of switches needed is ___________.
Note: This was Numerical Type question.

• 3
• 4
• 5
• 6

Question 57

What is the minimum number of 2-input NOR gates required to implement 4-variable function expressed in sum-of-minterms from as f = Σ(0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer ________ .
Note: This was Numerical Type question.

• 3
• 4
• 5
• 6

Question 58

In an RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also is known that φ(n) = 2880, where φ( ) denotes Euler’s Totient Function, then the prime factors of n which is greater than 50 is _________ .
Note: This was Numerical Type question.

• 97
• 31
• 37
• 91

Question 59

A relational database contains two tables Student and Performance as shown below:

The primary key of the Student table is Roll_no. For the Performance table, the columns Roll_no. and Subject_code together from the primary key. Consider the SQL query given below:

SELECT S.Student_name, sum(P.Marks)
FROM Student S, Performance P
WHERE  P.Marks  >  84
GROUP BY S.Student_name;

The number of rows returned by the above SQL query is _________ .
Note: This was Numerical Type question.

• 5
• 4
• 3
• None of these.

Question 60

Consider the following C program:

C

#include <stdio.h>

int main() {
 float sum = 0.0, j = 1.0, i = 2.0;
 
 while (i / j > 0.0625) {
    
    j = j + j;
    printf(\"%f\\n\", sum);
 };
 return 0;
}

The number of times variable sum will be printed When the above program is executed is _________ .
Note: This was Numerical Type question.

• 5
• 6
• 4
• 0