GATE CS question library

Consider the following program Program P2 var n : int; procedure W(var x : int) begin x = x + 1; print x; end procedure D begin var n : int; n = 3; W(n); end begin \\begin P2 n=10; D; end If the language has dynamic scooping and parameters are passed by reference, what will be printed by the program?

Consider the following three C functions: $[P1]$ int *g(void) { int x = 10; return (&x); } $[P2]$ int *g(void) { int *px; *px = 10; return px; } $[P3]$ int *g(void) { int *px; px = (int*) malloc (sizeof(int)); *px = 10; return px; } Which of the above three functions are likely to cause problems with pointers?

What is printed by the print statements in the program $P1$ assuming call by reference parameter passing? Program P1() { x = 10; y = 3; func1(y,x,x); print x; print y; } func1(x,y,z) { y = y + 4; z = x + y + z }

What is the minimum number of stacks of size $n$ required to implement a queue of size $n$?

How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices?

Consider an undirected, unweighted graph $G$. Let a breadth-first traversal of $G$ be done starting from a node $r$. Let $d(r,u)$ and $d(r,v)$ be the lengths of the shortest paths from $r$ to $u$ and $v$ respectively in $G$. If $u$ is visited before $v$ during the breadth-first traversal, which of the following statements is correct?

Consider the following data path of a simple non-pipelined CPU. The registers $A, B$, $A_{1},A_{2}, \textsf{MDR},$ the $\textsf{bus}$ and the $\textsf{ALU}$ are $8$-$bit$ wide. $\textsf{SP}$ and $\textsf{MAR}$ are $16$-$bit$ registers. The $\textsf{MUX}$ is of size $8 \times (2:1)$ and the $\textsf{DEMUX}$ is of size …

Consider the circuit given below with initial state $Q_0=1, Q_1=Q_2=0$. The state of the circuit is given by the value $4Q_2+2Q_1+Q_0$ Which one of the following is correct state sequence of the circuit?

Consider the circuit shown below. The output of a $2:1$ MUX is given by the function $(ac' + bc)$. Which of the following is true?

The $2's$ complement representation of (-539)10 in hexadecimal is

Which is the most appropriate match for the items in the first column with the items in the second column: …

Consider the following circuit with initial state $Q_0 = Q_1 = 0$. The D Flip-flops are positive edged triggered and have set up times 20 nanosecond and hold times $0.$ Consider the following timing diagrams of X and C. The clock period of $C \geq 40$ nanosecond. Which one is the correct plot of Y?

Consider the following problem $X$. Given a Turing machine $M$ over the input alphabet $\Sigma$, any state $q$ of $M$ and a word $w \in \Sigma^*$, does the computation of $M$ on $w$ visit the state of $q$? Which of the following statements about $X$ is correct?

Consider the following languages: $L1=\left\{ww \mid w \in \{a,b\}^*\right\}$ $L2=\left\{ww^R \mid w \in \{a,b\}^*, w^R \text{ is the reverse of w} \right\}$ $L3=\left\{0^{2i} \mid \text{ i is an integer} \right\}$ $L4= \left\{ 0^{i^2} \mid \text{ i is an integer} \right\}$ Which of the languages are regular?

Consider a DFA over $\Sigma=\{a,b\}$ accepting all strings which have number of a's divisible by $6$ and number of $b$'s divisible by $8$. What is the minimum number of states that the DFA will have?

Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S_1: f(E \cup F) = f(E) \cup f(F)$ $S_2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2?

How many $4$-digit even numbers have all $4$ digits distinct?

Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ is rational. Which of the following is true about $S_1$ and $S_2$?

Let r and s be two relations over the relation schemes R and S respectively, and let A be an attribute in R. The relational algebra expression $\sigma_{A=a}(r \bowtie s)$ is always equal to

Which of the following requires a device driver?