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Consider the following functional dependencies in a database Date_of_Birth gt Age Age gt Eligibility Name gt Roll_number Roll_number gt Name Course_number gt Course_name Course_number gt Instructor Roll_number Course_number gt Grade The relation Roll_number Name Date_of_birth Age is in second normal form but not in third normal form in third normal form but not in BCNF in BCNF in none of the above | Database Normalization | 37 |
A database of research articles in a journal uses the following schema ext VOLUME NUMBER STARTPAGE ENDPAGE TITLE YEAR PRICE The primary key is ext VOLUME NUMBER STARTPAGE ENDPAGE and the following functional dependencies exist in the schema begin align amp ext VOLUME NUMBER STARTPAGE ENDPAGE amp rightarrow ext TITLE amp ext VOLUME NUMBER amp rightarrow ext YEAR amp ext VOLUME NUMBER STARTPAGE ENDPAGE amp rightarrow ext PRICE end align The database is redesigned to use the following schemas ext VOLUME NUMBER STARTPAGE ENDPAGE TITLE PRICE ext VOLUME NUMBER YEAR Which is the weakest normal form that the new database satisfies but the old one does not 1NF 2NF 3NF ext BCNF | Database Normalization | 37 |
Which of the following is NOT a superkey in a relational schema with attributes V W X Y Z and primary key V Y VXYZ VWXZ VWXY VWXYZ | Database Normalization | 37 |
Let R A B C D E F be a relation scheme with the following dependencies C rightarrow F E rightarrow A EC rightarrow D A rightarrow B Which one of the following is a key for R CD EC AE AC | Database Normalization | 37 |
For a database relation R a b c d where the domains a b c d include only atomic values only the following functional dependencies and those that can be inferred from them hold a rightarrow c b rightarrow d This relation is in first normal form but not in second normal form in second normal form but not in first normal form in third normal form none of the above | Database Normalization | 37 |
Consider the following database relations containing the attributes Book_id Subject_Category_of_book Name_of_Author Nationality_of_Author With Book_id as the primary key What is the highest normal form satisfied by this relation Suppose the attributes Book_title and Author_address are added to the relation and the primary key is changed to Name_of_Author Book_title what will be the highest normal form satisfied by the relation | Database Normalization | 37 |
Consider a schema R A B C D and functional dependencies A rightarrow B and C rightarrow D Then the decomposition of R into R_1 A B and R_2 C D is dependency preserving and lossless join lossless join but not dependency preserving dependency preserving but not lossless join not dependency preserving and not lossless join | Database Normalization | 37 |
Let L be a language over Sigma i e L subseteq Sigma Suppose L satisfies the two conditions given below L is in NP and For every n there is exactly one string of length n that belongs to L Let L c be the complement of L over Sigma Show that L c is also in NP | Decidability | 38 |
Consider two languages L_1 and L_2 each on the alphabet Sigma Let f Sigma o Sigma be a polynomial time computable bijection such that forall x x in L_1 iff f x in L_2 Further let f 1 be also polynomial time computable Which of the following CANNOT be true L_1 in P and L_2 is finite L_1 in NP and L_2 in P L_1 is undecidable and L_2 is decidable L_1 is recursively enumerable and L_2 is recursive | Decidability | 38 |
Consider the following problem X Given a Turing machine M over the input alphabet Sigma any state q of M and a word w in Sigma does the computation of M on w visit the state of q Which of the following statements about X is correct X is decidable X is undecidable but partially decidable X is undecidable and not even partially decidable X is not a decision problem | Decidability | 38 |
Consider the following decision problems P1 Does a given finite state machine accept a given string P2 Does a given context free grammar generate an infinite number of strings Which of the following statements is true Both P1 and P2 are decidable Neither P1 nor P2 is decidable Only P1 is decidable Only P2 is decidable | Decidability | 38 |
Choose the correct alternatives More than one may be correct It is undecidable whether An arbitrary Turing machine halts after 100 steps A Turing machine prints a specific letter A Turing machine computes the products of two numbers None of the above | Decidability | 38 |
