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3
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1
GATE2020CS40
Let $G = (V,E)$ be a directed, weighed graph with weight function $w: E \rightarrow \mathbb{R}$. For some function $f: V \rightarrow \mathbb{R}$, for each edge$(u,v)\in E$, define ${w}'(u,v)$ as $w(u,v)+f(u)f(v)$. Which one of the options completes ... from $s$ to $u$ in the graph obtained by adding a new vertex $s$ to $G$ and edges of zero weight from $s$ to every verex of $G$
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2
GATE2020CS38
An organization requires a range of IP address to assign one to each of its $1500$ computers. The organization has approached an Internet Service Provider (ISP) for this task. The ISP uses CIDR and serves the requests from the available IP address space $202.61.0.0/17$. The ISP wants ... $202.61.64.0/21$ $202.61.144.0/21$ I and II only II and III only III and IV only I and IV only
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GATE2020CS37
Consider a schedule of transactions $T_1$ and $T_2$ ...
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GATE2020CS36
Consider a relational table $R$ that is in $3NF$, but not in BCNF. Which one of the following statements is TRUE? $R$ has a nontrivial functional dependency $X \rightarrow A$, where $X$ is not a superkey and $A$ is a prime attribute. $R$ has a nontrivial ... is a nonprime attribute and $X$ is a proper subset of some key A cell in $R$ holds a set instead of an atomic value.
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gate2020cs
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GATE2020CS35
Consider the following five disk five disk access requests of the form (request id, cylinder number) that are present in the disk scheduler queue at a given time. $(P, 155), (Q,85), (R,110),(S, 30), (T,115)$ Assume the head is positioned at cylinder $100$. ... $S$,but before $T$. The head reverses its direction of movement between servicing of $Q$ and $P$. $R$ is serviced before $P$.
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gate2020cs
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6
GATE2020CS34
Each of a set of $n$ processes executes the following code using two semaphores $a$ and $b$ initialized to $1$ and $0$, respectively. Assume that $\text{count}$ is a shared variable initialized to $0$ ... that all processes execute CODE SECTION P mutually exclusively. It ensures that at most $n1$ processes are in CODE SECTION P at any time.
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gate2020cs
+3
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3
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7
GATE2020CS33
Consider the productions $A \rightarrow PQ$ and $A \rightarrow XY$. Each of the five nonterminals $A, P, Q, X$, and $Y$ has two attributes: $s$ is a synthesized attribute, and $i$ is an inherited attribute. Consider the following rules. Rule $1$ ... . Only Rule $1$ is $L$attributed. Only Rule $2$ is $L$attributed. Neither Rule $1$ nor Rule $2$ is $L$attributed.
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gate2020cs
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4
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8
GATE2020CS32
Consider the following languages. $\begin{array}{ll} L_1= \{ wxyx \mid w,x,y \in (0+1)^{+} \} \\ L_2= \{xy \mid x,y \in (a+b)^{*}, \mid x \mid=\mid y \mid, x \neq y \} \end{array}$ Which one of the following is TRUE? $L_1$ is ... $L_2$ is contextfree. Neither $L_1$ nor $L_2$ is context free. $L_1$ context free but $L_2$ is not contextfree.
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gate2020cs
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9
GATE2020CS31
Let $G = (V, G)$ be a weighted undirected graph and let $T$ be a Minimum Spanning Tree (MST) of $G$ maintained using adjacency lists. Suppose a new weighed edge $(u, v) \in V \times V$ is added to $G$. The worst case time complexity of determining if $T$ is still an MST of the ... $\Theta (\mid E \mid \mid V \mid) \\$ $\Theta(E \mid \log \mid V \mid) \\$ $\Theta( \mid V \mid)$
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10
GATE2020CS30
A computer system with a word length of $32$ bits has a $16$ MB byte addressable main memory and a $64$ KB, $4$way set associative cache memory with a block size of $256$ ... cache set. $A3$ and $A4$ are mapped to the same cache set. $A1$ and $A3$ are mapped to the same cache set.
