GATE 2006 questions from Computer Science & Engineering

# Recent questions tagged gate2006 1
Statement for Linked Answer Questions 76 & 77: A $3$-ary max heap is like a binary max heap, but instead of $2$ children, nodes have $3$ children. A $3$-ary heap can be represented by an array as follows: The root is stored in the first location, $a$ ... $10, 9, 4, 5, 7, 6, 8, 2, 1, 3$ $10, 8, 6, 9, 7, 2, 3, 4, 1, 5$
2
The grammar $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid \epsilon$ $A\rightarrow aA\mid a$ $B\rightarrow Bb\mid b$ generates the language $L=\left \{ a^{i}b^{j}\mid i\neq j \right \}$. In this grammar what is the length of the derivation (number of steps starting from $S$) to generate the string $a^{l}b^{m}$ with $l\neq m$ $\max (l,m) + 2$ $l + m + 2$ $l + m + 3$ $\max (l,m) + 3$
3
Consider the diagram shown below where a number of LANs are connected by (transparent) bridges. In order to avoid packets looping through circuits in the graph, the bridges organize themselves in a spanning tree. First, the root bridge is identified as the bridge with the least serial number. Next, the root ...
4
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$
5
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The maximum degree of a vertex in $G$ is: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$
6
Consider two cache organizations. First one is $32$ $kB$ $2$-way set associative with $32$ $byte$ block size, the second is of same size but direct mapped. The size of an address is $32$ $bits$ in both cases . A $2$-to-$1$ multiplexer has latency of $0.6 ns$ while a $k-$bit comparator has ... while that of direct mapped is $h_2$. The value of $h_2$ is: $2.4$ $ns$ $2.3$ $ns$ $1.8$ $ns$ $1.7$ $ns$
7
Barrier is a synchronization construct where a set of processes synchronizes globally i.e., each process in the set arrives at the barrier and waits for all others to arrive and then all processes leave the barrier. Let the number of processes in the set be ... switch is disabled at the beginning of the barrier and re-enabled at the end. The variable process_left is made private instead of shared
8
A CPU has a $32$ $KB$ direct mapped cache with $128$ byte-block size. Suppose $A$ is two dimensional array of size $512 \times512$ with elements that occupy $8-bytes$ each. Consider the following two $C$ code segments, $P1$ and $P2$. $P1$: for (i=0; i<512; i++) { for (j=0; j<512; j++) ... and that for $P2$ be $M2$. The value of the ratio $\frac{M_{1}}{M_{2}}$: $0$ $\frac{1}{16}$ $\frac{1}{8}$ $16$
9
Which one of the following grammars generates the language $L=\left \{ a^{i}b^{j}\mid i\neq j \right \}$? $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid a\mid b$ $A\rightarrow aA\mid \varepsilon$ $B\rightarrow Bb\mid \varepsilon$ ... $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid \varepsilon$ $A\rightarrow aA\mid a$ $B\rightarrow Bb\mid b$
10
Consider the diagram shown below where a number of LANs are connected by (transparent) bridges. In order to avoid packets looping through circuits in the graph, the bridges organize themselves in a spanning tree. First, the root bridge is identified as the bridge with the least serial number. Next, the root sends out ... $\text{B1, B5, B2, B3, B4}$ $\text{B1, B3, B4, B5, B2}$
11
A CPU has a $32 KB$ direct mapped cache with $128$ byte-block size. Suppose A is two dimensional array of size $512 \times512$ with elements that occupy $8$-bytes each. Consider the following two C code segments, $P1$ and $P2$. P1: for (i=0; i<512; i++) { for (j=0; j<512; j++ ... misses experienced by $P1$ be $M_{1}$and that for $P2$ be $M_{2}$. The value of $M_{1}$ is: $0$ $2048$ $16384$ $262144$
12
Barrier is a synchronization construct where a set of processes synchronizes globally i.e., each process in the set arrives at the barrier and waits for all others to arrive and then all processes leave the barrier. Let the number of processes in the set be ... to $10$ need not be inside a critical section The barrier implementation is correct if there are only two processes instead of three.
