GATE CS 2016 Set 2 question paper: all 65 questions with answers and solutions

General Aptitude

10 questions, 15 marks

General AptitudeMCQ1 markEasy (estimate)
Q.1 (GA Q.1)
The man who is now Municipal Commissioner worked as ____________________.
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.2 (GA Q.2)
Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia. Choose the option which is closest in meaning to the under...
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.3 (GA Q.3)
Find the odd one in the following group of words. mock, deride, praise, jeer
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.4 (GA Q.4)
Pick the odd one from the following options.
Analytical and Logical Reasoning
General AptitudeMCQ1 markEasy (estimate)
Q.5 (GA Q.5)
In a quadratic function, the value of the product of the roots $(α, β)$ is 4. Find the value of $\frac{α ^{n} + β ^{n}}{α ^{- n} + β ^{- n}}$
Quantitative Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.6 (GA Q.6)
Among 150 faculty members in an institute, 55 are connected with each other through Facebook and 85 are connected through WhatsApp. 30 faculty members do not have Facebook or Wh...
Quantitative Aptitude
General AptitudeMCQ2 marksMedium (estimate)
Q.7 (GA Q.7)
Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example,...
Reading Comprehension and Verbal Deduction
General AptitudeMCQ2 marksEasy (estimate)
Q.8 (GA Q.8)
All hill-stations have a lake. Ooty has two lakes. Which of the statement(s) below is/are logically valid and can be inferred from the above sentences? (i) Ooty is not a hill-st...
Analytical and Logical Reasoning
General AptitudeMCQ2 marksEasy (estimate)
Q.9 (GA Q.9)
In a $2 \times 4$ rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid? A 2 by 4 rectangular grid consisting of 2 rows and 4 col...
Quantitative Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.10 (GA Q.10)
Choose the correct expression for $f (x)$ given in the graph. Cartesian coordinate plot of function f(x) against x. The horizontal x-axis ranges from -4 to 3 with integer tick ma...
Quantitative Aptitude

Computer Science and Information Technology

55 questions, 85 marks

Engineering MathematicsNAT1 markMedium (estimate)
Q.11 (CS Q.1)
Consider the following expressions: (i) $false$ (ii) $Q$ (iii) $true$ (iv) $P \lor Q$ (v) $\neg Q \lor P$ The number of expressions given above that are logically...
Propositional and First-Order Logic
Engineering MathematicsNAT1 markMedium (estimate)
Q.12 (CS Q.2)
Let $f (x)$ be a polynomial and $g (x) = f^{'} (x)$ be its derivative. If the degree of $(f (x) + f (- x))$ is 10, then the degree of $(g (x) - g (- x))$ is ________.
Calculus
Engineering MathematicsNAT1 markEasy (estimate)
Q.13 (CS Q.3)
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.
Graph Theory
Engineering MathematicsMCQ1 markEasy (estimate)
Q.14 (CS Q.4)
Consider the systems, each consisting of $m$ linear equations in $n$ variables. I. If $m < n$ , then all such systems have a solution II. If $m > n$ , then none of these systems h...
Linear Algebra
Engineering MathematicsNAT1 markEasy (estimate)
Q.15 (CS Q.5)
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and gi...
Probability and Statistics
Engineering MathematicsNAT1 markEasy (estimate)
Q.16 (CS Q.6)
Suppose that the eigenvalues of matrix $A$ are 1, 2, 4. The determinant of $(A^{- 1})^{T}$ is ________.
Linear Algebra
Digital LogicNAT1 markMedium (estimate)
Q.17 (CS Q.7)
Consider an eight-bit ripple-carry adder for computing the sum of $A$ and $B$ , where $A$ and $B$ are integers represented in 2's complement form. If the decimal value of $A$ is...
Number Representations and Computer Arithmetic
Digital LogicMCQ1 markEasy (estimate)
Q.18 (CS Q.8)
Let $x_{1} \oplus x_{2} \oplus x_{3} \oplus x_{4} = 0$ where $x_{1}, x_{2}, x_{3}, x_{4}$ are Boolean variables, and $\oplus$ is the XOR operator. Which one of the following must always be TRUE?