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gate2020cs
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11
GATE2020CS29
Consider three registers $R1$, $R2$, and $R3$ that store numbers in $IEEE754$ single precision floating point format. Assume that $R1$ and $R2$ contain the values (in hexadecimal notation) $0x42200000$ and $0xC1200000$, respectively. If $R3=\frac{R1}{R2}$, what is the value stored in $R3$? $0x40800000$ $0xC0800000$ $0x83400000$ $0xC8500000$
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gate2020cs
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12
GATE2020CS28
Consider the Boolean function $z(a,b,c)$. Which one of the following minterm lists represents the circuit given above? $z=\sum (0,1,3,7)$ $z=\sum (1,4,5,6,7)$ $z=\sum (2,4,5,6,7)$ $z=\sum (2,3,5)$
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gate2020cs
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13
GATE2020CS27
Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider the following statements. $\text{rank}(AB) = \text{rank }(A) \text{rank }(B)$ ... Which of the above statements are TRUE? I and II only I and IV only II and III only III and IV only
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gate2020cs
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4
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14
GATE2020CS26
Which of the following languages are undecidable? Note that $\left \langle M \right \rangle$ indicates encoding of the Turing machine M. $L_1 = \{\left \langle M \right \rangle \mid L(M) = \varnothing \}$ ... $L_1$, $L_3$, and $L_4$ only $L_1$ and $L_3$ only $L_2$ and $L_3$ only $L_2$, $L_3$, and $L_4$ only
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901
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897
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gate2020cs
+2
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3
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15
GATE2020CS25
Assume that you have made a request for a web page through your web browser to a web server. Initially the browser cache is empty. Further, the browser is configured to send HTTP requests in nonpersistent mode. The web page contains text and five very small images.The minimum number of TCP connections required to display the web page completely in your browser is__________.
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896
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gate2020cs
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+2
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3
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16
GATE2020CS24
Consider the following grammar. $S \rightarrow aSB \mid d$ $B \rightarrow b$ The number of reduction steps taken by a bottomup parser while accepting the string $aaadbbb$ is___________.
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901
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722
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gate2020cs
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+2
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2
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17
GATE2020CS23
Consider a double hashing scheme in which the primary hash function is $h_1(k)= k \text{ mod } 23$, and the secondary hash function is $h_2(k)=1+(k \text{ mod } 19)$. Assume that the table size is $23$. Then the address returned by probe $1$ in the probe sequence (assume that the probe sequence begins at probe $0$) for key value $k=90$ is_____________.
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1k
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gate2020cs
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+1
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2
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18
GATE2020CS22
Consider the following C program. #include <stdio.h> int main () { int a[4] [5] = {{1, 2, 3, 4, 5}, {6, 7,8, 9, 10}, {11, 12, 13, 14, 15}, {16, 17,18, 19, 20}}; printf(“%d\n”, *(*(a+**a+2)+3)); return(0); } The output of the program is _______.
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801
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gate2020cs
numericalanswers
+2
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2
answers
19
GATE2020CS21
A direct mapped cache memory of $1$ MB has a block size of $256$ bytes. The cache has an access time of $3$ ns and a hit rate of $94 \%$. During a cache miss, it takes $2$0 ns to bring the first word of a block from the main memory, while each subsequent word takes $5$ ns. The word size is $64$ bits. The average memory access time in ns (round off to $1$ decimal place) is______.
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1.9k
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gate2020cs
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+1
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4
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20
GATE2020CS20
If there are $m$ input lines $n$ output lines for a decoder that is used to uniquely address a byte addressable $1$ KB RAM, then the minimum value of $m+n$ is ________ .
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1k
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gate2020cs
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3
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21
GATE2020CS19
A multiplexer is placed between a group of $32$ registers and an accumulator to regulate data movement such that at any given point in time the content of only one register will move to the accumulator. The number of select lines needed for the multiplexer is ______.
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767
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gate2020cs
numericalanswers
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5
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22
GATE2020CS18
Let $G$ be a group of $35$ elements. Then the largest possible size of a subgroup of $G$ other than $G$ itself is _______.
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865
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gate2020cs
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+2
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4
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23
GATE2020CS17
Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen relation is reflexive (round off to $3$ decimal places) is ______.
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901
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934
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gate2020cs
numericalanswers
+9
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7
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24
GATE2020CS16
What is the worst case time complexity of inserting $n$ elements into an empty linked list, if the linked list needs to be maintained in sorted order? $\Theta(n)$ $\Theta(n \log n)$ $\Theta ( n)^{2}$ $\Theta(1)$
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901
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3.2k
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gate2020cs
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3
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25
GATE2020CS15
Consider the following statements about the functionality of an IP based router. A router does not modify the IP packets during forwarding. It is not necessary for a router to implement any routing protocol. A router should reassemble IP fragments if the MTU of the outgoing ... incoming IP packet. Which of the above statements is/are TRUE? I and II only I only II and III only II only
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901
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763
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gate2020cs
+2
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4
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26
GATE2020CS14
Which one of the following is used to represent the supporting manyone relationships of a weak entity set in an entityrelationship diagram? Diamonds with double/bold border Rectangles with double/bold border Ovals with double/bold border Ovals that contain underlined identifiers
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901
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754
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gate2020cs
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4
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27
GATE2020CS13
Consider a relational database containing the following schemas. $\begin{array}{c} \text{Catalogue} \end{array} $ ... FROM Catalogue WHERE pno = P4' GROUP BY pno) ; The number of rows returned by the above SQL query is $4$ $5$ $0$ $2$
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901
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770
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gate2020cs
+3
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5
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28
GATE2020CS12
Consider the following statements about process state transitions for a system using preemptive scheduling. A running process can move to ready state. A ready process can move to running state. A blocked process can move to running state. A blocked process can move to ready state. Which of ... are TRUE? I, II, and III only II and III only I, II, and IV only I, II, III and IV only
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901
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756
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gate2020cs
+2
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3
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29
GATE2020CS11
Consider allocation of memory to a new process. Assume that none of the existing holes in the memory will exactly fit the process's memory requirement. Hence, a new hole of smaller size will be created if allocation is made in any of the existing holes. Which ... larger than the hole created by first fit. The hole created by next fit is never larger than the hole created by best fit.