Answer the following questions Which of the following problems are undecidable Membership problem in context free languages Whether a given context free language is regular Whether a finite state automation halts on all inputs Membership problem for type 0 languages | Decidability | 38 |
Which one of the following is not decidable Given a Turing machine M a string s and an integer k M accepts s within k steps Equivalence of two given Turing machines Language accepted by a given finite state machine is not empty Language generated by a context free grammar is non empty | Decidability | 38 |
Consider three decision problems P_1 P_2 and P_3 It is known that P_1 is decidable and P_2 is undecidable Which one of the following is TRUE P_3 is decidable if P_1 is reducible to P_3 P_3 is undecidable if P_3 is reducible to P_2 P_3 is undecidable if P_2 is reducible to P_3 P_3 is decidable if P_3 is reducible to P_2 s complement | Decidability | 38 |
How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 | Decoder | 39 |
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order Which of the following sequences can not be the degree sequence of any graph 7 6 5 4 4 3 2 1 6 6 6 6 3 3 2 2 7 6 6 4 4 3 2 2 8 7 7 6 4 2 1 1 I and II III and IV IV only II and IV | Degree Of Graph | 40 |
The 2 n vertices of a graph G corresponds to all subsets of a set of size n for n geq 6 Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements The number of vertices of degree zero in G is 1 n n 1 2 n | Degree Of Graph | 40 |
The 2 n vertices of a graph G corresponds to all subsets of a set of size n for n geq 6 Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements The maximum degree of a vertex in G is binom frac n 2 2 2 frac n 2 2 n 2 2 n 3 imes 3 2 n 1 | Degree Of Graph | 40 |
Show that all vertices in an undirected finite graph cannot have distinct degrees if the graph has at least two vertices | Degree Of Graph | 40 |
Prove that in finite graph the number of vertices of odd degree is always even | Degree Of Graph | 40 |
In a graph the degree of a vertex is the number of edges incident connected on it Which of the following is true for every graph G There are even number of vertices of even degree There are odd number of vertices of even degree There are even number of vertices of odd degree There are odd number of vertices of odd degree All the vertices are of even degree | Degree Of Graph | 40 |
In a directed graph every vertex has exactly seven edges coming in What can one always say about the number of edges going out of its vertices Exactly seven edges leave every vertex Exactly seven edges leave some vertex Some vertex has at least seven edges leaving it The number of edges coming out of vertex is odd None of the above | Degree Of Graph | 40 |
An undirected graph has 10 vertices labelled 1 2 dots 10 and 37 edges Vertices 1 3 5 7 9 have degree 8 and vertices 2 4 6 8 have degree 7 What is the degree of vertex 10 5 6 7 8 | Degree Of Graph | 40 |
An ordered n tuple d_1 d_2 d_n with d_1 geq d_2 geq geq d_n is called graphic if there exists a simple undirected graph with n vertices having degrees d_1 d_2 d_n respectively Which one of the following 6 tuples is NOT graphic 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 1 0 0 3 2 1 1 1 0 | Degree Of Graph | 40 |
A graph G V E satisfies E leq 3 V 6 The min degree of G is defined as min_ v in V left degree v right Therefore min degree of G cannot be 3 4 5 6 | Degree Of Graph | 40 |
G is an undirected graph with n vertices and 25 edges such that each vertex of G has degree at least 3 Then the maximum possible value of n is _________ | Degree Of Graph | 40 |
The determinant of the matrix given below is begin bmatrix 0 amp 1 amp 0 amp 2 1 amp 1 amp 1 amp 3 0 amp 0 amp 0 amp 1 1 amp 2 amp 0 amp 1 end bmatrix 1 0 1 2 | Determinant | 41 |
The determinant of the matrix begin bmatrix 6 amp 8 amp 1 amp 1 0 amp 2 amp 4 amp 6 0 amp 0 amp 4 amp 8 0 amp 0 amp 0 amp 1 end bmatrix 11 48 0 24 | Determinant | 41 |
The determinant of the matrix begin bmatrix 2 amp 0 amp 0 amp 0 8 amp 1 amp 7 amp 2 2 amp 0 amp 2 amp 0 9 amp 0 amp 6 amp 1 end bmatrix 4 0 15 20 | Determinant | 41 |
If the matrix A is such that A begin bmatrix 2 u22124 7 end bmatrix begin bmatrix 1 amp 9 amp 5 end bmatrix then the determinant of A is equal to ______ | Determinant | 41 |
Let the function f heta begin vmatrix sin heta amp cos heta amp an heta sin frac pi 6 amp cos frac pi 6 amp an frac pi 6 amp sin frac pi 3 amp cos frac pi 3 amp an frac pi 3 end vmatrix where heta in left frac pi 6 frac pi 3 right and f heta denote the derivative of f with respect to heta Which of the following statements is are TRUE There exists heta in frac pi 6 frac pi 3 such that f heta 0 There exists heta in frac pi 6 frac pi 3 such that f heta eq 0 I only II only Both I and II Neither I Nor II | Differentiability | 42 |
