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Consider the relations r1 P Q R and r2 R S T with primary keys P and R respectively The relation r1 contains 2000 tuples and r2 contains 2500 tuples The maximum size of the join r1 u22c8 r2 is 2000 2500 4500 5000 | Joins | 88 |
Consider the following relation schemas b Schema b name b city assets a Schema a num b name bal d Schema c name a number Let branch account and depositor be respectively instances of the above schemas Assume that account and depositor relations are much bigger than the branch relation Consider the following query u041fc name u03c3b city Agra u22c0 bal lt 0 branch u22c8 account u22c8 depositor Which one of the following queries is the most efficient version of the above query u041fc name u03c3bal lt 0 u03c3b city Agra branch u22c8 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor | Joins | 88 |
Consider the following relation schema pertaining to a students database Students rollno name address Enroll rollno courseno coursename where the primary keys are shown underlined The number of tuples in the student and Enroll tables are 120 and 8 respectively What are the maximum and minimum number of tuples that can be present in Student Enroll where u2018 u2019 denotes natural join 8 8 120 8 960 8 960 120 | Joins | 88 |
Consider a join relation algebra between relations r R and s S using the nested loop method There are 3 buffers each of size equal to disk block size out of which one buffer is reserved for intermediate results Assuming size r R lt size s S the join will have fewer number of disk block accesses if relation r R is in the outer loop relation s S is in the outer loop join selection factor between r R and s S is more than 0 5 join selection factor between r R and s S is less than 0 5 | Joins | 88 |
A database table T_1 has 2000 records and occupies 80 disk blocks Another table T_2 has 400 records and occupies 20 disk blocks These two tables have to be joined as per a specified join condition that needs to be evaluated for every pair of records from these two tables The memory buffer space available can hold exactly one block of records for T_1 and one block of records for T_2 simultaneously at any point in time No index is available on either table If Nested loop join algorithm is employed to perform the join with the most appropriate choice of table to be used in outer loop the number of block accesses required for reading the data are 800000 40080 32020 100 | Joins | 88 |
A database table T_1 has 2000 records and occupies 80 disk blocks Another table T_2 has 400 records and occupies 20 disk blocks These two tables have to be joined as per a specified join condition that needs to be evaluated for every pair of records from these two tables The memory buffer space available can hold exactly one block of records for T_1 and one block of records for T_2 simultaneously at any point in time No index is available on either table If instead of Nested loop join Block nested loop join is used again with the most appropriate choice of table in the outer loop the reduction in number of block accesses required for reading the data will be 0 30400 38400 798400 | Joins | 88 |
Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following relational algebra expression contain Assume that the schema of A cup B is the same as that of A A cup B bowtie _ A Id gt 40 vee C Id lt 15 C 7 4 5 9 | Joins | 88 |
Which functions does NOT implement the Karnaugh map given below w x y xy yw w x bar w y bar x y None of the above | K Map | 89 |
What is the minimal form of the Karnaugh map shown below Assume that X denotes a don u2019t care term A bar b bar d B bar b bar d bar b bar c C bar b bar d a bar b bar c d D bar b bar d bar b bar c bar c bar d | K Map | 89 |
What is the equivalent Boolean expression in product of sums form for the Karnaugh map given in Fig B overline D overline B D B overline C D overline B C overline D B D overline B overline D B overline D overline B D | K Map | 89 |
The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression For example the literal count of left xy xz right is 4 What are the minimum possible literal counts of the product of sum and sum of product representations respectively of the function given by the following Karnaugh map Here X denotes don t care 11 9 9 13 9 10 11 11 | K Map | 89 |