Boolean Algebra and Logic Minimization
Digital LogicNAT1 markEasy (estimate)
Q.19 (CS Q.9)
Let $X$ be the number of distinct 16-bit integers in 2's complement representation. Let $Y$ be the number of distinct 16-bit integers in sign magnitude representation. Then…
Number Representations and Computer Arithmetic
Computer Organization and ArchitectureNAT1 markEasy (estimate)
Q.20 (CS Q.10)
A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction word has an opcode, two register operands and an immediate operand. The number of...
Machine Instructions and Addressing Modes
AlgorithmsNAT1 markMedium (estimate)
Q.21 (CS Q.11)
Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex $t$ at a distance four from the root. If $t$ is the $n$ -th vertex in thi...
Graph Traversals, Topological Sort and Connectivity
Programming in CNAT1 markEasy (estimate)
Q.22 (CS Q.12)
The value printed by the following program is ________. void f(int* p, int m){ m = m + 5; *p = *p + m; return; } void main(){ int i=5, j=10; f(&i, j); printf("%d", i+j); }
Functions, Recursion, Scope and Storage Classes
AlgorithmsMCQ1 markMedium (estimate)
Q.23 (CS Q.13)
Assume that the algorithms considered here sort the input sequences in ascending order. If the input is already in ascending order, which of the following are TRUE? I. Quicksort...
Searching and Sorting Algorithms
AlgorithmsMCQ1 markEasy (estimate)
Q.24 (CS Q.14)
The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
Dynamic Programming
Data StructuresMCQ1 markMedium (estimate)
Q.25 (CS Q.15)
$N$ items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided to the record to be deleted. For a decrease-key operation, a pointer is provid...
Arrays and Linked Lists
Theory of ComputationNAT1 markEasy (estimate)
Q.26 (CS Q.16)
The number of states in the minimum sized DFA that accepts the language defined by the regular expression $(0 + 1)^{*} (0 + 1) (0 + 1)^{*}$ is ________.
Regular Expressions, Finite Automata and Regular Languages
Theory of ComputationMCQ1 markEasy (estimate)
Q.27 (CS Q.17)
Language $L_{1}$ is defined by the grammar: $S_{1} \to a S_{1} b ∣ ε$ Language $L_{2}$ is defined by the grammar: $S_{2} \to ab S_{2} ∣ ε$ Consider the following...
Regular Expressions, Finite Automata and Regular Languages · Context-Free Grammars, Pushdown Automata and CFLs
Theory of ComputationMCQ1 markMedium (estimate)
Q.28 (CS Q.18)
Consider the following types of languages: $L_{1}$ : Regular, $L_{2}$ : Context-free, $L_{3}$ : Recursive, $L_{4}$ : Recursively enumerable. Which of the following is/are TRUE? I.…
Regular Expressions, Finite Automata and Regular Languages
Compiler DesignMCQ1 markEasy (estimate)
Q.29 (CS Q.19)
Match the following: (P) Lexical analysis (Q) Top down parsing (R) Semantic analysis (S) Runtime environments (i) Leftmost derivation (ii) Type checking (iii) Regular expression...
Lexical Analysis
Operating SystemsMCQ1 markEasy (estimate)
Q.30 (CS Q.20)
In which one of the following page replacement algorithms it is possible for the page fault rate to increase even when the number of allocated frames increases?
Memory Management and Virtual Memory
DatabasesMCQ1 markEasy (estimate)
Q.31 (CS Q.21)
B+ Trees are considered BALANCED because
File Organization, B-Trees and B+ Trees Indexing
DatabasesMCQ1 markEasy (estimate)
Q.32 (CS Q.22)
Suppose a database schedule $S$ involves transactions $T_{1}, \dots, T_{n}$ . Construct the precedence graph of $S$ with vertices representing the transactions and edges representing...
