GATE 2016 CSE & IT

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 equivalen...

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.

Consider the Boolean operator $$ \ne $$ with the following properties: $$x \ne 0 = x,\,\,x \ne 1 = \overline x ,\,\,x \ne x = 0$$ and $$x \ne \overline x = 1.$$ Then $$x \ne y$$ is...

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 x = A, B,...

Consider the recurrence relation $${a_1} = 8,\,{a_n} = 6{n^2} + 2n + {a_{n - 1}}.$$ Let $${a_{99}} = K \times {10^4}.$$ The value of $$K$$ is ____________.

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

Consider the following statements relating to the level of poker play of four players $$P, Q, R$$ and $$S.$$ $$\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,$$ P always beats Q $$\,\,\...

Consider the following Syntax Directed Translation Scheme $$(SDTS),$$ with non-terminals $$\left\{ {S,A} \right\}$$ and terminals $$\left\{ {A,B} \right\}.$$ $$S \to aA$$ $$\,\,\,\...

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 hal...

Consider the following two phase locking protocol. Suppose a transaction $$T$$ accesses (for read or write operations), a certain set of objects $$\left\{ {{O_1},...,{O_k}} \right\...

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 of t...

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=0, c=4, d...

Two eigenvalues of a $$3 \times 3$$ real matrix $$P$$ are $$\left( {2 + \sqrt { - 1} } \right)$$ and $$3.$$ The determinant of $$P$$ is _______.

A function $$f:\,\,{N^ + } \to {N^ + },$$ defined on the set of positive integers $${N^ + },$$ satisfies the following properties: $$$\eqalign{ & f\left( n \right) = f\left( {n/2}...

Consider a computer system with ten physical page frames. The system is provided with an access sequence $$\left( {{a_1},{a_2},....,{a_{20}},{a_1},{a_2},...,{a_{20}}} \right),$$ wh...

Consider a disk queue with requests for $${\rm I}/O$$ to blocks on cylinders $$47, 38, 121, 191,$$ $$87, 11, 92, 10.$$ The $$C$$-$$LOOK$$ scheduling algorithm is used. The head is...

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 segment to stat...

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...

Which one of the following protocols is NOT used to resolve one form of address to another one?

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...

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 $${a_n}$$?

If $$f\left( x \right) = 2{x^7} + 3x - 5,$$ which of the following is a factor of $$f(x)$$?

Let $$p,q,r,s$$ represent the following propositions. $$p:\,\,\,x \in \left\{ {8,9,10,11,12} \right\}$$ $$q:\,\,\,x$$ is a composite number $$r:\,\,\,x$$ is a perfect square $$s:\,...

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 numb...

Consider the following experiment. Step1: Flip a fair coin twice. Step2: If the outcomes are (TAILS, HEADS) then output $$Y$$ and stop. Step3: If the outcomes are either (HEADS, HE...

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...

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 t...

$$\mathop {\lim }\limits_{x \to 4} {{\sin \left( {x - 4} \right)} \over {x - 4}} = \_\_\_\_\_\_\_.$$

Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given by the entry $${W_{ij}}$$ in the matrix $$W.$$ $$$W = \left...

$$G = (V,E)$$ 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 spanning...

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 bit...

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 expressions, w...

The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:

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 scheduli...

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 __...

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 Execut...

Which of the following is/are example(s) of stateful application layer protocols? (i) HTTP (ii) FTP (iii) TCP (iv) POP3

A database of research articles in a journal uses the following schema. (VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE) The primary key is (VOLUME, NUMBER, STARTPAGE, ENDP...

A rewording of something written or spoken is a ______________.

The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal representation is ____________.

Which one of the following is NOT a part of the $$ACID$$ properties of database transactions?

If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’ ?

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 le...

Which of the following is NOT a superkey in a relational schema with attributes $$V, W, X, Y, Z$$ and primary key $$V Y?$$

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 second...

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.

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 followi...

The coefficient of $${x^{12}}$$ in $${\left( {{x^3} + {x^4} + {x^5} + {x^6} + ...} \right)^3}\,\,\,\,\,\,$$ is _____________.

A probability density function on the interval $$\left[ {a,1} \right]$$ is given by $$1/{x^2}$$ and outside this interval the value of the function is zero. The value of $$a$$ is _...

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 b...

The attributes of three arithmetic operators in some programming language are given below. Operator Precedence Associativity Arity + High Left Binary _ Medium Right Binary * Low Le...

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 $$\overline Y $$ reduces to $$W,$...

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive $$0s$$ and two consecutive $$1s?$$

Consider the following context-free grammars: $$\eqalign{ & {G_1}:\,\,\,\,\,S \to aS|B,\,\,B \to b|bB \cr & {G_2}:\,\,\,\,\,S \to aA|bB,\,\,A \to aA|B|\varepsilon ,\,\,B \to bB|\va...

Which of the following decision problems are undecidable? $$\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ Given $$NFAs$$ $${N_1}$$ and $${N_2},$$ is $$L\left( {{N_1}} \right)...

