GATE CS question library

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?

Identify the correct order in which a server process must invoke the function calls accept, bind, listen, and recv according to UNIX socket API.

Match the following: …

The cardinality of the power set of $\{0, 1, 2, \dots , 10\}$ is _______

Consider a complete binary tree where the left and right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap is

Consider the following function written in the C programming langauge : void foo(char *a) { if (*a && *a != ' ') { foo(a+1); putchar(*a); } } The output of the above function on input "$ABCD \ EFGH$" is

Let $R$ be the relation on the set of positive integers such that $aRb$ and only if $a$ and $b$ are distinct and let have a common divisor other than $1.$ Which one of the following statements about $R$ is true?

In the context of abstract-syntax-tree (AST) and control-flow-graph (CFG), which one of the following is TRUE?

Which of the following statements is NOT correct about HTTP cookies?

Consider the basic COCOMO model where $E$ is the effort applied in person-months, $D$ is the development time in chronological months, $KLOC$ is the estimated number of delivered lines of code (in thousands) and $a_b, b_b, c_b, d_b$ have their useful meanings. The basic COCOMO equations are of the form