Transactions, Serializability and Concurrency Control
Computer NetworksMCQ1 markEasy (estimate)
Q.33 (CS Q.23)
Anarkali digitally signs a message and sends it to Salim. Verification of the signature by Salim requires
Application Layer: DNS, HTTP, SMTP, FTP
Computer NetworksMCQ1 markEasy (estimate)
Q.34 (CS Q.24)
In an Ethernet local area network, which one of the following statements is TRUE?
Medium Access Control (ALOHA, CSMA/CD) and Ethernet/Switching
Computer NetworksMCQ1 markEasy (estimate)
Q.35 (CS Q.25)
Identify the correct sequence in which the following packets are transmitted on the network by a host when a browser requests a webpage from a remote server, assuming that the h...
Application Layer: DNS, HTTP, SMTP, FTP · Transport Layer: UDP, TCP Flow and Congestion Control, Sockets
Engineering MathematicsMCQ2 marksMedium (estimate)
Q.36 (CS Q.26)
A binary relation $R$ on $N \times N$ is defined as follows: $(a, b) R (c, d)$ if $a \leq c$ or $b \leq d$ . Consider the following propositions: $P$ : $R$ is reflex...
Sets, Relations, Functions, Partial Orders and Lattices
Engineering MathematicsMCQ2 marksMedium (estimate)
Q.37 (CS Q.27)
Which one of the following well-formed formulae in predicate calculus is NOT valid?
Propositional and First-Order Logic
Engineering MathematicsMCQ2 marksMedium (estimate)
Q.38 (CS Q.28)
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...
Graph Theory
Engineering MathematicsNAT2 marksEasy (estimate)
Q.39 (CS Q.29)
The value of the expression $1 3^{99} (mod 17)$ , in the range 0 to 16, is ________.
Combinatorics, Counting, Recurrence Relations and Generating Functions
Computer Organization and ArchitectureNAT2 marksMedium (estimate)
Q.40 (CS Q.30)
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…
ALU, Datapath and Control Unit
Computer Organization and ArchitectureNAT2 marksMedium (estimate)
Q.41 (CS Q.31)
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 des...
Machine Instructions and Addressing Modes
Computer Organization and ArchitectureNAT2 marksMedium (estimate)
Q.42 (CS Q.32)
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.
Memory Hierarchy: Cache, Main Memory and Secondary Storage
Computer Organization and ArchitectureNAT2 marksMedium (estimate)
Q.43 (CS Q.33)
Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies $τ_{1}, τ_{2},$ and $τ_{3}$ such that $τ_{1} = 3 τ_{2} /4 = 2 τ_{3}$ . If the longest...
Instruction Pipelining and Hazards
Data StructuresNAT2 marksMedium (estimate)
Q.44 (CS Q.34)
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...
Binary Heaps and Priority Queues
Programming in CMCQ2 marksMedium (estimate)
Q.45 (CS Q.35)
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;...
Functions, Recursion, Scope and Storage Classes
Data StructuresMCQ2 marksMedium (estimate)
Q.46 (CS Q.36)
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; Th...
Binary Trees, Binary Search Trees and Balanced Trees
Programming in CNAT2 marksEasy (estimate)
Q.47 (CS Q.37)
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}; printf("%d", f(a,5)); }...
Functions, Recursion, Scope and Storage Classes
AlgorithmsNAT2 marksMedium (estimate)
Q.48 (CS Q.38)
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 multipl...
Dynamic Programming
AlgorithmsNAT2 marksHard (estimate)
Q.49 (CS Q.39)
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...
Asymptotic Analysis and Time/Space Complexity
Data StructuresNAT2 marksMedium (estimate)
Q.50 (CS Q.40)
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 hei...
Binary Trees, Binary Search Trees and Balanced Trees
Data StructuresMCQ2 marksMedium (estimate)
Q.51 (CS Q.41)
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 $[u]$ ...
