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GATE 2016 Computer Science Set 2 Questions

Recent questions tagged gate2016-2

74 votes
10 answers
1
Suppose the functions $F$ and $G$ can be computed in $5$ and $3$ nanoseconds by functional units $U_{F}$ and $U_{G}$, respectively. Given two instances of $U_{F}$ and two instances of $U_{G}$, it is required to implement the computation $F(G(X_{i}))$ for $1 \leq i \leq 10$. Ignoring all other delays, the minimum time required to complete this computation is ____________ nanoseconds.
asked Feb 12, 2016 in CO and Architecture Akash Kanase 9.9k views
22 votes
2 answers
2
Consider the following processes, with the arrival time and the length of the CPU burst given in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time first. ... $} & 8 & 3 \\\hline \end{array}$The average turn around time of these processes is ___________ milliseconds.
asked Feb 12, 2016 in Operating System Akash Kanase 3.4k views
36 votes
3 answers
3
The width of the physical address on a machine is $40$ bits. The width of the tag field in a $512$ KB $8$-way set associative cache is ________ bits.
asked Feb 12, 2016 in CO and Architecture Akash Kanase 8.1k views
57 votes
5 answers
4
In an adjacency list representation of an undirected simple graph $G=(V, E)$, each edge $(u, v)$ has two adjacency list entries: $[v]$ in the adjacency list of $u$, and $[u]$ in the adjacency list of $v$. These are called twins of each other. A twin pointer is a pointer from an ... list? $\Theta\left(n^{2}\right)$ $\Theta\left(n+m\right)$ $\Theta\left(m^{2}\right)$ $\Theta\left(n^{4}\right)$
asked Feb 12, 2016 in Algorithms Akash Kanase 7.6k views
46 votes
6 answers
5
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ $(\exists x p(x) \vee \exists x q (x)) \implies \exists x (p(x) \vee q (x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
asked Feb 12, 2016 in Mathematical Logic Akash Kanase 7.3k views
34 votes
2 answers
6
Consider the following languages: $L_{1}=\left\{a^{n}b^{m}c^{n+m}:m, n\geq 1\right\}$ $L_{2}=\left\{a^{n}b^{n}c^{2n} :n\geq 1\right\}$ Which one of the following is TRUE? Both $L_{1}$ and $L_{2}$ are context-free. $L_{1}$ is context-free while $L_{2}$ is not context-free. $L_{2}$ is context-free while $L_{1}$ is not context-free. Neither $L_{1}$ nor $L_{2}$ is context-free.
asked Feb 12, 2016 in Theory of Computation Akash Kanase 5.6k views
41 votes
1 answer
7
Consider the following database table named water_schemes: ... district_name with total_avg (capacity) as select avg (capacity) from total select name from total, total_avg where total.capacity ≥ total_avg.capacity
asked Feb 12, 2016 in Databases Akash Kanase 4.4k views
33 votes
6 answers
8
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
asked Feb 12, 2016 in Set Theory & Algebra Akash Kanase 5.7k views
28 votes
4 answers
9
Consider the following program: int f (int * p, int n) { if (n <= 1) return 0; else return max (f (p+1, n-1), p[0] - p[1]); } int main () { int a[] = {3, 5, 2, 6, 4}; print f(" %d", f(a, 5)); } Note: $max (x, y)$ returns the maximum of $x$ and $y$. The value printed by this program is ________.
asked Feb 12, 2016 in Programming Akash Kanase 5.1k views
47 votes
4 answers
10
Consider a processor with $64$ registers and an instruction set of size twelve. Each instruction has five distinct fields, namely, opcode, two source register identifiers, one destination register identifier, and twelve-bit immediate value. Each instruction must be stored in memory ... . If a program has $100$ instructions, the amount of memory (in bytes) consumed by the program text is _________.
asked Feb 12, 2016 in CO and Architecture Akash Kanase 8.1k views
30 votes
5 answers
11
Consider the following two-process synchronization solution. ... two- process synchronization solution. This solution violates mutual exclusion requirement. This solution violates progress requirement. This solution violates bounded wait requirement.
