GATE CS question library

If $p, q, r, s$ are distinct integers such that: $f (p, q, r, s) = \text{ max } (p, q, r, s)$ $g (p, q, r, s) = \text{ min } (p, q, r, s)$ $h (p, q, r, s) = \text{remainder of } \frac{(p \times q)} {(r \times s)} \text{ if } (p \times q) > (r \times s)$ …

In a triangle $PQR, PS$ is the angle bisector of $\angle QPR \text{ and } \angle QPS =60^\circ$. What is the length of $PS$ ?

Four branches of a company are located at $\text{M, N, O}$ and $\text{P. M}$ is north of $\text{N}$ at a distance of $4\;\text{km; P}$ is south of $\text{O}$ at a distance of $2\;\text{km; N}$ is southeast of $\text{O}$ by $1\;\text{km}$. What is the distance between $\text{M}$ and $\text{P}$ in $\text{km}$?

If the list of letters $P$, $R$, $S$, $T$, $U$ is an arithmetic sequence, which of the following are also in arithmetic sequence? $2P, 2R, 2S, 2T, 2U$ $P-3, R-3, S-3, T-3, U-3$ $P^2, R^2, S^2, T^2, U^2$

Based on the given statements, select the most appropriate option to solve the given question. What will be the total weight of $10$ poles each of same weight? Statements: One fourth of the weight of the pole is $5\;\text{Kg}$. The total weight of these poles is $160\;\text{Kg}$ more than the total weight of two poles.

A generic term that includes various items of clothing such as a skirt, a pair of trousers and a shirt is

Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are:

Choose the statement where underlined word is used correctly.

We __________ our friends's birthday and we _________ how to make it up to him.

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