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gate2020cs
+6
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3
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30
GATE2020CS9
Consider the following statements. Symbol table is accessed only during lexical analysis and syntax analysis. Compilers for programming languages that support recursion necessarily need heap storage for memory allocation in the runtime environment. Errors violating the condition any variable must ... the above statements is/are TRUE? I only I and III only Ⅱ only None of Ⅰ, Ⅱ and Ⅲ
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1k
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gate2020cs
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31
GATE2020CS8
Consider the following statements. If $L_1 \cup L_2$ is regular, then both $L_1$ and $L_2$ must be regular. The class of regular languages is closed under infinite union. Which of the above statements is/are TRUE? Ⅰ only Ⅱ only Both Ⅰ and Ⅱ Neither Ⅰ nor Ⅱ
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gate2020cs
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32
GATE2020CS6
What is the worst case time complexity of inserting $n^{2}$ elements into an AVLtree with $n$ elements initially? $\Theta (n^{4})$ $\Theta (n^{2})$ $\Theta (n^{2}\log n)$ $\Theta (n^{3})$
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gate2020cs
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33
GATE2020CS5
The preorder traversal of a binary search tree is $15, 10, 12, 11, 20, 18, 16, 19$. Which one of the following is the postorder traversal of the tree? $10,11,12,15,16,18,19,20$ $11,12,10,16,19,18,20,15$ $20,19,18,16,15,12,11,10$ $19,16,18,20,11,12,10,15$
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gate2020cs
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3
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34
GATE2020CS4
Consider the following data path diagram. Consider an instruction: $R0 \leftarrow R1 +R2$. The following steps are used to execute it over the given data path. Assume that PC is incremented appropriately. The subscripts $r$ and $w$ ... execution of the above steps? $2,1,4,5,3$ $1,2,4,3,5$ $3,5,2,1,4$ $3,5,1,2,4$
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gate2020cs
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35
GATE2020CS3
Consider the following statements. Daisy chaining is used to assign priorities in attending interrupts. When a device raises a vectored interrupt, the CPU does polling to identify the source of interrupt. In polling,the CPU periodically checks the status bits to know if any device needs ... time. Which of the above statements is/are TRUE? Ⅰ and Ⅱ only Ⅰ and Ⅳ only Ⅰ and Ⅲ only Ⅲ only
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gate2020cs
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4
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36
GATE2020CS1
Consider the functions $e^{x}$ $x^{2}\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
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gate2020cs
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37
GATE2020CS2
For parameters $a$ and $b$, both of which are $\omega(1)$, $T(n) = T(n^{1/a})+1$, and $T(b)=1$. Then $T(n)$ is $\Theta (\log_a \log _b n)$ $\Theta (\log_{ab} n$) $\Theta (\log_{b} \log_{a} \: n$) $\Theta (\log_{2} \log_{2} n$)
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0
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38
GATE2020CS49
Consider a graph $G = (V,E)$, where $V = \{v_1,v_2, \dots ,v_{100}\}$, $E = \{(v_i,v_j) \mid 1\leq i < j \leq 100\}$, and weight of the edge $(v_i,v_j)$ is $\mid i – j \mid$. The weight of minimum spanning tree of $G$ is _________
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39
TIFR2020B5
Let $u$ be a point on the unit circle in the first quadrant (i.e., both coordinates of $u$ are positive). Let $\theta$ be the angle subtended by $u$ and the $x$ axis at the origin. Let $l_{u}$ denote the infinite line passing through the origin and $u.$ Consider the following ... $x$axis at the origin? $50^{\circ}$ $85^{\circ}$ $90^{\circ}$ $145^{\circ}$ $165^{\circ}$
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40
GATE2020CS52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edgecolour $G$ is _______
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