GATE CS question library

Consider the following software items: Program-$X$, Control Flow Diagram of Program-$Y$ and Control Flow Diagram of Program-$Z$ as shown below The values of McCabe's Cyclomatic complexity of program-$X$, program-$Y$, and program-$Z$ respectively are

Consider the following C program: #include<stdio.h> int f1(void); int f2(void); int f3(void); int x=10; int main() { int x=1; x += f1() + f2 () + f3() + f2(); printf("%d", x); return 0; } int f1() { int x = 25; x++; return x;} int f2() { static int x = 50; x++; return x;} int f3() { x *= 10; return x;} The output of the program is ______.

Language $L_1$ is polynomial time reducible to language $L_2$. Language $L_3$ is polynomial time reducible to language $L_2$, which in turn polynomial time reducible to language $L_4$. Which of the following is/are true? $\text{ if } L_4 \in P, \text{ then } L_2 \in P$ $\text{ if } L_1 \in P\text{ or } L_3 \in P, \text{ then } L_2 \in P$ …

Consider the following policies for preventing deadlock in a system with mutually exclusive resources. Process should acquire all their resources at the beginning of execution. If any resource is not available, all resources acquired so far are released. The resources are numbered uniquely, and processes are allowed to request for resources only in …

Consider the following reservation table for a pipeline having three stages $S_1, S_2 \text{ and } S_3$. …

The velocity $v$ (in kilometer/minute) of a motorbike which starts form rest, is given at fixed intervals of time $t$ (in minutes) as follows: t2468101214161820 v10182529322011520 The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is ________.

Suppose $c = \langle c[0], \dots, c[k-1]\rangle$ is an array of length $k$, where all the entries are from the set $\{0, 1\}$. For any positive integers $a \text{ and } n$, consider the following pseudocode. DOSOMETHING (c, a, n) z ← 1 for i ← 0 to k-1 do z ← z² mod n if c[i]=1 then z ← (z × a) mod n return z If …

Consider the following C program: #include<stdio.h> int main() { int i, j, k = 0; j=2 * 3 / 4 + 2.0 / 5 + 8 / 5; k-=--j; for (i=0; i<5; i++) { switch(i+k) { case 1: case 2: printf("\n%d", i+k); case 3: printf("\n%d", i+k); default: printf("\n%d", i+k); } } return 0; } The number of times printf statement is executed is _______.

Consider the following code sequence having five instructions from $I_1 \text{ to } I_5$. Each of these instructions has the following format. OP Ri, Rj, Rk Where operation OP is performed on contents of registers Rj and Rk and the result is stored in register Ri. $I_1$: ADD R1, R2, R3 $I_2$: MUL R7, R1, R3 $I_3$: SUB R4, R1, R5 $I_4$: ADD R3, R2, …

Consider a $B^+$ tree in which the search key is $12$ $\text{bytes}$ long, block size is $1024$ $\text{bytes}$, record pointer is $10$ $\text{bytes}$ long and the block pointer is $8$ $\text{bytes}$ long. The maximum number of keys that can be accommodated in each non-leaf node of the tree is ______.

If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where $a \neq b \text{ then } \int\limits_1^2 f(x)dx$ is

Given the function $F = P' +QR$, where $F$ is a function in three Boolean variables $P, Q$ and $R$ and $P'=!P$, consider the following statements. $(S1) F = \sum(4, 5, 6)$ $(S2) F = \sum(0, 1, 2, 3, 7)$ $(S3) F = \Pi (4, 5, 6)$ $(S4) F = \Pi (0, 1, 2, 3, 7)$ Which of the following is true?

The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________

Let $f(n) = n$ and $g(n) = n^{(1 + \sin \: n)}$, where $n$ is a positive integer. Which of the following statements is/are correct? $f(n) = O(g(n))$ $f(n) = \Omega(g(n))$

Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about $R$?

Let $G$ be a connected undirected graph of $100$ vertices and $300$ edges. The weight of a minimum spanning tree of $G$ is $500$. When the weight of each edge of $G$ is increased by five, the weight of a minimum spanning tree becomes ______.

Consider the following recursive C function. void get(int n) { if (n<1) return; get (n-1); get (n-3); printf("%d", n); } If $get(6)$ function is being called in $main()$ then how many times will the $get()$ function be invoked before returning to the $main()$?

In the network $200.10.11.144/27$, the $\text{fourth}$ octet (in decimal) of the last $\text{IP}$ address of the network which can be assigned to a host is _______.

Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} \text{ for } i = 1, 2, 3$. Define another random variable $Y = X_1X_2 \oplus X_3$, where $\oplus$ denotes XOR. Then $Pr[Y=0 \mid X_3 = 0] =$______.

Two hosts are connected via a packet switch with $10^7$ bits per second links. Each link has a propagation delay of $20$ microseconds. The switch begins forwarding a packet $35$ microseconds after it receives the same. If $10000$ bits of data are to be transmitted between the two hosts using a packet size of $5000$ bits, the time elapsed between …