GATE 2018 CSE & IT

Consider the minterm list form of a Boolean function 𝐹 given below. $$F\left( {P,Q,R,S} \right) = $$ $$\sum {m\left( {0,2,5,7,9,11} \right)} $$ $$ + \,\,d\left( {3,8,10,12,14} \ri...

Consider an $$IP$$ packet with a length of $$4,500$$ bytes that includes a $$20$$-byte $$IPv$$$$4$$ header and a $$40$$-byte $$TCP$$ header. The packet is forwarded to an $$IPv4$$...

Consider a matrix $$A = u{v^T}$$ where $$u = \left( {\matrix{ 1 \cr 2 \cr } } \right),v = \left( {\matrix{ 1 \cr 1 \cr } } \right).$$ Note that $${v^T}$$ denotes the transpose of $...

The postorder traversal of a binary tree is $$8,9,6,7,4,5,2,3,1.$$ The inorder traversal of the same tree is $$8,6,9,4,7,2,5,1,3.$$ The height of a tree is the length of the longes...

Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is $$M$$ units if the corresponding memory page is a...

The instruction pipeline of a $$RISC$$ processor has the following stages: Instruction Fetch $$(IF),$$ Instruction Decode $$(ID),$$ Operand Fetch $$(OF),$$ Perform Operation $$(PO)...

A $$32$$-bit wide main memory unit with a capacity of $$1$$ $$GB$$ is built using $$256M\,\, \times \,\,4$$-bit $$DRAM$$ chips. The number of rows of memory cells in the $$DRAM$$ c...

In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs $$750$$ to each male senior citizen in the town and Rs $$1000$$ to each...

Consider the unsigned $$8$$-bit fixed point binary number representation below $$${b_7}\,\,{b_6}\,\,{b_5}\,\,{b_4}\,\,{b_3}\,\,.\,\,{b_2}\,\,{b_1}\,\,{b_0}$$$ where the position of...

Consider Guwahati $$(G)$$ and Delhi $$(D)$$ whose temperatures can be classified as high $$(H),$$ medium $$(M)$$ and low $$(L).$$ Let $$P\left( {{H_G}} \right)$$ denote the probabi...

“From where are they bringing their books? ________ bringing _______ books from _____.” The words that best fill the blanks in the above sentence are

Two people, $$P$$ and $$Q,$$ decide to independently roll two identical dice, each with $$6$$ faces, numbered $$1$$ to $$6.$$ The person with the lower number wins. In case of a ti...

Match the following Field Length in bits P. UDP Header’s Port Number I. 48 Q. Ethernet MAC Address II. 8 R. IPv6 Next Header III. 32 S. TCP Header’s Sequence Number IV. 16

What would be the smallest natural number which when divided either by $$20$$ or by $$42$$ or by $$76$$ leaves a remainder of $$7$$ in each case?

Consider a system with $$3$$ processes that share $$4$$ instances of the same resource type. Each process can request a maximum of $$K$$ instances. Resource instances can be reques...

Consider a simple communication system where multiple nodes are connected by a shared broadcast medium (like Ethernet or wireless). The nodes in the system use the following carrie...

In a system, there are three types of resources: $$E, F$$ and $$G.$$ Four processes $${P_0},$$ $${P_1},$$ $${P_2}$$ and $${P_3}$$ execute concurrently. At the outset, the processes...

Let $$G$$ be a graph with $$100!$$ vertices, with each vertex labelled by a distinct permutation of the numbers $$1,2, … , 100.$$ There is an edge between vertices $$u$$ and $$v$$...

Consider the following two tables and four queries in SQL. Book ( isbn , bname), Stock ( isbn , copies) Query 1: SELECT B.isbn, S.copies FROM Book B INNER JOIN Stock S ON B.isbn =...

The area of a square is $$𝑑.$$ What is the area of the circle which has the diagonal of the square as its diameter?

Consider the following C program: #include < stdio.h > int counter = 0; int calc (int a, int b) { int c; counter++; if (b==3) return (a*a*a); else { c = calc(a, b/3); return (c*c*c...

Consider the relations $$r(A, B)$$ and $$s(B, C),$$ where $$s.B$$ is a primary key and $$r.B$$ is a foreign key referencing $$s.B.$$ Consider the query $$Q:$$ $$\,\,\,\,\,\,\,\,\,$...

The following are some events that occur after a device controller issues an interrupt while process $$L$$ is under execution. $$(P)$$ The processor pushes the process status of $$...

What would be the smallest natural number which when divided either by $$20$$ or by $$42$$ or by $$76$$ leaves a remainder of $$7$$ in each case?

Consider the following C code. Assume that unsigned long int type length is 64 bits. unsigned long int fun(unsigned long int n){ unsigned long int i, j = 0, sum = 0; for (i = n; i...

Consider the following statements regarding the slow start phase of the $$TCP$$ congestion control algorithm. Note that $$cwnd$$ stands for the $$TCP$$ congestion window and $$MSS$...