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Statement for Linked Answer Questions 76 & 77: A $3$-ary max heap is like a binary max heap, but instead of $2$ children, nodes have $3$ children. A $3$-ary heap can be represented by an array as follows: The root is stored in the first location, $a$ ... $1, 3, 5, 6, 8, 9$ $9, 6, 3, 1, 8, 5$ $9, 3, 6, 8, 5, 1$ $9, 5, 6, 8, 3, 1$
14
Consider two cache organizations. First one is $32 \hspace{0.2cm} KB$ $2-way$ set associative with $32 \hspace{0.2cm} byte$ block size, the second is of same size but direct mapped. The size of an address is $32 \hspace{0.2cm} bits$ in both cases . A $2-to-1$ ... $h_1$ is: $2.4 \text{ ns}$ $2.3 \text{ ns}$ $1.8 \text{ ns}$ $1.7 \text{ ns}$
15
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of vertices of degree zero in $G$ is: $1$ $n$ $n + 1$ $2^n$
16
The following functional dependencies are given: $AB\rightarrow CD,AF\rightarrow D,DE\rightarrow F,$C\rightarrow G,F\rightarrow E,G\rightarrow A $Which one of the following options is false?$ \left \{ CF \right \}^{*}=\left \{ ACDEFG \right \} \left \{ BG \right \}^{*}=\left \{ ABCDG ... $\left \{ AB \right \}^{*}=\left \{ ABCDG \right \}$
17
Consider the relation enrolled (student, course) in which (student, course) is the primary key, and the relation paid (student, amount) where student is the primary key. Assume no null values and no foreign keys or integrity constraints. Assume that amounts 6000, 7000, 8000 ... , Plan 1 executes faster than Plan 2 for all databases For x = 9000, Plan I executes slower than Plan 2 for all databases
18
Consider the relation enrolled (student, course) in which (student, course) is the primary key, and the relation paid (student, amount) where student is the primary key. Assume no null values and no foreign keys or integrity constraints. Given the ... for which Query3 returns strictly fewer rows than Query2 There exist databases for which Query4 will encounter an integrity violation at runtime
19
Consider the relation account (customer, balance) where the customer is a primary key and there are no null values. We would like to rank customers according to decreasing balance. The customer with the largest balance gets rank 1. Ties are not broke but ranks are skipped: if ... order assigning ranks using ODBC. Which two of the above statements are correct? 2 and 5 1 and 3 1 and 4 3 and 5
20
Consider the following snapshot of a system running $n$ processes. Process $i$ is holding $x_i$ instances of a resource $R$, $1\leq i\leq n$ . Currently, all instances of $R$ are occupied. Further, for all $i$, process $i$ has placed a request for an additional $y_i$ instances while holding the $x_i$ ... $\max(x_{p},x_{q})>1$ $\min(x_{p},x_{q})>1$
21
Consider three processes, all arriving at time zero, with total execution time of $10$, $20$ and $30$ units, respectively. Each process spends the first $\text{20%}$ of execution time doing I/O, the next $\text{70%}$ of time doing computation, and the last $\text{10%}$ of time doing ... . For what percentage of time does the CPU remain idle? $\text{0%}$ $\text{10.6%}$ $\text{30.0%}$ $\text{89.4%}$
22
Consider three processes (process id $0$, $1$, $2$ respectively) with compute time bursts $2$, $4$ and $8$ time units. All processes arrive at time zero. Consider the longest remaining time first (LRTF) scheduling algorithm. In LRTF ties are broken by giving priority to the process with the lowest process id. The average turn around time is: $13$ units $14$ units $15$ units $16$ units
23
A computer system supports $32$-bit virtual addresses as well as $32$-bit physical addresses. Since the virtual address space is of the same size as the physical address space, the operating system designers decide to get rid of the virtual memory entirely. ... can be made more efficient now Hardware support for memory management is no longer needed CPU scheduling can be made more efficient now
24
A CPU generates $32$-bit virtual addresses. The page size is $4$ KB. The processor has a translation look-aside buffer (TLB) which can hold a total of $128$ page table entries and is $4$-way set associative. The minimum size of the TLB tag is: $\text{11 bits}$ $\text{13 bits}$ $\text{15 bits}$ $\text{20 bits}$
25
The atomic fetch-and-set $x, y$ instruction unconditionally sets the memory location $x$ to $1$ and fetches the old value of $x$ in $y$ without allowing any intervening access to the memory location $x$. Consider the following implementation of $P$ and $V$ functions ... -set, a pair of normal load/store can be used The implementation of $V$ is wrong The code does not implement a binary semaphore
26
Consider the following C code segment. for (i = 0, i < n; i++) { for (j = 0; j < n; j++) { if (i%2) { x += (4*j + 5*i); y += (7 + 4*j); } } } Which one of the following is false? The code contains loop invariant computation There is scope of common sub-expression elimination in this code There is scope of strength reduction in this code There is scope of dead code elimination in this code
27
Consider the following translation scheme. $S\rightarrow ER$ $R\rightarrow ^{*}E\left \{ print('*'); \right \} R\mid \varepsilon$ $E\rightarrow F+E\left \{ print('+'); \right \}\mid F$ $F\rightarrow (S)\mid id \left \{ print(id.value); \right \}$ Here id is a token that represents an ... $2 * 3 + 4$', this translation scheme prints $2 * 3 + 4$ $2 * +3 \ 4$ $2 \ 3 * 4 +$ $2 \ 3 \ 4+*$
Consider the following grammar: $S\rightarrow FR$ $R\rightarrow * S\mid \varepsilon$ $F\rightarrow id$ In the predictive parser table, M, of the grammar the entries M[S,id] and M[R,\$] respectively are$ \left \{ S\rightarrow FR \right \} $and$ \left \{ R\rightarrow \ ... $\left \{ F\rightarrow id \right \}$ and $\left \{ R\rightarrow \varepsilon \right \}$