The function represented by the Karnaugh map is given below is A B AB BC CA overline B oplus C A BC | K Map | 89 |
The Boolean function in sum of products form where K map is given below figure is _______ | K Map | 89 |
The boolean function for a combinational circuit with four inputs is represented by the following Karnaugh map Which of the product terms given below is an essential prime implicant of the function QRS PQS PQ S Q S | K Map | 89 |
Minimum sum of product expression for f w x y z shown in Karnaugh map below xz y z xz zx x y zx None of the above | K Map | 89 |
In the Karnaugh map shown below X denotes a don u2019t care term What is the minimal form of the function represented by the Karnaugh map bar b bar d bar a bar d bar a bar b bar b bar d bar a b bar d bar b bar d bar a b bar d bar a bar b bar b bar d bar a bar d | K Map | 89 |
Given the following karnaugh map which one of the following represents the minimal Sum Of Products of the map XY Y Z WX Y XY XZ W X Y Z XY XZ Y | K Map | 89 |
Consider the Karnaugh map given below where X represents don t care and blank represents 0 Assume for all inputs left a b c d right the respective complements left bar a bar b bar c bar d right are also available The above logic is implemented using 2 input NOR gates only The minimum number of gates required is ____________ | K Map | 89 |
Consider the following expression a bar d bar a bar c b bar cd Which of the following Karnaugh Maps correctly represents the expression c d c d cd cd a b X X a b X X ab X X X ab X X c d c d cd cd a b X X a b X ab X X X ab X X X c d c d cd cd a b X X a b X X X ab X X X ab X X c d c d cd cd a b X X a b X X X ab X X X ab X X X | K Map | 89 |
Consider the following expression a bar d bar a bar c b bar cd Which of the following expressions does not correspond to the Karnaugh Map obtained for the given expression bar c bar d a bar d ab bar c bar a bar cd bar a bar c bar c bar d a bar d ab bar cd bar a bar c a bar d ab bar c bar cd bar b bar c bar d ac bar d bar a bar c ab bar c | K Map | 89 |
A Boolean function f is to be realized only by NOR gates Its K map is given below The realization is | K Map | 89 |
The following is the Hasse diagram of the poset a b c d e u227a The poset is not a lattice a lattice but not a distributive lattice a distributive lattice but not a Boolean algebra a Boolean algebra | Lattice | 90 |
In the lattice defined by the Hasse diagram given in following figure how many complements does the element u2018e u2019 have 2 3 0 1 | Lattice | 90 |
Consider the set X a b c d e under partial ordering R a a a b a c a d a e b b b c b e c c c e d d d e e e The Hasse diagram of the partial order X R is shown below The minimum number of ordered pairs that need to be added to R to make X R a lattice is ______ | Lattice | 90 |
Consider the following Hasse diagrams Which all of the above represent a lattice i and iv only ii and iii only iii only i ii and iv only | Lattice | 90 |
Suppose L left p q r s t right is a lattice represented by the following Hasse diagram For any x y isin L not necessarily distinct x or y and x and y are join and meet of x y respectively Let L 3 left left x y z right x y z isin L right be the set of all ordered triplets of the elements of L Let p_ r be the probability that an element left x y z right isin L 3 chosen equiprobably satisfies x or y and z x or y and x or z Then p_r 0 p_r 1 0 lt p_r le frac 1 5 frac 1 5 lt p_r lt 1 | Lattice | 90 |
S 1 2 2 1 is binary relation on set A 1 2 3 Is it irreflexive Add the minimum number of ordered pairs to S to make it an equivalence relation Give the modified S Let S a b and let square S be the powerset of S Consider the binary relation subseteq set inclusion on square S Draw the Hasse diagram corresponding to the lattice square S subseteq | Lattice | 90 |
Let wedge vee denote the meet and join operations of lattice A lattice is called distributive if for all x y z x wedge left y vee z right left x wedge y right vee left x wedge z right It is called complete if meet and join exist for every subset It is called modular if for all x y z z leq x Rightarrow x wedge left y vee z right left x wedge y right vee z The positive integers under divisibility ordering i e p leq q if p divides q forms a Complete lattice Modular but not distributive lattice Distributive lattice Lattice but not a complete lattice Under the give ordering positive integers do not form a lattice | Lattice | 90 |
