GATE 2016 Computer Science Set 2 Questions

# Recent questions tagged gate2016-2

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.
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.
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.
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? $\Theta\left(n^{2}\right)$ $\Theta\left(n+m\right)$ $\Theta\left(m^{2}\right)$ $\Theta\left(n^{4}\right)$
5
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ $(\exists x p(x) \vee \exists x q (x)) \implies \exists x (p(x) \vee q (x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
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.
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
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.
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 ________.
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 _________.
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.
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
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: ... $1 \ 7 \ 6 * + \ 2 \ 5 \ 4 \ 3 \ * \ - \wedge -$
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
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.
16
Which one of the following grammars is free from left recursion? $S \rightarrow AB$ $A \rightarrow Aa \mid b$ $B \rightarrow c$ $S \rightarrow Ab \mid Bb \mid c$ $A \rightarrow Bd \mid \epsilon$ $B \rightarrow e$ $S \rightarrow Aa \mid B$ $A \rightarrow Bb \mid Sc \mid \epsilon$ $B \rightarrow d$ $S \rightarrow Aa \mid Bb \mid c$ $A \rightarrow Bd \mid \epsilon$ $B \rightarrow Ae \mid \epsilon$
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
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.
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
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.
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.
22
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
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 _________.
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 $0$.
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 _________.
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 $A(n)$.
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.
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? $X^{Y} = a^{b}$ $(res * a)^{Y} = (res * X)^{b}$ $X^{Y} = res * a^{b}$ $X^{Y} = (res * a)^{b}$
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 ________.
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 _______