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 __________ | Differentiability | 42 |
Let f be a function defined by f x begin cases x 2 amp ext for x leq 1 ax 2 bx c amp ext for 1 lt x leq 2 x d amp ext for x gt 2 end cases Find the values for the constants a b c and d so that f is continuous and differentiable everywhere on the real line | Differentiability | 42 |
If f x R sin frac pi x 2 S f u2019 frac 1 2 sqrt 2 and int_0 1 f x dx frac 2R pi then the constants R and S are frac 2 pi and frac 16 pi frac 2 pi and 0 frac 4 pi and 0 frac 4 pi and frac 16 pi | Differentiability | 42 |
In the following truth table V 1 if and only if the input is valid Inputs Outputs D_0 D_1 D_2 D_3 X_0 X_1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent Priority encoder Decoder Multiplexer Demultiplexer | Digital Circuits | 43 |
Consider the following combinational function block involving four Boolean variables x y a b where x a b are inputs and y is the output f x a b y if x is 1 y a else y b Which one of the following digital logic blocks is the most suitable for implementing this function Full adder Priority encoder Multiplexor Flip flop | Digital Circuits | 43 |
A logic network has two data inputs A and B and two control inputs C_0 and C_1 It implements the function F according to the following table C_1 C_2 F 0 0 overline A B 0 1 A B 1 0 A oplus B Implement the circuit using one 4 to 1 Multiplexer one 2 input Exclusive OR gate one 2 input AND gate one 2 input OR gate and one Inverter | Digital Circuits | 43 |
The number of flip flops required to construct a binary modulo N counter is __________ | Digital Counter | 44 |
The next state table of a 2 bit saturating up counter is given below begin array cc cc Q_1 amp Q_0 amp Q_1 amp Q_0 hline 0 amp 0 amp 0 amp 1 0 amp 1 amp 1 amp 0 1 amp 0 amp 1 amp 1 1 amp 1 amp 1 amp 1 end array The counter is built as a synchronous sequential circuit using T flip flops The expressions for T_1 and T_0 are T_1 Q_1Q_0 quad T_0 bar Q_1 bar Q_0 T_1 bar Q_1 Q_0 quad T_0 bar Q_1 bar Q_0 T_1 Q_1 Q_0 quad T_0 bar Q_1 bar Q_0 T_1 bar Q_1 Q_0 quad T_0 Q_1 Q_0 | Digital Counter | 44 |
The minimum number of JK flip flops required to construct a synchronous counter with the count sequence 0 0 1 1 2 2 3 3 0 0 is _______ | Digital Counter | 44 |
The minimum number of ext D flip flops needed to design a mod 258 counter is 9 8 512 258 | Digital Counter | 44 |
Let k 2 n A circuit is built by giving the output of an n bit binary counter as input to an n ext to 2 n bit decoder This circuit is equivalent to a k bit binary up counter k bit binary down counter k bit ring counter k bit Johnson counter | Digital Counter | 44 |
How many pulses are needed to change the contents of a 8 bit up counter from 10101100 to 00100111 rightmost bit is the LSB 134 133 124 123 | Digital Counter | 44 |
Consider a 4 bit Johnson counter with an initial value of 0000 The counting sequence of this counter is 0 1 3 7 15 14 12 8 0 0 1 3 5 7 9 11 13 15 0 0 2 4 6 8 10 12 14 0 0 8 12 14 15 7 3 1 0 | Digital Counter | 44 |
We want to design a synchronous counter that counts the sequence 0 1 0 2 0 3 and then repeats The minimum number of ext J K flip flops required to implement this counter is _____________ | Digital Counter | 44 |
Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii | Dining Philosopher | 45 |
There are five buildings called V W X Y and Z in a row not necessarily in that order V is to the West of W Z is to the East of X and the West of V W is to the West of Y Which is the building in the middle V W X Y | Direction Sense | 46 |
Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 | Direction Sense | 46 |
The head of a moving head disk with 100 tracks numbered 0 to 99 is currently serving a request at track 55 If the queue of requests kept in FIFO order is 10 70 75 23 65 which of the two disk scheduling algorithms FCFS First Come First Served and SSTF Shortest Seek Time First will require less head movement Find the head movement for each of the algorithms | Disk Scheduling | 47 |
The head of a hard disk serves requests following the shortest seek time first SSTF policy The head is initially positioned at track number 180 Which of the request sets will cause the head to change its direction after servicing every request assuming that the head does not change direction if there is a tie in SSTF and all the requests arrive before the servicing starts 11 139 170 178 181 184 201 265 10 138 170 178 181 185 201 265 10 139 169 178 181 184 201 265 10 138 170 178 181 185 200 265 | Disk Scheduling | 47 |