What is the value of lim_ n o infty left 1 frac 1 n right 2n 0 e 2 e 1 2 1 | Limits | 91 |
The value of lim_ x rightarrow infty 1 x 2 e x is u00a0 0 frac 1 2 1 infty | Limits | 91 |
The value of lim_ x rightarrow 1 frac x 7 2x 5 1 x 3 3x 2 2 is 0 is 1 is 1 does not exist | Limits | 91 |
lim_ x rightarrow infty x frac 1 x is infty 0 1 Not defined | Limits | 91 |
lim_ x o infty frac x sin x x cos x equals 1 1 infty infty | Limits | 91 |
lim _ x rightarrow 4 frac sin x 4 x 4 ____ | Limits | 91 |
The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only | Line Graph | 92 |
The following C function takes a singly linked list of integers as a parameter and rearranges the elements of the list The list is represented as pointer to a structure The function is called with the list containing the integers 1 2 3 4 5 6 7 in the given order What will be the contents of the list after the function completes execution struct node int value struct node next void rearrange struct node list struct node p q int temp if list list gt next return p list q list gt next while q temp p gt value p gt value q gt value q gt value temp p q gt next q p p gt next 0 1 2 3 4 5 6 7 2 1 4 3 6 5 7 1 3 2 5 4 7 6 2 3 4 5 6 7 1 | Linked Lists | 93 |
The following C function takes a singly linked list as input argument It modifies the list by moving the last element to the front of the list and returns the modified list Some part of the code is left blank ypedef struct node int value struct node next node Node move_to front Node head Node p q if head NULL head gt next NULL return head q NULL p head while p gt next NULL q p p p gt next _______________ return head Choose the correct alternative to replace the blank line q NULL p rightarrow next head head p q rightarrow next NULL head p p rightarrow next head head p p rightarrow next q q rightarrow next NULL q rightarrow next NULL p rightarrow next head head p | Linked Lists | 93 |
The following C function takes a single linked list of integers as a parameter and rearranges the elements of the list The function is called with the list containing the integers 1 2 3 4 5 6 7 in the given order What will be the contents of the list after function completes execution struct node int value struct node next void rearrange struct node list struct node p q int temp if list list gt next return p list q list gt next while q temp p gt value p gt value q gt value q gt value temp p q gt next q p p gt next 0 1 2 3 4 5 6 7 2 1 4 3 6 5 7 1 3 2 5 4 7 6 2 3 4 5 6 7 1 | Linked Lists | 93 |
The concatenation of two lists is to be performed on O 1 time Which of the following implementations of a list should be used Singly linked list Doubly linked list Circular doubly linked list Array implementation of list | Linked Lists | 93 |
Suppose each set is represented as a linked list with elements in arbitrary order Which of the operations among ext union intersection membership cardinality will be the slowest ext union only ext intersection membership ext membership cardinality ext union intersection | Linked Lists | 93 |
Linked lists are not suitable data structures for which one of the following problems Insertion sort Binary search Radix sort Polynomial manipulation | Linked Lists | 93 |
Let P be a singly linked list Let Q be the pointer to an intermediate node x in the list What is the worst case time complexity of the best known algorithm to delete the node x from the list O n O log 2 n O log n O 1 | Linked Lists | 93 |
In the worst case the number of comparisons needed to search a single linked list of length n for a given element is log n frac n 2 log_2 n 1 n | Linked Lists | 93 |
In a circular linked list oraganisation insertion of a record involves modification of One pointer Two pointers Multiple pointers No pointer | Linked Lists | 93 |
Consider the function f defined below struct item int data struct item next int f struct item p return p NULL p gt next NULL p gt data lt p gt next gt data amp amp f p gt next For a given linked list p the function f returns 1 if and only if the list is empty or has exactly one element the elements in the list are sorted in non decreasing order of data value the elements in the list are sorted in non increasing order of data value not all elements in the list have the same data value | Linked Lists | 93 |