In an Entity-Relationship $$(ER)$$ model, suppose $$R$$ is a many-to-one relationship from entity set $$E1$$ to entity set $$E2.$$ Assume that $$E1$$ and $$E2$$ participate totally...

The size of the physical address space of a processor is $${2^P}$$ bytes. The word length is $${2^W}$$ bytes. The capacity of cache memory is $${2^N}$$ bytes. The size of each cach...

Assume that multiplying a matrix $${G_1}$$ of dimension $$p \times q$$ with another matrix $${G_2}$$ of dimension $$q \times r$$ requires $$pqr$$ scalar multiplications. Computing...

A lexical analyzer uses the following patterns to recognize three tokens $${T_1},{T_2},$$ and $${T_3}$$ over the alphabet $$\left\{ {a,b,c} \right\}.$$ $$\eqalign{ & {T_1}:\,\,\,a?...

Consider a matrix P whose only eigenvectors are the multiples of $$\left[ {\matrix{ 1 \cr 4 \cr } } \right].$$ Consider the following statements. $$\left( {\rm I} \right)$$ $$\,\,\...

Consider the weights and values of items listed below. Note that there is only one unit of each item. Item number Weight (in Kgs) Value (in Rupees) 1 10 60 2 7 28 3 4 20 4 2 24 The...

The number of possible min-heaps containing each value from $$\left\{ {1,2,3,4,5,6,7} \right\}$$ exactly once is _____.

In a party, $$60\% $$ of the invited guests are male and $$400\% $$ are female. If $$80\% $$ of the invited guests attended the party and if all the invited female guests attended,...

Consider the following processor design characteristics. $$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ Register-to-register arithmetic operations only $$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,$...

A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?

A processor has $$16$$ integer registers $$\left( {R0,\,\,R1,\,\,..\,\,,\,\,R15} \right)$$) and $$64$$ floating point registers $$(F0, F1,… , F63).$$ It uses a $$2$$-byte instructi...

Consider a storage disk with $$4$$ platters (numbered as $$0, 1, 2$$ and $$3$$), $$200$$ cylinders (numbered as $$0, 1,$$ … , $$199$$), and $$256$$ sectors per track (numbered as $...

Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

Which one of the following is a closed form expression for the generating function of the sequence $$\left\{ {{a_n}} \right\},$$ where $${a_n} = 2n + 3$$ for all $$n = 0,1,2,....?$...

If $$pqr \ne 0$$ and $${p^{ - x}} = {1 \over q},{q^{ - y}} = {1 \over r},\,{r^{ - z}} = {1 \over p},$$ what is the value of the product $$𝑥𝑦𝑧$$?

Let $$G$$ be a simple undirected graph. Let $${T_D}$$ be a depth first search tree of $$G.$$ Let $${T_B}$$ be a breadth first search tree of $$G.$$ Consider the following statement...

Consider the following C program. #include< stdio.h > struct Ournode{ char x,y,z; }; int main(){ struct Ournode p = {'1', '0', 'a'+2}; struct Ournode *q = &p; printf ("%c, %c", *((...

Let $$G$$ be a finite group on $$84$$ elements. The size of a largest possible proper subgroup of $$G$$ is ________.

Let N be the set of natural numbers. Consider the following sets. $$\,\,\,\,\,\,\,\,$$ $$P:$$ Set of Rational numbers (positive and negative) $$\,\,\,\,\,\,\,\,$$ $$Q:$$ Set of fun...

Consider the following C program: #include< stdio.h > void fun1(char *s1, char *s2){ char *tmp; tmp = s1; s1 = s2; s2 = tmp; } void fun2(char **s1, char **s2){ char *tmp; tmp = *s1...

Consider the first-order logic sentence $$\varphi \equiv \,\,\,\,\,\,\,\exists s\exists t\exists u\forall v\forall w$$ $$\forall x\forall y\psi \left( {s,t,u,v,w,x,y} \right)$$ whe...

The value of $$\int_0^{\pi /4} {x\cos \left( {{x^2}} \right)dx} $$ correct to three decimal places (assuming that $$\pi = 3.14$$ ) is ________.

Which one of the following statements is FALSE?

“A _________ investigation can sometimes yield new facts, but typically organized ones are more successful.” The word that best fills the blank in the above sentence is

What is the missing number in the following sequence? $$$2,\,12,\,60,\,240,\,720,\,1440,\,\_\_\_,\,0$$$

Consider a long-lived $$TCP$$ session with an end-to-end bandwidth of $$1$$ $$Gbps$$ ($$ = {10^9}\,$$ bits-persecond). The session starts with a sequence number of $$1234.$$ The mi...

The set of all recursively enumerable languages is

Consider the following problems. $$L(G)$$ denotes the language generated by a grammar $$G.$$ $$L(M)$$ denotes the language accepted by a machine $$M.$$ $$\,\,\,\,\,\,\,\,{\rm I}.\,...

Consider the following languages: $$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m + p = n + q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$ $$\...

Let $$N$$ be an $$NFA$$ with $$n$$ states. Let $$k$$ be the number of states of a minimal $$DFA$$ which is equivalent to $$N.$$ Which one of the following is necessarily true?