The head of a hard disk serves requests following the shortest seek time first SSTF policy The head is initially positioned at track number 180 What is the maximum cardinality of the request set so that the head changes its direction after servicing every request if the total number of tracks are 2048 and the head can start from any track 9 10 11 12 | Disk Scheduling | 47 |
The correct matching for the following pairs is A Disk Scheduling 1 Round robin B Batch Processing 2 SCAN C Time sharing 3 LIFO D Interrupt processing 4 FIFO A 3 B 4 C 2 D 1 A 4 B 3 C 2 D 1 A 2 B 4 C 1 D 3 A 3 B 4 C 3 D 2 | Disk Scheduling | 47 |
Suppose the following disk request sequence track numbers for a disk with 100 tracks is given 45 20 90 10 50 60 80 25 70 Assume that the initial position of the R W head is on track 50 The additional distance that will be traversed by the R W head when the Shortest Seek Time First SSTF algorithm is used compared to the SCAN Elevator algorithm assuming that SCAN algorithm moves towards 100 when it starts execution is________________tracks | Disk Scheduling | 47 |
Suppose a disk has 201 cylinders numbered from 0 to 200 At some time the disk arm is at cylinder 100 and there is a queue of disk access requests for cylinders 30 85 90 100 105 110 135 and 145 If Shortest Seek Time First SSTF is being used for scheduling the disk access the request for cylinder 90 is serviced after servicing ____________ number of requests | Disk Scheduling | 47 |
Provide short answers to the following questions Disk requests come to disk driver for cylinders 10 22 20 2 40 6 and 38 in that order at a time when the disk drive is reading from cylinder 20 The seek time is 6 msec per cylinder Compute the total seek time if the disk arm scheduling algorithm is First come first served Closest cylinder next | Disk Scheduling | 47 |
Cylinder 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 number 63 moving towards larger cylinder numbers on its servicing pass The cylinders are numbered from 0 to 199 The total head movement in number of cylinders incurred while servicing these requests is__________ | Disk Scheduling | 47 |
Consider an operating system capable of loading and executing a single sequential user process at a time The disk head scheduling algorithm used is First Come First Served FCFS If FCFS is replaced by Shortest Seek Time First SSTF claimed by the vendor to give 50 better benchmark results what is the expected improvement in the I O performance of user programs 50 40 25 0 | Disk Scheduling | 47 |
Consider a disk system with 100 cylinders The requests to access the cylinders occur in following sequence 4 34 10 7 19 73 2 15 6 20 Assuming that the head is currently at cylinder 50 what is the time taken to satisfy all requests if it takes 1ms to move from one cylinder to adjacent one and shortest seek time first policy is used 95 ms 119 ms 233 ms 276 ms | Disk Scheduling | 47 |
A disk has 200 tracks numbered 0 through 199 At a given time it was servicing the request of reading data from track 120 and at the previous request service was for track 90 The pending requests in order of their arrival are for track numbers 30 70 115 130 110 80 20 25 How many times will the head change its direction for the disk scheduling policies SSTF Shortest Seek Time First and FCFS First Come Fist Serve 2 and 3 3 and 3 3 and 4 4 and 4 | Disk Scheduling | 47 |
The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 | Dual Function | 48 |
Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds | Effective Memory Access | 49 |
What are the eigenvalues of the matrix P given below P begin pmatrix a amp 1 amp 0 1 amp a amp 1 0 amp 1 amp a end pmatrix a a u221a2 a u221a2 a a a 0 a 2a a 2a 2a | Eigen Value | 50 |
Two eigenvalues of a 3 imes 3 real matrix P are 2 sqrt 1 and 3 The determinant of P is _______ | Eigen Value | 50 |
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4 by 4 symmetric positive definite matrix is ___________ | Eigen Value | 50 |
The product of the non zero eigenvalues of the matrix is ____ begin pmatrix 1 amp 0 amp 0 amp 0 amp 1 0 amp 1 amp 1 amp 1 amp 0 0 amp 1 amp 1 amp 1 amp 0 0 amp 1 amp 1 amp 1 amp 0 1 amp 0 amp 0 amp 0 amp 1 end pmatrix | Eigen Value | 50 |
The larger of the two eigenvalues of the matrix begin bmatrix 4 amp 5 2 amp 1 end bmatrix is _______ | Eigen Value | 50 |