Consider the following piece of C code fragment that removes duplicates from an ordered list of integers Node remove duplicates Node head int j Node t1 t2 j 0 t1 head if t1 NULL t2 t1 gt next else return head j 1 if t2 NULL return head while t2 NULL if t1 val t2 val gt S1 j t1 gt next t2 t1 t2 gt S2 t2 t2 gt next t1 gt next NULL return head Assume the list contains n elements n geq 2 in the following questions How many times is the comparison in statement S1 made What is the minimum and the maximum number of times statements marked S2 get executed What is the significance of the value in the integer pointed to by j when the function completes | Linked Lists | 93 |
A circularly linked list is used to represent a Queue A single variable p is used to access the Queue To which node should p point such that both the operations ext enQueue and ext deQueue can be performed in constant time rear node front node not possible with a single pointer node next to front | Linked Lists | 93 |
Let p be a pointer as shown in the figure in a single linked list What do the following assignment statements achieve q p gt next p gt next q gt next q gt next q gt next gt next p gt next gt next q | Linked Lists | 93 |
The Boolean function obtained by adding an inverter to each and every input of an AND gate is OR XOR NAND NOR None of the above | Logic Gates | 94 |
Consider the following circuit composed of XOR gates and non inverting buffers The non inverting buffers have delays delta_1 2 ns and delta_2 4 ns as shown in the figure Both XOR gates and all wires have zero delay Assume that all gate inputs outputs and wires are stable at logic level 0 at time 0 If the following waveform is applied at input A how many transition s change of logic levels occur s at B during the interval from 0 to 10 ns 1 2 3 4 | Logic Gates | 94 |
Choose the correct alternatives more than one may be correct and write the corresponding letters only All digital circuits can be realized using only Ex OR gates Multiplexers Half adders OR gates | Logic Gates | 94 |
Express the function f x y z xy yz with only one complement operation and one or more AND OR operations Draw the logic circuit implementing the expression obtained using a single NOT gate and one or more AND OR gates Transform the following logic circuit without expressing its switching function into an equivalent logic circuit that employs only 6 NAND gates each with 2 inputs | Logic Gates | 94 |
Three candidates Amar Birendra and Chanchal stand for the local election Opinion polls are conducted and show that fraction a of the voters prefer Amar to Birendra fraction b prefer Birendra to Chanchal and fraction c prefer Chanchal to Amar Which of the following is impossible a b c 0 51 0 51 0 51 a b c 0 61 0 71 0 67 a b c 0 68 0 68 0 68 a b c 0 49 0 49 0 49 None of the above | Logical Reasoning | 95 |
There are three boxes One contains apples another contains oranges and the last one contains both apples and oranges All three are known to be incorrectly labeled If you are permitted to open just one box and then pull out and inspect only one fruit which box would you open to determine the contents of all three boxes The box labeled u2018Apples u2019 The box labeled u2018Apples and Oranges u2019 The box labeled u2018Oranges u2019 Cannot be determined | Logical Reasoning | 95 |
There are eight bags of rice looking alike seven of which have equal weight and one is slightly heavier The weighing balance is of unlimited capacity Using this balance the minimum number of weighings required to identify the heavier bag is A 2 B 3 C 4 D 8 | Logical Reasoning | 95 |
The action for this problem takes place in an island of Knights and Knaves where Knights always make true statements and Knaves always make false statements and everybody is either a Knight or a Knave Two friends A and B lives in a house The census taker an outsider knocks on the door and it is opened by A The census taker says I need information about you and your friend Which if either is a Knight and which if either is a Knave We are both Knaves says A angrily and slams the door What if any thing can the census taker conclude A is a Knight and B is a Knave A is a Knave and B is a Knight Both are Knaves Both are Knights No conclusion can be drawn | Logical Reasoning | 95 |
Six people are seated around a circular table There are at least two men and two women There are at least three right handed persons Every woman has a left handed person to her immediate right None of the women are right handed The number of women at the table is 2 3 4 Cannot be determined | Logical Reasoning | 95 |