asked Feb 12, 2016 in Operating System Akash Kanase 6k views
30 votes
1 answer
12
A student wrote two context-free grammars G1 and G2 for generating a single C-like array declaration. The dimension of the array is at least one. For example, int a[10] [3]; The grammars use D as the start symbol, and use six terminal symbols int ; id [ ] ... Which of the grammars correctly generate the declaration mentioned above? Both G1 and G2 Only G1 Only G2 Neither G1 nor G2
asked Feb 12, 2016 in Compiler Design Akash Kanase 3.3k views
41 votes
5 answers
13
Consider the following New-order strategy for traversing a binary tree: Visit the root; Visit the right subtree using New-order; Visit the left subtree using New-order; The New-order traversal of the expression tree corresponding to the reverse polish expression 3 4 * 5 - 2 ^ 6 7 * 1 + - is given by: ... $1 \ 7 \ 6 * + \ 2 \ 5 \ 4 \ 3 \ * \ - \wedge -$
asked Feb 12, 2016 in DS Akash Kanase 6.5k views
76 votes
6 answers
14
Consider the following languages. $L_{1} = \left\{\left\langle M \right\rangle \mid M \text{ takes at least 2016 steps on some input} \right\}$, $L_{2} = \left\{\left\langle M \right\rangle \mid M \text { takes at least 2016 steps on all inputs} \right\}$ ... $L_{1}, L_{2}$ are recursive and $L_{3}$ is not recursive $L_{1}, L_{2}, L_{3}$ are recursive
asked Feb 12, 2016 in Theory of Computation Akash Kanase 15.2k views
61 votes
8 answers
15
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an odd number of ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
asked Feb 12, 2016 in Set Theory & Algebra Akash Kanase 6.5k views
29 votes
2 answers
16
Which one of the following grammars is free from left recursion? $S \rightarrow AB$ $A \rightarrow Aa \mid b$ $B \rightarrow c$ $S \rightarrow Ab \mid Bb \mid c$ $A \rightarrow Bd \mid \epsilon$ $B \rightarrow e$ $S \rightarrow Aa \mid B$ $A \rightarrow Bb \mid Sc \mid \epsilon$ $ B \rightarrow d$ $S \rightarrow Aa \mid Bb \mid c$ $A \rightarrow Bd \mid \epsilon$ $B \rightarrow Ae \mid \epsilon$
asked Feb 12, 2016 in Compiler Design Akash Kanase 3.3k views
29 votes
3 answers
17
For the $IEEE$ $802.11$ MAC protocol for wireless communication, which of the following statements is/are TRUE? At least three non-overlapping channels are available for transmissions. The RTS-CTS mechanism is used for collision detection. Unicast frames are ACKed. All I, II, and III I and III only II and III only II only
asked Feb 12, 2016 in Computer Networks Akash Kanase 6.5k views
43 votes
12 answers
18
A file system uses an in-memory cache to cache disk blocks. The miss rate of the cache is shown in the figure. The latency to read a block from the cache is $1$ ms and to read a block from the disk is $10$ ms. Assume that the cost of checking whether a ... sizes are in multiples of $10$ MB. The smallest cache size required to ensure an average read latency of less than $6$ ms is _________ MB.
asked Feb 12, 2016 in CO and Architecture Akash Kanase 6.2k views
51 votes
2 answers
19
Consider the following two statements: If all states of an NFA are accepting states then the language accepted by the NFA is $\Sigma_{}^{*}$. There exists a regular language $A$ such that for all languages $B$, $A \cap B$ is regular. Which one of the following is CORRECT? Only I is true Only II is true Both I and II are true Both I and II are false
asked Feb 12, 2016 in Theory of Computation Akash Kanase 9k views
41 votes
5 answers
20
Consider the following database schedule with two transactions $T_{1}$ and $T_{2}$. $S= r_{2}\left(X\right); r_{1}\left(X\right); r_{2} \left(Y\right); w_{1} \left(X\right); r_{1} \left(Y\right); w_{2} \left(X\right); a_{1}; a_{2}$ ... the above schedule is TRUE? $S$ is non-recoverable. $S$ is recoverable, but has a cascading abort. $S$ does not have a cascading abort. $S$ is strict.