Let A be the matrix begin bmatrix 3 amp 1 1 amp 2 end bmatrix What is the maximum value of xT Ax where the maximum is taken over all x that are the unit eigenvectors of A 3 frac 5 u221a5 2 3 frac 5 u221a5 2 | Eigen Value | 50 |
Let A be the 2 u00d7 2 matrix with elements a_ 11 a_ 12 a_ 21 1 and a_ 22 u22121 Then the eigenvalues of the matrix A 19 are A 1024 and u22121024 B 1024 sqrt 2 and u22121024 sqrt 2 C 4 sqrt 2 and u22124 sqrt 2 D 512 sqrt 2 and u2212512 sqrt 2 | Eigen Value | 50 |
Let A be a 4 imes 4 matrix with eigen values 5 2 1 4 Which of the following is an eigen value of the matrix begin bmatrix A amp I I amp A end bmatrix where I is the 4 imes 4 identity matrix 5 7 2 1 | Eigen Value | 50 |
In questions 1 1 to 1 7 below one or more of the alternatives are correct Write the code letter s a b c d corresponding to the correct alternative s in the answer book Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up 1 1 The eigen vector s of the matrix begin bmatrix 0 amp 0 amp alpha 0 amp 0 amp 0 0 amp 0 amp 0 end bmatrix alpha eq 0 is are a 0 0 alpha b alpha 0 0 c 0 0 1 d 0 alpha 0 | Eigen Value | 50 |
How many of the following matrices have an eigenvalue 1 left begin array cc 1 amp 0 0 amp 0 end array right left begin array cc 0 amp 1 0 amp 0 end array right left begin array cc 1 amp 1 1 amp 1 end array right and left begin array cc 1 amp 0 1 amp 1 end array right one two three four | Eigen Value | 50 |
Consider the matrix as given below begin bmatrix 1 amp 2 amp 3 0 amp 4 amp 7 0 amp 0 amp 3 end bmatrix Which one of the following options provides the CORRECT values of the eigenvalues of the matrix A 1 4 3 B 3 7 3 C 7 3 2 D 1 2 3 | Eigen Value | 50 |
Consider the following matrix A left begin array cc 2 amp 3 x amp y end array right If the eigenvalues of A are 4 and 8 then x 4 y 10 x 5 y 8 x 3 y 9 x 4 y 10 | Eigen Value | 50 |
Consider the following 2 imes 2 matrix A where two elements are unknown and are marked by a and b The eigenvalues of this matrix are 1 and 7 What are the values of a and b qquad A bigl begin smallmatrix 1 amp 4 b amp a end smallmatrix bigr a 6 b 4 a 4 b 6 a 3 b 5 a 5 b 3 | Eigen Value | 50 |
Obtain the eigen values of the matrix A begin bmatrix 1 amp 2 amp 34 amp 49 0 amp 2 amp 43 amp 94 0 amp 0 amp 2 amp 104 0 amp 0 amp 0 amp 1 end bmatrix | Eigen Value | 50 |
The Tamil version of __________ John Abraham starrer Madras Cafe __________ cleared by the Censor Board with no cuts last week but the film s distributor _______ no takers among the exhibitors for a release in Tamilnadu _______ this Friday Mr was found on a was found at the was found on a being find at | English Grammar | 51 |
The man who is now Municipal Commissioner worked as ________________ the security guard at a university a security guard at the university a security guard at university the security guard at the university | English Grammar | 51 |
Saturn is ___________ to be seen on a clear night with the naked eye enough bright bright enough as enough bright bright as enough | English Grammar | 51 |
Out of the following 4 sentences select the most suitable sentence with respect to grammar and usage Since the report lacked needed information it was of no use to them The report was useless to them because there were no needed information in it Since the report did not contain the needed information it was not real useful to them Since the report lacked needed information it would not had been useful to them | English Grammar | 51 |
Didn t you buy ____ when you went shopping any paper much paper no paper a few paper | English Grammar | 51 |
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 figurative collateral literal figurine | English Grammar | 51 |
Which one of the parts A B C D in the sentence contains an ERROR No sooner had the doctor seen the results of the blood test than he suggested the patient to see the specialist A no sooner had B results of the blood test C suggested the patient D see the specialist | English Grammar | 51 |
Out of the following four sentences select the most suitable sentence with respect to grammar and usage I will not leave the place until the minister does not meet me I will not leave the place until the minister doesn t meet me I will not leave the place until the minister meet me I will not leave the place until the minister meets me | English Grammar | 51 |
Choose the grammatically CORRECT sentence He laid in bed till 8 o u2019clock in the morning He layed in bed till 8 o u2019clock in the morning He lain in bed till 8 o u2019clock in the morning He lay in bed till 8 o u2019clock in the morning | English Grammar | 51 |