Rahul Murali Srinivas and Arul are seated around a square table Rahul is sitting to the left of Murali Srinivas is sitting to the right of Arul Which of the following pairs are seated opposite each other Rahul and Murali Srinivas and Arul u200b u200b u200b u200b u200b u200b u200bSrinvas and Murali u200b u200b u200b u200b u200b u200b u200bSrinivas and Rahul | Logical Reasoning | 95 |
Long ago in a planet far far away there lived three races of intelligent inhabitants the blues who always tell the truth the whites who always lie and the pinks who when asked a series of questions start with a lie and then tell the truth and lie alternately To three creatures chosen from the planet and seated facing each other at A B and C see figure the following three questions are put i What race is your left hand neighbour ii What race is your right hand neighbour iii What race are you Here are their answers A i White ii Pink iii Blue B i Pink ii Pink iii Blue C i White ii Blue iii Blue What is the actual race of each of the three creatures A is Pink B is White C is Blue A is Blue B is Pink C is White A is Pink B is Blue C is Pink A is White B is Pink C is Blue Cannot be determined from the above data | Logical Reasoning | 95 |
In a room there are only two types of people namely Type 1 and Type 2 Type 1 people always tell the truth and Type 2 people always lie You give a fair coin to a person in that room without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it Upon asking the person replies the following The result of the toss is head if and only if I am telling the truth Which of the following options is correct The result is head The result is tail If the person is of Type 2 then the result is tail If the person is of Type 1 then the result is tail | Logical Reasoning | 95 |
If either wages or prices are raised there will be inflation If there is inflation then either the government must regulate it or the people will suffer If the people suffer the government will be unpopular Government will not be unpopular Which of the following can be validly concluded from the above statements People will not suffer If the inflation is not regulated then wages are not raised Prices are not raised If the inflation is not regulated then the prices are not raised Wages are not raised | Logical Reasoning | 95 |
Consider the following two statements S1 If a candidate is known to be corrupt then he will not be elected S2 If a candidate is kind he will be elected Which one of the following statements follows from S1 and S2 as per sound inference rules of logic If a person is known to be corrupt he is kind If a person is not known to be corrupt he is not kind If a person is kind he is not known to be corrupt If a person is not kind he is not known to be corrupt | Logical Reasoning | 95 |
Consider the following logical inferences I_ 1 If it rains then the cricket match will not be played The cricket match was played Inference There was no rain I_ 2 If it rains then the cricket match will not be played It did not rain Inference The cricket match was played Which of the following is TRUE A Both I_ 1 and I_ 2 are correct inferences B I_ 1 is correct but I_ 2 is not a correct inference C I_ 1 is not correct but I_ 2 is a correct inference D Both I_ 1 and I_ 2 are not correct inferences | Logical Reasoning | 95 |
All that glitters is gold No gold is silver Claims 1 No silver glitters 2 Some gold glitters Then which of the following is TRUE Only claim 1 follows Only claim 2 follows Either claim 1 or claim 2 follows but not both Neither claim 1 nor claim 2 follows Both claim 1 and claim 2 follow | Logical Reasoning | 95 |
If relftaga means carefree otaga means careful and fertaga means careless which of the following could mean aftercare zentaga tagafer tagazen relffer | Logical Reasoning | 95 |
Consider the following two statements There are infinitely many interesting whole numbers There are finitely many uninteresting whole numbers Which of the following is true Statements 1 and 2 are equivalent Statement 1 implies statement 2 Statement 2 implies statement 1 None of the above | Logical Reasoning | 95 |