asked Feb 12, 2016 in Databases Akash Kanase 7.4k views
24 votes
4 answers
21
A network has a data transmission bandwidth of $20 \times 10^{6}$ bits per second. It uses CSMA/CD in the MAC layer. The maximum signal propagation time from one node to another node is $40$ microseconds. The minimum size of a frame in the network is __________ bytes.
asked Feb 12, 2016 in Computer Networks Akash Kanase 3.5k views
31 votes
7 answers
22
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
asked Feb 12, 2016 in Combinatory Akash Kanase 8.4k views
36 votes
6 answers
23
Let $A_{1}, A_{2}, A_{3}$ and $A_{4}$ be four matrices of dimensions $10 \times 5, 5 \times 20, 20 \times 10$ and $10 \times 5$, respectively. The minimum number of scalar multiplications required to find the product $A_{1}A_{2}A_{3}A_{4}$ using the basic matrix multiplication method is _________.
asked Feb 12, 2016 in Algorithms Akash Kanase 7.1k views
103 votes
14 answers
24
The number of ways in which the numbers $1, 2, 3, 4, 5, 6, 7$ can be inserted in an empty binary search tree, such that the resulting tree has height $6$, is _________. Note: The height of a tree with a single node is $0$.
asked Feb 12, 2016 in DS Akash Kanase 16.9k views
52 votes
5 answers
25
A complete binary min-heap is made by including each integer in $[1, 1023]$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth $0$. The maximum depth at which integer $9$ can appear is _________.
asked Feb 12, 2016 in DS Akash Kanase 9.4k views
41 votes
2 answers
26
The given diagram shows the flowchart for a recursive function $A(n)$. Assume that all statements, except for the recursive calls, have $O(1)$ time complexity. If the worst case time complexity of this function is $O(n^{\alpha})$, then the least possible value (accurate up to two decimal positions) of $\alpha$ is ________. Flow chart for Recursive Function $A(n)$.
asked Feb 12, 2016 in Algorithms Akash Kanase 5.9k views
53 votes
6 answers
27
Consider a $3 \ \text{GHz}$ (gigahertz) processor with a three stage pipeline and stage latencies $\large\tau_1,\tau_2$ and $\large\tau_3$ such that $\large\tau_1 =\dfrac{3 \tau_2}{4}=2\tau_3$. If the longest pipeline stage is split into two pipeline stages of equal latency , the new frequency is __________ $\text{GHz}$, ignoring delays in the pipeline registers.
asked Feb 12, 2016 in CO and Architecture Akash Kanase 8.1k views
34 votes
7 answers
28
The following function computes $X^{Y}$ for positive integers $X$ and $Y$. int exp (int X, int Y) { int res =1, a = X, b = Y; while (b != 0) { if (b % 2 == 0) {a = a * a; b = b/2; } else {res = res * a; b = b - 1; } } return res; } Which one of the following conditions is TRUE before every ... the loop? $X^{Y} = a^{b}$ $(res * a)^{Y} = (res * X)^{b}$ $X^{Y} = res * a^{b}$ $X^{Y} = (res * a)^{b}$
asked Feb 12, 2016 in Programming Akash Kanase 4.3k views
35 votes
5 answers
29
Consider a $128 \times 10^3$ bits/second satellite communication link with one way propagation delay of $150$ milliseconds. Selective retransmission (repeat) protocol is used on this link to send data with a frame size of $1$ kilobyte. Neglect the transmission time of acknowledgement. The minimum number of bits required for the sequence number field to achieve $100 \%$ utilization is ________.
asked Feb 12, 2016 in Computer Networks Akash Kanase 8.7k views
35 votes
9 answers
30
Consider a non-negative counting semaphore $S$. The operation $P(S)$ decrements $S$, and $V(S)$ increments $S$. During an execution, $20$ $P(S)$ operations and $12$ $V(S)$ operations are issued in some order. The largest initial value of $S$ for which at least one $P(S)$ operation will remain blocked is _______
asked Feb 12, 2016 in Operating System Akash Kanase 5.8k views
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