GATE CS question library

The set $\{1, 2, 4, 7, 8, 11, 13, 14\}$ is a group under multiplication modulo $15$. The inverses of $4$ and $7$ are respectively:

Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of G is $8$. Then, the size of the maximum independent set of $G$ is:

Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is :

Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is:

Let $A, B$ and $C$ be non-empty sets and let $X = ( A - B ) - C$ and $Y = ( A - C ) - ( B - C ).$ Which one of the following is TRUE?

The following is the Hasse diagram of the poset $\left[\{a,b,c,d,e\},≺\right]$ The poset is :

Suppose there are $\lceil \log n \rceil$ sorted lists of $\lfloor n /\log n \rfloor$ elements each. The time complexity of producing a sorted list of all these elements is: (Hint:Use a heap data structure)

Consider the following circuit involving a positive edge triggered D FF. Consider the following timing diagram. Let $A_{i}$ represents the logic level on the line $A$ in the $i$-th clock period. Let $A'$ represent the complement of $A$. The correct output sequence on $Y$ over the clock periods $1$ through $5$ is:

Consider the following code fragment: if (fork() == 0) { a = a + 5; printf("%d, %p n", a, &a); } else { a = a - 5; printf ("%d, %p n", a,& a); } Let $u,v$ be the values printed by the parent process and $x,y$ be the values printed by the child process. Which one of the following is TRUE?