Consider the following statements relating to the level of poker play of four players P Q R and S P always beats Q R always beats S S loses to P only sometimes R always loses to Q Which of the following can be logically inferred from the above statements P is likely to beat all the three other players S is the absolute worst player in the set i only ii only i and ii only neither i nor ii | Logical Reasoning | 95 |
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 else res res a b b 1 return res Which one of the following conditions is TRUE before every iteration of the loop X Y a b res a Y res X b X Y res a b X Y res a b | Loop Invariants | 96 |
Consider the program where a b are integers with b gt 0 x a y b z 0 while y gt 0 do if odd x then z z x y y 1 else y y 2 x 2 x fi Invariant of the loop is a condition which is true before and after every iteration of the loop In the above program the loop invariant is given by 0 leq y and z x y a b Which of the following is true of the program The program will not terminate for some values of a b The program will terminate with z 2 b The program will terminate with z a b The program will not terminate for some values of a b but when it does terminate the condition z a b will hold The program will terminate with z a b | Loop Invariants | 96 |
Consider the following pseudo code where x and y are positive integers begin q 0 r x while r u2265 y do begin r r y q q 1 end end The post condition that needs to be satisfied after the program terminates is r qx y wedge r lt y x qy r wedge r lt y y qx r wedge 0 lt r lt y q 1 lt r y wedge y gt 0 | Loop Invariants | 96 |
Consider the following program fragment for reversing the digits in a given integer to obtain a new integer Let n d_1 d_2 ldots d_m int n rev rev 0 while n gt 0 rev rev 10 n 10 n n 10 The loop invariant condition at the end of the i th iteration is n d_1 d_2 ldots d_ m i qquad mathbf and qquad ext rev d_m d_ m 1 ldots d_ m i 1 n d_ m i 1 ldots d_ m 1 d_m qquad mathbf or qquad ext rev d_ m i ldots d_2 d_1 n eq ext rev n d_1 d_2 ldots d_m qquad mathbf or qquad ext rev d_m ldots d_2 d_1 | Loop Invariants | 96 |
Consider the following program for summing the entries of the array b array 0 N 1 of integers where N is a positive integer The symbol lt gt denotes not equal to var i s integer Program i 0 s 0 while i lt gt N do s s b i i i 1 od Which of the following gives the invariant that holds at the beginning of each loop that is each time the program arrives at point s sum limits N _ j 0 b j amp 0 leq i leq N s sum limits i 1 _ j 0 b j amp 0 leq i lt N s sum limits i _ j 0 b j amp 0 lt i leq N s sum limits N _ j 1 b j amp 0 leq i lt N s sum limits i 1 _ j 0 b j amp 0 leq i leq N | Loop Invariants | 96 |
Consider the C program fragment below which is meant to divide x by y using repeated subtractions The variables x y q and r are all unsigned int while r gt y r r y q q 1 Which of the following conditions on the variables x y q and r before the execution of the fragment will ensure that the loop terminated in a state satisfying the condition x y q r q r amp amp r 0 x gt 0 amp amp r x amp amp y gt 0 q 0 amp amp r x amp amp y gt 0 q 0 amp amp y gt 0 | Loop Invariants | 96 |
Consider the following PASCAL program segment if i mod 2 0 then while i gt 0 do begin i i div 2 if i mod 2 lt gt 0 then i i 1 else i i ndash 2 end An appropriate loop invariant for the while loop is ________ | Loop Invariants | 96 |
The number of different n imes n symmetric matrices with each element being either 0 or 1 is Note ext power left 2 X right is same as 2 X ext power left 2 n right ext power left 2 n 2 right ext power left 2 frac left n 2 n right 2 right ext power left 2 frac left n 2 n right 2 right | Matrices | 97 |
The matrices begin bmatrix cos heta amp amp sin heta sin heta amp amp cos heta end bmatrix and begin bmatrix a amp amp 0 0 amp amp b end bmatrix commute under multiplication if a b ext or heta n pi n an integer always never if a cos heta b sin heta | Matrices | 97 |
Let A be an n u00d7 n matrix of the following form What is the value of the determinant of A left frac 5 sqrt3 2 right n 1 left frac 5 sqrt3 7 2 sqrt 3 right left frac 5 sqrt3 2 right n 1 left frac 5 sqrt3 7 2 sqrt 3 right left frac 7 sqrt5 2 right n 1 left frac 7 sqrt5 3 2 sqrt 5 right left frac 7 sqrt5 2 right n 1 left frac 7 sqrt5 3 2 sqrt 5 right left frac 3 sqrt7 2 right n 1 left frac 3 sqrt7 5 2 sqrt 7 right left frac 3 sqrt7 2 right n 1 left frac 3 sqrt7 5 2 sqrt 7 right left frac 3 sqrt5 2 right n 1 left frac 3 sqrt5 7 2 sqrt 5 right left frac 3 sqrt5 2 right n 1 left frac 3 sqrt5 7 2 sqrt 5 right | Matrices | 97 |