Let E_1 and E_2 be two entities in an E R diagram with simple valued attributes R_1 and R_2 are two relationships between E_1 and E_2 where R_1 is one to many and R_2 is many to many R_1 and R_2 do not have any attributes of their own What is the minimum number of tables required to represent this situation in the relational model 2 3 4 5 | Er Diagram | 52 |
Given the basic ER and relational models which of the following is INCORRECT An attribute of an entity can have more than one value An attribute of an entity can be composite In a row of a relational table an attribute can have more than one value In a row of a relational table an attribute can have exactly one value or a NULL value | Er Diagram | 52 |
Consider the following ER diagram The minimum number of tables needed to represent M N P R1 R2 is 2 3 4 5 | Er Diagram | 52 |
Consider the following ER diagram The minimum number of tables needed to represent M N P R1 R2 is Which of the following is a correct attribute set for one of the tables for the minimum number of tables needed to represent M N P R1 R2 M1 M2 M3 P1 M1 P1 N1 N2 M1 P1 N1 M1 P1 | Er Diagram | 52 |
Consider the following entity relationship diagram ERD where two entities E1 and E2 have a relation R of cardinality 1 m The attributes of E1 are A11 A12 and A13 where A11 is the key attribute The attributes of E2 are A21 A22 and A23 where A21 is the key attribute and A23 is a multi valued attribute Relation R does not have any attribute A relational database containing minimum number of tables with each table satisfying the requirements of the third normal form 3NF is designed from the above ERD The number of tables in the database is 2 3 5 4 | Er Diagram | 52 |
Consider the entities hotel room and person with a many to many relationship lodging as shown below If we wish to store information about the rent payment to be made by person s occupying different hotel rooms then this information should appear as an attribute of Person Hotel Room Lodging None of these | Er Diagram | 52 |
Consider an Entity Relationship ER model in which entity sets E _ 1 and E _ 2 are connected by an m n relationship R _ 12 E _ 1 and E _ 3 are connected by a 1 n 1 on the side of E _ 1 and n on the side of E _ 3 relationship R _ 13 E _ 1 has two singled attributes a _ 11 and a _ 12 of which a _ 11 is the key attribute E _ 2 has two singled valued attributes a _ 21 and a _ 22 of which a _ 21 is the key attribute E _ 3 has two single valued attributes a _ 31 and a _ 32 of which a _ 31 is the key attribute The relationships do not have any attributes If a relational model is derived from the above ER model then the minimum number of relations that would be generated if all relation are in 3NF is________________ | Er Diagram | 52 |
We are given a set X X_1 X_n where X_i 2 i A sample S subseteq X is drawn by selecting each X_i independently with probability P_i frac 1 2 The expected value of the smallest number in sample S is left frac 1 n right 2 sqrt n n | Expectation | 53 |
Suppose that the expectation of a random variable X is 5 Which of the following statements is true There is a sample point at which X has the value 5 There is a sample point at which X has value greater than 5 There is a sample point at which X has a value greater than equal to 5 None of the above | Expectation | 53 |
Consider an undirected random graph of eight vertices The probability that there is an edge between a pair of vertices is dfrac 1 2 What is the expected number of unordered cycles of length three dfrac 1 8 1 7 8 | Expectation | 53 |
Assume that you are flipping a fair coin i e probability of heads or tails is equal Then the expected number of coin flips required to obtain two consecutive heads for the first time is 4 3 6 10 5 | Expectation | 53 |
An examination paper has 150 multiple choice questions of one mark each with each question having four choices Each incorrect answer fetches 0 25 marks Suppose 1000 students choose all their answers randomly with uniform probability The sum total of the expected marks obtained by all these students is 0 2550 7525 9375 | Expectation | 53 |
Ram has a fair coin i e a toss of the coin results in either head or tail and each event happens with probability exactly half 1 2 He repeatedly tosses the coin until he gets heads in two consecutive tosses The expected number of coin tosses that Ram does is 2 4 6 8 None of the above | Expectation | 53 |
Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta | Exponential Distribution | 54 |
What is the average of all multiples of 10 from 2 to 198 90 100 110 120 | Factors | 55 |
Subsets and Splits