GATE CS question library

The value of the definite integral $$\int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x$$ is _________. (Rounded off to the nearest integer)

A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.

Consider a $3$-stage pipelined processor having a delay of $10 \mathrm{~ns}$ (nanoseconds), $20 \mathrm{~ns}$, and $14 \mathrm{~ns},$ for the first, second, and the third stages, respectively. Assume that there is no other delay and the processor does not suffer from any pipeline hazards. Also assume that one instruction is fetched every cycle. The …

A keyboard connected to a computer is used at a rate of $1$ keystroke per second. The computer system polls the keyboard every $10 \mathrm{~ms}$ (milli seconds) to check for a keystroke and consumes $100\; \mu \mathrm{s}$ (micro seconds) for each poll. If it is determined after polling that a key has been pressed, the system consumes an additional …

The integer value printed by the $\textsf{ANSI-C}$ program given below is _______________ #include<stdio.h> int funcp(){ static int x = 1; x++; return x; } int main(){ int x,y; x = funcp(); y = funcp()+x; printf("%d\n", (x+y)); return 0; }

Consider the following program: int main() { f1 (); f2(2); f3(); return (0); } int f1 () { return(1); } int f2 (int X) { f3(); if (X==1); return f1 (); else return (X * f2 (X - 1)); } int f3 () { return (5); } Which one of the following options represents the activation tree corresponding to the main function?

Consider the control flow graph shown. Which one of the following choices correctly lists the set of live variables at the exit point of each basic block?

Consider the two functions $\textsf{incr}$ and $\textsf{decr}$ shown below. incr(){ decr(){ wait(s); wait(s); X = X+1; X = X-1; signal(s); signal(s); } } There are $5$ threads each invoking $\textsf{incr}$ once, and $3$ threads each invoking $\textsf{decr}$ once, on the same shared variable $\mathrm{X}$. The initial value of $\mathrm{X}$ is …

Consider the context-free grammar $G$ below $$\begin{array}{l} S \rightarrow a S b \mid X \\ X \rightarrow a X \mid X b \mid a \mid b, \end{array}$$ where $S$ and $X$ are non-terminals, and $a$ and $b$ are terminal symbols. The starting non-terminal is $S$. Which one of the following statements is $\text{CORRECT}?$

Consider the pushdown automaton $\text{(PDA)}\;P$ below, which runs on the input alphabet $\{a, b\}$, has stack alphabet $\{\perp, A\}$, and has three states $\{s, p, q\}$, with $s$ being the start state. A transition from state $u$ to state $v$, labelled $c / X / \gamma$, where $c$ is an input symbol or $\epsilon, X$ is a stack symbol, …

Consider the given $\text{C}$-code and its corresponding assembly code, with a few operands $\text{U1-U4}$ being unknown. Some useful information as well as the semantics of each unique assembly instruction is annotated as inline comments in the code. The memory is byte-addressable. //C-code int a[10], b[10], i; // int is 32 bit for(i=0; i<10; i++) …

Consider a sequential digital circuit consisting of $\mathrm{T}$ flip-flops and $\mathrm{D}$ flip-flops as shown in the figure. $\text{CLKIN}$ is the clock input to the circuit. At the beginning, $\text{Q1, Q2}$ and $\text{Q3}$ have values $0,1$ and $1,$ respectively. Which one of the given values of $\text{(Q1, Q2, Q3)}$ can $\text{NEVER}$ …

A $4$ kilobyte $\text{(KB)}$ byte-addressable memory is realized using four $1 \mathrm{~KB}$ memory blocks. Two input address lines $\text{(IA4 and IA3)}$ are connected to the chip select $\text{(CS)}$ port of these memory blocks through a decoder as shown in the figure. The remaining ten input address lines from $\text{IA11-IA0}$ are connected …

A Boolean digital circuit is composed using two $4$-input multiplexers $\text{(M1 and M2)}$ and one $2$-input multiplexer $\text{(M3)}$ as shown in the figure. $\text{X0-X7}$ are the inputs of the multiplexers $\text{M1 and M2}$ and could be connected to either $0$ or $1.$ The select lines of the multiplexers are connected to Boolean …

Consider the $\textsf{IEEE-754}$ single precision floating point numbers $\text{P} = \textsf{0xC1800000}$ and $\text{Q} = \textsf{0x3F5C2EF4}.$ Which one of the following corresponds to the product of these numbers $(\text{i.e., P} \times \mathrm{Q} ),$ represented in the $\textsf{IEEE-754}$ single precision format?

Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if one of the following is true. All members of $A$ appear in the …

Let $A$ be a priority queue for maintaining a set of elements. Suppose $A$ is implemented using a max-heap data structure. The operation $\text{EXTRACT-MAX} (A)$ extracts and deletes the maximum element from $A$. The operation $\operatorname{INSERT}(A, key )$ inserts a new element $key$ in $A$. The properties of a max-heap are preserved at the …

Consider the $\text{C}$ function $\text{foo}$ and the binary tree shown. typedef struct node { int val; struct node *left, *right; } node; int foo(node *p) { int retval; if (p == NULL) return 0; else { retval = p->val + foo(p->left) + foo(p->right); printf("%d ", retval); return retval; } } When $\textsf{foo}$ is called with a pointer to the …

Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as $$a_{1} \sim a_{2} \text{ if } f\left(a_{1}\right)=f\left(a_{2}\right),$$ where $a_{1}, a_{2} \in A$. Let $\mathcal{E}=\{[x]: x \in A\}$ be the set of all the equivalence classes under …

Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: $$A \Delta B=(A-B) \cup(B-A) \text{. }$$ Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct?