GATE CS 2016 Set 1 question paper: all 65 questions with answers and solutions

General Aptitude

10 questions, 15 marks

General AptitudeMCQ1 markEasy (estimate)
Q.1 (GA Q.1)
Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.2 (GA Q.2)
A rewording of something written or spoken is a ______________.
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.3 (GA Q.3)
Archimedes said, "Give me a lever long enough and a fulcrum on which to place it, and I will move the world." The sentence above is an example of a ___________ statement.
Verbal Ability and Grammar
General AptitudeMCQ1 markMedium (estimate)
Q.4 (GA Q.4)
If 'relftaga' means carefree, 'otaga' means careful and 'fertaga' means careless, which of the following could mean 'aftercare'?
Verbal Ability and Grammar
General AptitudeMCQ1 markMedium (estimate)
Q.5 (GA Q.5)
A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in s...
Spatial Aptitude
General AptitudeMCQ2 marksMedium (estimate)
Q.6 (GA Q.6)
A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 17...
Data Interpretation and Graphs
General AptitudeMCQ2 marksEasy (estimate)
Q.7 (GA Q.7)
Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation's diversity, nothing else is. Which of the foll...
Verbal Ability and Grammar
General AptitudeMCQ2 marksMedium (estimate)
Q.8 (GA Q.8)
Consider the following statements relating to the level of poker play of four players P, Q, R and S. I. P always beats Q II. R always beats S III. S loses to P only sometimes IV...
Analytical and Logical Reasoning
General AptitudeMCQ2 marksEasy (estimate)
Q.9 (GA Q.9)
If $f (x) = 2 x^{7} + 3 x - 5$ , which of the following is a factor of $f (x)$ ?
Quantitative Aptitude
General AptitudeMCQ2 marksMedium (estimate)
Q.10 (GA Q.10)
In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved,...
Quantitative Aptitude

Computer Science and Information Technology

55 questions, 85 marks

Engineering MathematicsNAT1 markMedium (estimate)
Q.11 (CS Q.1)
Let $p, q, r, s$ represent the following propositions. $p : x \in {8, 9, 10, 11, 12}$ $q : x$ is a composite number $r : x$ is a perfect square $s : x$ is a prime number The integ...
Propositional and First-Order Logic
Engineering MathematicsMCQ1 markEasy (estimate)
Q.12 (CS Q.2)
Let $a_{n}$ be the number of $n$ -bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for $a_{n}$ ?
Combinatorics, Counting, Recurrence Relations and Generating Functions
Engineering MathematicsNAT1 markEasy (estimate)
Q.13 (CS Q.3)
The value of $lim_{x \to 4} \frac{s i n ( x - 4 )}{x - 4}$ is _____.
Calculus
Engineering MathematicsNAT1 markEasy (estimate)
Q.14 (CS Q.4)
A probability density function on the interval $[a, 1]$ is given by $1/ x^{2}$ and outside this interval the value of the function is zero. The value of $a$ is _____.
Probability and Statistics
Engineering MathematicsNAT1 markEasy (estimate)
Q.15 (CS Q.5)
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2 + - 1)$ and $3$ . The determinant of $P$ is _____.
Linear Algebra
Digital LogicMCQ1 markEasy (estimate)
Q.16 (CS Q.6)
Consider the Boolean operator $#$ with the following properties: $x #0 = x$ , $x #1 = x ˉ$ , $x # x = 0$ and $x # x ˉ = 1$ . Then $x # y$ is equivalent to
Boolean Algebra and Logic Minimization
Digital LogicNAT1 markEasy (estimate)
Q.17 (CS Q.7)
The 16-bit 2's complement representation of an integer is 1111 1111 1111 0101; its decimal representation is _____.
Number Representations and Computer Arithmetic
Digital LogicNAT1 markMedium (estimate)
Q.18 (CS Q.8)
We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is _____.
Sequential Circuits, Counters and Registers
Computer Organization and ArchitectureNAT1 markEasy (estimate)
Q.19 (CS Q.9)
A processor can support a maximum memory of 4 GB, where the memory is word-addressable (a word consists of two bytes). The size of the address bus of the processor is at least _...
Machine Instructions and Addressing Modes
Data StructuresMCQ1 markEasy (estimate)
Q.20 (CS Q.10)
A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT ( $n$ refers to the num...
Stacks and Queues
AlgorithmsNAT1 markMedium (estimate)
Q.21 (CS Q.11)
Consider the following directed graph: Directed acyclic graph with six vertices labeled a, b, c, d, e, and f. Directed edges are from a to b, a to d, b to c, d to e, c to f, and...
Graph Traversals, Topological Sort and Connectivity
Programming in CMCQ1 markEasy (estimate)
Q.22 (CS Q.12)
Consider the following C program. void f(int, short); void main() { int i = 100; short s = 12; short *p = &s; __________ ; // call to f() } Which one of the following e...
Pointers, Arrays and Strings
AlgorithmsMCQ1 markEasy (estimate)
Q.23 (CS Q.13)
The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:
Searching and Sorting Algorithms
AlgorithmsMCQ1 markMedium (estimate)
Q.24 (CS Q.14)
Let $G$ be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increased by the same value, then which of the following statements...
Minimum Spanning Trees
Programming in CNAT1 markEasy (estimate)
Q.25 (CS Q.15)
Consider the following C program. #include <stdio.h> void mystery(int *ptra, int *ptrb) { int *temp; temp = ptrb; ptrb = ptra; ptra = temp; } int main() { int a = 2016, b =...
Pointers, Arrays and Strings
Theory of ComputationMCQ1 markEasy (estimate)
Q.26 (CS Q.16)
Which of the following languages is generated by the given grammar? $S \to a S ∣ b S ∣ ε$
Context-Free Grammars, Pushdown Automata and CFLs
Theory of ComputationMCQ1 markMedium (estimate)
Q.27 (CS Q.17)
Which of the following decision problems are undecidable? I. Given NFAs $N_{1}$ and $N_{2}$ , is $L (N_{1}) \cap L (N_{2}) = \emptyset$ ? II. Given a CFG $G = (N, Σ, P, S)$ and a strin...
Decidability, Reducibility and Undecidability
Theory of ComputationMCQ1 markEasy (estimate)
Q.28 (CS Q.18)
Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive 0s and two consecutive 1s?
Regular Expressions, Finite Automata and Regular Languages
Compiler DesignNAT1 markMedium (estimate)
Q.29 (CS Q.19)
Consider the following code segment. x = u - t; y = x * v; x = y + w; y = t - z; y = x * y; The minimum number of total variables required to convert the above code...
Intermediate Code Generation, Data Flow Analysis and Code Optimization
Operating SystemsMCQ1 markEasy (estimate)
Q.30 (CS Q.20)
Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths submitted at the same time to a computer system. Which one of the following process scheduling al...
CPU Scheduling
DatabasesMCQ1 markEasy (estimate)
Q.31 (CS Q.21)
Which of the following is NOT a superkey in a relational schema with attributes $V, W, X, Y, Z$ and primary key $V Y$ ?
ER Model and Relational Schema Design
DatabasesMCQ1 markEasy (estimate)
Q.32 (CS Q.22)
Which one of the following is NOT a part of the ACID properties of database transactions?
Transactions, Serializability and Concurrency Control
DatabasesMCQ1 markMedium (estimate)
Q.33 (CS Q.23)
A database of research articles in a journal uses the following schema.…
Functional Dependencies and Normalization
Computer NetworksMCQ1 markEasy (estimate)
Q.34 (CS Q.24)
Which one of the following protocols is NOT used to resolve one form of address to another one?
Application Layer: DNS, HTTP, SMTP, FTP
Computer NetworksMCQ1 markMedium (estimate)
Q.35 (CS Q.25)
Which of the following is/are example(s) of stateful application layer protocols? (i) HTTP (ii) FTP (iii) TCP (iv) POP3
Application Layer: DNS, HTTP, SMTP, FTP
Engineering MathematicsNAT2 marksMedium (estimate)
Q.36 (CS Q.26)
The coefficient of $x^{12}$ in $(x^{3} + x^{4} + x^{5} + x^{6} + \dots)^{3}$ is _____.
Combinatorics, Counting, Recurrence Relations and Generating Functions
Engineering MathematicsNAT2 marksMedium (estimate)
Q.37 (CS Q.27)
Consider the recurrence relation $a_{1} = 8$ , $a_{n} = 6 n^{2} + 2 n + a_{n - 1}$ . Let $a_{99} = K \times 1 0^{4}$ . The value of $K$ is _____.
Combinatorics, Counting, Recurrence Relations and Generating Functions
Engineering MathematicsNAT2 marksHard (estimate)
Q.38 (CS Q.28)
A function $f : N^{+} \to N^{+}$ , defined on the set of positive integers $N^{+}$ , satisfies the following properties…
Sets, Relations, Functions, Partial Orders and Lattices
Engineering MathematicsNAT2 marksEasy (estimate)
Q.39 (CS Q.29)
Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop. Step 3. If the outcomes are either (HEADS,...
Probability and Statistics
Digital LogicMCQ2 marksMedium (estimate)
Q.40 (CS Q.30)
Consider the two cascaded 2-to-1 multiplexers as shown in the figure. Logic circuit diagram of two cascaded 2-to-1 multiplexers. The first multiplexer has select input P, data i...
Combinational Circuits
Computer Organization and ArchitectureNAT2 marksMedium (estimate)
Q.41 (CS Q.31)
The size of the data count register of a DMA controller is 16 bits. The processor needs to transfer a file of 29,154 kilobytes from disk to main memory. The memory is byte addre...
I/O Interface, Interrupts and DMA
Computer Organization and ArchitectureNAT2 marksEasy (estimate)
Q.42 (CS Q.32)
The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The first stage (with delay 800 picoseconds) is replaced with a functionally equivalent design invo...
Instruction Pipelining and Hazards
Digital LogicMCQ2 marksMedium (estimate)
Q.43 (CS Q.33)
Consider a carry lookahead adder for adding two $n$ -bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is
Number Representations and Computer Arithmetic
Programming in CMCQ2 marksEasy (estimate)
Q.44 (CS Q.34)
The following function computes the maximum value contained in an integer array p[] of size $n$ ( $n \geq 1$ ). int max(int *p, int n) { int a = 0, b = n - 1; while (_______...
Pointers, Arrays and Strings
Programming in CMCQ2 marksMedium (estimate)
Q.45 (CS Q.35)
What will be the output of the following C program? #include <stdio.h> void count(int n) { static int d = 1; printf("%d ", n); printf("%d ", d); d++; if (n > 1) count(n - 1...
Functions, Recursion, Scope and Storage Classes
Compiler DesignMCQ2 marksHard (estimate)
Q.46 (CS Q.36)
What will be the output of the following pseudo-code when parameters are passed by reference and dynamic scoping is assumed? a = 3; void n(x) { x = x * a; print(x); } vo...
Runtime Environments and Parameter Passing
Data StructuresMCQ2 marksMedium (estimate)
Q.47 (CS Q.37)
An operator delete(i) for a binary heap data structure is to be designed to delete the item in the $i$ -th node. Assume that the heap is implemented in an array and $i$ refers...
Binary Heaps and Priority Queues
AlgorithmsNAT2 marksMedium (estimate)
Q.48 (CS Q.38)
Consider the weighted undirected graph with 4 vertices, where the weight of edge ${i, j}$ is given by the entry $W_{ij}$ in the matrix $W$ …
Single-Source and All-Pairs Shortest Paths
AlgorithmsNAT2 marksMedium (estimate)
Q.49 (CS Q.39)
Let $G$ be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2, 3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of...
Minimum Spanning Trees
AlgorithmsMCQ2 marksMedium (estimate)
Q.50 (CS Q.40)
$G = (V, E)$ is an undirected simple graph in which each edge has a distinct weight, and $e$ is a particular edge of $G$ . Which of the following statements about the minimum spa...
Minimum Spanning Trees
Data StructuresNAT2 marksMedium (estimate)
Q.51 (CS Q.41)
Let $Q$ denote a queue containing sixteen numbers and $S$ be an empty stack. $Head (Q)$ returns the element at the head of the queue $Q$ without removing it from $Q$ . Simi...
Stacks and Queues
Theory of ComputationMCQ2 marksMedium (estimate)
Q.52 (CS Q.42)
Consider the following context-free grammars: $G_{1} : S \to a S ∣ B, B \to b ∣ b B$ …
Context-Free Grammars, Pushdown Automata and CFLs
Theory of ComputationMCQ2 marksMedium (estimate)
Q.53 (CS Q.43)
Consider the transition diagram of a PDA given below with input alphabet $Σ = {a, b}$ and stack alphabet $Γ = {X, Z}$ . $Z$ is the initial stack symbol. Let $L$ den...
Context-Free Grammars, Pushdown Automata and CFLs
Theory of ComputationMCQ2 marksMedium (estimate)
Q.54 (CS Q.44)
Let $X$ be a recursive language and $Y$ be a recursively enumerable but not recursive language. Let $W$ and $Z$ be two languages such that $Y$ reduces to $W$ , and $Z$ ...
Decidability, Reducibility and Undecidability
Programming in CNAT2 marksMedium (estimate)
Q.55 (CS Q.45)
The attributes of three arithmetic operators in some programming language are given below. Operator Precedence Associativity Arity + High Left Binary - Medium Right Binary * Low...
Data Types, Operators and Control Flow
Compiler DesignMCQ2 marksEasy (estimate)
Q.56 (CS Q.46)
Consider the following Syntax Directed Translation Scheme (SDTS), with non-terminals ${S, A}$ and terminals ${a, b}$ …
Syntax-Directed Translation
Operating SystemsNAT2 marksEasy (estimate)
Q.57 (CS Q.47)
Consider a computer system with 40-bit virtual addressing and page size of sixteen kilobytes. If the computer system has a one-level page table per process and each page table e...
Memory Management and Virtual Memory
Operating SystemsNAT2 marksEasy (estimate)
Q.58 (CS Q.48)
Consider a disk queue with requests for I/O to blocks on cylinders 47, 38, 121, 191, 87, 11, 92, 10. The C-LOOK scheduling algorithm is used. The head is initially at cylinder n...
File Systems, I/O and Disk Scheduling
Operating SystemsNAT2 marksMedium (estimate)
Q.59 (CS Q.49)
Consider a computer system with ten physical page frames. The system is provided with an access sequence $(a_{1}, a_{2}, \dots, a_{20}, a_{1}, a_{2}, \dots, a_{20})$ , where each $a_{i}$ i...
Memory Management and Virtual Memory
Operating SystemsMCQ2 marksHard (estimate)
Q.60 (CS Q.50)
Consider the following proposed solution for the critical section problem. There are $n$ processes: $P_{0} \dots P_{n - 1}$ . In the code, function pmax returns an integer not smal...
Process Synchronization and Concurrency
DatabasesMCQ2 marksEasy (estimate)
Q.61 (CS Q.51)
Consider the following two phase locking protocol. Suppose a transaction $T$ accesses (for read or write operations), a certain set of objects ${O_{1}, \dots, O_{k}}$ . This is don...
Transactions, Serializability and Concurrency Control
Computer NetworksMCQ2 marksEasy (estimate)
Q.62 (CS Q.52)
Consider that $B$ wants to send a message $m$ that is digitally signed to $A$ . Let the pair of private and public keys for $A$ and $B$ be denoted by $K_{x}^{-}$ and $K_{x}^{+}$ for…
Application Layer: DNS, HTTP, SMTP, FTP
Computer NetworksNAT2 marksEasy (estimate)
Q.63 (CS Q.53)
An IP datagram of size 1000 bytes arrives at a router. The router has to forward this packet on a link whose MTU (maximum transmission unit) is 100 bytes. Assume that the size o...
IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT
Computer NetworksNAT2 marksMedium (estimate)
Q.64 (CS Q.54)
For a host machine that uses the token bucket algorithm for congestion control, the token bucket has a capacity of 1 megabyte and the maximum output rate is 20 megabytes per sec...
Transport Layer: UDP, TCP Flow and Congestion Control, Sockets
Computer NetworksNAT2 marksMedium (estimate)
Q.65 (CS Q.55)
A sender uses the Stop-and-Wait ARQ protocol for reliable transmission of frames. Frames are of size 1000 bytes and the transmission rate at the sender is 80 Kbps (1Kbps = 1000...
Data Link Layer: Framing, Error Detection and Sliding Window