Which of the following languages is generated by the given grammar? $$$S \to aS|bS|\varepsilon $$$

Suppose a database schedule $$S$$ involves transactions $${T_1},\,...,\,{T_n}.$$ Construct the precedence graph of $$S$$ with vertices representing the transactions and edges repre...

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 $$12$$...

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 $$...

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...

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 sc...

Anarkali digitally signs a message and sends it to Salim. Verification of the signature by Salim requires

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,...

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)$...

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 representati...

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 operati...

Consider a 128 × 10 3 bits/second satellite communication link with one way propagation delay of 150 milliseconds. Selective retransmission (repeat) protocol is used on this link t...

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...

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...

Consider the following expressions: $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(i)$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ false $$\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(ii)$$ $$\,\,\,\,\,\,\,\,\,\,\,\,...

Consider a $$3$$ $$GHz$$ (gigahertz) processor with a three-stage pipeline and stage latencies $${\tau _1},{\tau _2},$$ and $${\tau _3}$$ such that $${\tau _1} = 3{\tau _2}/4 = 2{\...

Pick the odd one from the following options.

The minimum number of colours that is sufficient to vertex-colour any planar graph is _____________ .

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 de...

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.

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...

Match the following: GROUP - 1 GROUP - 2 (P) Lexical analysis (i) Leftmost derivation (Q) Top down parsing (ii) Type checking (R) Semantic analysis (iii) Regular expressions (S) Ru...

A binary relation $$R$$ on $$N \times N$$ is defined as follows: $$(a,b)R(c,d)$$ if $$a \le c$$ or $$b \le d.$$ Consider the following propositions: $$P:$$ $$R$$ is reflexive $$Q:$...

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 transmissio...

Consider the following database table named $$water$$_$$schemes :$$ water_schemes scheme_no district_name capacity 1 Ajmer 20 1 Bikaner 10 2 Bikaner 10 3 Bikaner 20 1 Churu 10 2 Ch...

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 th...

Which one of the following grammars is free from $$left$$ $$recursion$$?

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 _____________. $$N...

The Floyd-Warshall algorithm for all-pair shortest paths computation is based on

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?

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...

Let $$f(x)$$ be a polynomial and $$g\left( x \right) = f'\left( x \right)$$ be its derivative. If the degree of $$\left( {f\left( x \right) + f\left( { - x} \right)} \right)$$ is $...

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 ? $$\,\,\,\,\,\,...

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...

Suppose that the eigen values of matrix $$A$$ are $$1, 2, 4.$$ The determinant of $${\left( {{A^{ - 1}}} \right)^T}$$ is _______.

In an Ethernet local area network, which one of the following statements is TRUE?

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 underlin...

Find the odd one in the following group of words mock, deride, praise, jeer

$$N$$ 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 pointe...

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 h...

B + Trees are considered BALANCED because

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, $$${\mathop{\rm i...

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, is...

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 host...

In a quadratic function, the value of the product of the roots $$\left( {\alpha ,\beta } \right)$$ is $$4.$$ Find the value of $$${{{\alpha ^n} + {\beta ^n}} \over {{\alpha ^{ - n}...

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 o...

A network has a data transmission bandwidth of 20 × 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...

Consider the following $$New-order$$ strategy for traversing a binary tree: $$\,\,\,\,\,\,\, \bullet \,\,\,\,\,$$ Visit the root; $$\,\,\,\,\,\,\, \bullet \,\,\,\,\,$$ Visit the ri...

Consider the system, each consisting of m linear equations in $$n$$ variables. $$I.$$ $$\,\,\,$$ If $$m < n,$$ then all such system have a solution $$II.$$ $$\,\,\,$$ If $$m > n,$$...

Which one of the following well-formed formulae in predicate calculus is NOT valid?

The value of the expression $${13^{99}}$$ ($$mod$$ $$17$$), in the range $$0$$ to $$16,$$ is ______________ .

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 f...

The man who is now Municipal Commissioner worked as ____________________.

Consider the following two statements : $$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ If all states of an $$NFA$$ are accepting states then the language accepted by the $$\,\,\,\,\,\,\,\,\,...

The number of states in the minimum sized $$DFA$$ that accepts the language defined by the regular expression $$${\left( {0 + 1} \right)^ * }\left( {0 + 1} \right){\left( {0 + 1} \...

Consider the following languages : $$$\eqalign{ & {L_1} = \left\{ {{a^n}{b^m}{c^{n + m}}:m,n \ge 1} \right\} \cr & {L_2} = \left\{ {{a^n}{b^n}{c^{2n}}:n \ge 1} \right\} \cr} $$$ Wh...

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...

Consider the following languages. $$\,\,\,\,\,\,\,\,\,\,\,\,$$ $${L_1} = \left\{ {\left\langle M \right\rangle |M} \right.$$ takes at least $$2016$$ steps on some input $$\left. \,...

Language $${L_1}$$ is defined by the grammar: $$S{}_1 \to a{S_1}b|\varepsilon $$ Language $${L_2}$$ is defined by the grammar: $$S{}_2 \to ab{S_2}|\varepsilon $$ Consider the follo...