GATE CS question library

The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.

The secant method is used to find the root of an equation $f(x)=0$. It is started from two distinct estimates $x_a$ and $x_b$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_b)$ is very small and then $x_b$ is the solution. The procedure is given below. Observe that there is an …

Consider the C program below #include <stdio.h> int *A, stkTop; int stkFunc (int opcode, int val) { static int size=0, stkTop=0; switch (opcode) { case -1: size = val; break; case 0: if (stkTop < size ) A[stkTop++]=val; break; default: if (stkTop) return A[--stkTop]; } return -1; } int main() { int B[20]; A=B; stkTop = -1; stkFunc (-1, 10); stkFunc …

Given below are some algorithms, and some algorithm design paradigms. …

The number of min-terms after minimizing the following Boolean expression is _______. $[D'+AB'+A'C+AC'D+A'C'D]'$

Consider the alphabet $\Sigma = \{0, 1\}$, the null/empty string $\lambda$ and the set of strings $X_0, X_1, \text{ and } X_2$ generated by the corresponding non-terminals of a regular grammar. $X_0, X_1, \text{ and } X_2$ are related as follows. $X_0 = 1 X_1$ $X_1 = 0 X_1 + 1 X_2$ $X_2 = 0 X_1 + \{ \lambda \}$ Which one of the following …

Assume that the bandwidth for a $\text{TCP}$ connection is $1048560$ bits/sec. Let $\alpha$ be the value of RTT in milliseconds (rounded off to the nearest integer) after which the $\text{TCP}$ window scale option is needed. Let $\beta$ be the maximum possible window size with window scale option. Then the values of $\alpha$ and $\beta$ are

Which one of the following hash functions on integers will distribute keys most uniformly over $10$ buckets numbered $0$ to $9$ for $i$ ranging from $0$ to $2020$?

Consider two relations $R_1(A,B)$ with the tuples $(1,5), (3,7)$ and $R_2(A,C) = (1,7),(4,9)$. Assume that $R(A,B,C)$ is the full natural outer join of $R_1$ and $R_2$. Consider the following tuples of the form $(A,B,C):$ $a = (1,5,null), b=(1,null,7), c=(3,null,9), d=(4,7,null), e=(1,5,7),$ $f=(3,7,null), g=(4,null,9).$ Which one of the …

A Young tableau is a $2D$ array of integers increasing from left to right and from top to bottom. Any unfilled entries are marked with $\infty$, and hence there cannot be any entry to the right of, or below a $\infty$. The following Young tableau consists of unique entries. …

Consider $6$ memory partitions of sizes $200$ $\text{KB}$, $400$ $\text{KB}$, $600$ $\text{KB}$, $500$ $\text{KB}$, $300$ $\text{KB}$ and $250$ $\text{KB}$, where $\text{KB}$refers to $\text{kilobyte}$. These partitions need to be allotted to four processes of sizes $357$ $\text{KB}$, $210$ $\text{KB}$, $468$ …

Consider the intermediate code given below. (1) i=1 (2) j=1 (3) t1 = 5 * i (4) t2 = t1 + j (5) t3 = 4 * t2 (6) t4 = t3 (7) a[t4] = -1 (8) j = j + 1 (9) if j <= 5 goto (3) (10) i = i +1 (11) if i < 5 goto (2) The number of nodes and edges in control-flow-graph constructed for the above code, respectively, are

A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on $n$ vertices, $n$ is

Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$ Add the third row to the second row Subtract the third column from the first column. The determinant of the resultant matrix is _____.

Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[-1, 1]$ $f$ is not bounded in $[-1, 1]$ $A$ is nonzero and finite

A computer system implements a $40\;\text{-bit}$ virtual address, page size of $8\;\text{kilobytes}$, and a $128\text{-entry}$ translation look-aside buffer $\text{(TLB)}$ organized into $32$ sets each having $4$ ways. Assume that the $\text{TLB}$ tag does not store any process id. The minimum length of the $\text{TLB}$ tag in bits is ______.

A system has $6$ identical resources and $N$ processes competing for them. Each process can request at most $2$ resources. Which one of the following values of $N$ could lead to a deadlock?

Assume that for a certain processor, a read request takes $50\:\text{nanoseconds}$ on a cache miss and $5\:\text{nanoseconds}$ on a cache hit. Suppose while running a program, it was observed that $80\%$ of the processor's read requests result in a cache hit. The average read access time in nanoseconds is ______.

An unordered list contains $n$ distinct elements. The number of comparisons to find an element in this list that is neither maximum nor minimum is

Consider the following statements. The complement of every Turing decidable language is Turing decidable There exists some language which is in NP but is not Turing decidable If L is a language in NP, L is Turing decidable Which of the above statements is/are true?