Graph Representations and Disjoint Sets · Asymptotic Analysis and Time/Space Complexity
Theory of ComputationMCQ2 marksMedium (estimate)
Q.52 (CS Q.42)
Consider the following two statements: I. If all states of an NFA are accepting states then the language accepted by the NFA is $Σ^{*}$ . II. There exists a regular language…
Regular Expressions, Finite Automata and Regular Languages
Theory of ComputationMCQ2 marksMedium (estimate)
Q.53 (CS Q.43)
Consider the following languages: $L_{1} = {a^{n} b^{m} c^{n + m} ∣ m, n \geq 1}$ $L_{2} = {a^{n} b^{n} c^{2 n} ∣ n \geq 1}$ Which one of the following is TRUE?
Context-Free Grammars, Pushdown Automata and CFLs
Theory of ComputationMCQ2 marksMedium (estimate)
Q.54 (CS Q.44)
Consider the following languages. $L_{1} = {⟨ M ⟩ ∣ M takes at least 2016 steps on some input}$ …
Decidability, Reducibility and Undecidability · Turing Machines and Chomsky Hierarchy
Compiler DesignMCQ2 marksMedium (estimate)
Q.55 (CS Q.45)
Which one of the following grammars is free from left recursion?
Parsing and Syntax Analysis (LL and LR)
Compiler DesignMCQ2 marksMedium (estimate)
Q.56 (CS Q.46)
A student wrote two context-free grammars $G_{1}$ and $G_{2}$ for generating a single C-like array declaration. The dimension of the array is at least one. For example, int a[1...
Parsing and Syntax Analysis (LL and LR) · Context-Free Grammars, Pushdown Automata and CFLs
Operating SystemsNAT2 marksMedium (estimate)
Q.57 (CS Q.47)
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-tim...
CPU Scheduling
Operating SystemsMCQ2 marksEasy (estimate)
Q.58 (CS Q.48)
Consider the following two-process synchronization solution. Process 0 -------- Entry: loop while (turn == 1); (critical section) Exit: turn = 1; Process 1 --------- Ent...
Process Synchronization and Concurrency
Operating SystemsNAT2 marksMedium (estimate)
Q.59 (CS Q.49)
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 $V (S)$ operation...
Process Synchronization and Concurrency
Operating SystemsNAT2 marksMedium (estimate)
Q.60 (CS Q.50)
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 b...
File Systems, I/O and Disk Scheduling · Memory Hierarchy: Cache, Main Memory and Secondary Storage
DatabasesMCQ2 marksMedium (estimate)
Q.61 (CS Q.51)
Consider the following database schedule with two transactions, $T_{1}$ and $T_{2}$ . $S = r_{2} (X); r_{1} (X); r_{2} (Y); w_{1} (X); r_{1} (Y); w_{2} (X); a_{1}; a_{2}$ where $r_{i} (Z)$ denotes a read o...
Transactions, Serializability and Concurrency Control
DatabasesNAT2 marksEasy (estimate)
Q.62 (CS Q.52)
Consider the following database table named water_schemes: scheme_no | district_name | capacity 1 | Ajmer | 20 1 | Bikaner | 10 2 | Bikaner | 10 3 | Bikaner | 20 1 | Churu | 1...
SQL Queries and Integrity Constraints
Computer NetworksNAT2 marksEasy (estimate)
Q.63 (CS Q.53)
A network has a data transmission bandwidth of $20 \times 1 0^{6}$ bits per second. It uses CSMA/CD in the MAC layer. The maximum signal propagation time from one node to another n...
Medium Access Control (ALOHA, CSMA/CD) and Ethernet/Switching · Data Link Layer: Framing, Error Detection and Sliding Window
Computer NetworksMCQ2 marksMedium (estimate)
Q.64 (CS Q.54)
For the IEEE 802.11 MAC protocol for wireless communication, which of the following statements is/are TRUE? I. At least three non-overlapping channels are available for transmis...
Medium Access Control (ALOHA, CSMA/CD) and Ethernet/Switching · Data Link Layer: Framing, Error Detection and Sliding Window
Computer NetworksNAT2 marksMedium (estimate)
Q.65 (CS Q.55)
Consider a $128 \times 1 0^{3}$ bits/second satellite communication link with one way propagation delay of 150 milliseconds. Selective retransmission (repeat) protocol is used on t...
Data Link Layer: Framing, Error Detection and Sliding Window