GATE CSE purpose:exam-prep PYQs & Answers — Page 78

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Questions 771–780 of 975. Imported answers require independent review unless marked reviewed.

Topic practice 975 questionsPage 78 of 98

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) ________.

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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) ________.

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Let Σ be the set of all bijections from {1, ..., 5} to {1, ..., 5}, where id denotes the identity function, i.e. id(i) = i, ∀i. Let ∘ denote composition on functions. For a string x = x₁ x₂ ··· xₙ ∈ Σⁿ, n ≥ 0, let π(x) = x₁ ∘ x₂ ∘ ··· ∘ xₙ. Consider the language L = {x ∈ Σ* | π(x) = id}. The minimum number of states in any DFA accepting L is ________.

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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 uplink ports. The minimum number of switches needed is ________.

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

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

Student

Roll no.	Student name
1	Amit
2	Priya
3	Vinit
4	Rohan
5	Sita

Performance

Roll no.	Subject_code	Marks
1	A	86
1	B	95
1	C	90
2	A	89
2	C	92
3	C	80

The primary key of the Student table is Roll_no. For the Performance table, the columns Roll_no. and Subject_code together form 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 ________.

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Consider the following C program:

#include <stdio.h>

int main(){

float sum = 0.0, j = 1.0, i = 2.0;

while (i/j > 0.0625){

j = j + j;

sum = sum + i/j;

printf("%f\n", sum);

}

return 0;

}

The number of times the variable sum will be printed, when the above program is executed, is ________.

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Consider the following C program:

#include <stdio.h>

int main()

{

int a[] = {2, 4, 6, 8, 10};

int i, sum = 0, *b = a + 4;

for (i = 0; i < 5; i++)

sum = sum + (*b - i) - *(b - i);

printf("%d\n", sum);

return 0;

}

The output of the above C program is ________.

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In an RSA cryptosystem, the value of the public modulus parameter n is 307. If it is also known that φ(n) = 288, where φ() denotes Euler’s Totient Function, then the prime factor of n which is greater than 50 is ________.

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Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V).

X	Y	Z
X1	Y1	Z1
X1	Y1	Z2
X2	Y2	Z2
X2	Y4	Z4

X	Y	T
X2	Y1	2
X1	Y2	5
X1	Y1	6
X3	Y3	1

Y	V
Y1	V1
Y3	V2
Y2	V3
Y2	V2

How many tuples will be returned by the following relational algebra query?

Answer: ________.

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