Let A B C D be n imes n matrices each with non zero determinant If ABCD I then B 1 is D 1 C 1 A 1 CDA ADC Does not necessarily exist | Matrices | 97 |
Let A and B be real symmetric matrices of size n imes n Then which one of the following is true AA I A A 1 AB BA AB BA | Matrices | 97 |
Let a a_ ij be an n rowed square matrix and I_ 12 be the matrix obtained by interchanging the first and second rows of the n rowed Identify matrix Then AI_ 12 is such that its first row is the same as its second row row is the same as the second row of A column is the same as the second column of A row is all zero | Matrices | 97 |
In an M imes N matrix all non zero entries are covered in a rows and b columns Then the maximum number of non zero entries such that no two are on the same row or column is leq a b leq max a b leq min M a N b leq min a b | Matrices | 97 |
If A begin pmatrix 1 amp 0 amp 0 amp 1 0 amp 1 amp 0 amp 1 0 amp 0 amp i amp i 0 amp 0 amp 0 amp i end pmatrix the matrix A 4 calculated by the use of Cayley Hamilton theorem or otherwise is ____ | Matrices | 97 |
Find the inverse of the matrix begin bmatrix 1 amp 0 amp 1 1 amp 1 amp 1 0 amp 1 amp 0 end bmatrix | Matrices | 97 |
Consider the following statements S1 The sum of two singular n imes n matrices may be non singular S2 The sum of two n imes n non singular matrices may be singular Which one of the following statements is correct S1 and S2 both are true S1 is true S2 is false S1 is false S2 is true S1 and S2 both are false | Matrices | 97 |
A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above | Matrices | 97 |
The rank of the matrix given below is begin bmatrix 1 amp 4 amp 8 amp 7 0 amp 0 amp 3 amp 0 4 amp 2 amp 3 amp 1 3 amp 12 amp 24 amp 2 end bmatrix 3 1 2 4 | Matrices | 97 |
The rank of the following n 1 imes n 1 matrix where a is a real number is begin bmatrix 1 amp a amp a 2 amp dots amp a n 1 amp a amp a 2 amp dots amp a n vdots amp vdots amp vdots amp amp vdots vdots amp vdots amp vdots amp amp vdots 1 amp a amp a 2 amp dots amp a n end bmatrix 1 2 n Depends on the value of a | Matrices | 97 |
The rank of matrix begin bmatrix 0 amp 0 amp 3 9 amp 3 amp 5 3 amp 1 amp 1 end bmatrix is 0 1 2 3 | Matrices | 97 |
Consider the following determinant Delta begin vmatrix 1 amp a amp bc 1 amp b amp ca 1 amp C amp ab end vmatrix Which of the following is a factor of Delta a b a b a b c abc | Matrices | 97 |
The number of roots of e x 0 5x 2 2 0 in the range 5 5 is 0 1 2 3 | Maxima Minima | 98 |
Find the minimum value of 3 4x 2x 2 Determine the number of positive integers amp le 720 which are not divisible by any of 2 3 or 5 | Maxima Minima | 98 |
Consider the function f x sin x in the interval x left frac pi 4 frac 7 pi 4 right The number and location s of the local minima of this function are A One at dfrac pi 2 B One at dfrac 3 pi 2 C Two at dfrac pi 2 and dfrac 3 pi 2 D Two at dfrac pi 4 and dfrac 3 pi 2 | Maxima Minima | 98 |
A point on a curve is said to be an extremum if it is a local minimum or a local maximum The number of distinct extrema for the curve 3x 4 16x 3 24x 2 37 is 0 1 2 3 | Maxima Minima | 98 |
Solve min x 2 y 2 subject to x y geq 10 2x 3y geq 20 x geq 4 y geq 4 32 50 52 100 None of the above | Maxima Minima | 98 |
Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB | Memory Allocation | 99 |
Let the page reference and the working set window be c c d b c e c e a d and 4 respectively The initial working set at time t 0 contains the pages a d e where a was referenced at time t 0 d was referenced at time t 1 and e was referenced at time t 2 Determine the total number of page faults and the average number of page frames used by computing the working set at each reference | Memory Management | 100 |
Let a memory have four free blocks of sizes 4k 8k 20k 2k These blocks are allocated following the best fit strategy The allocation requests are stored in a queue as shown below Request No J1 J2 J3 J4 J5 J6 J7 J8 Request Sizes 2k 14k 3k 6k 6k 10k 7k 20k Usage Time 4 10 2 8 4 1 8 6 The time at which the request for J7 will be completed will be 16 19 20 37 | Memory Management | 100 |
For each of the four processes P1 P2 P3 and P4 The total size in kilobytes KB and the number of segments are given below Process Total size in KB Number of segments P1 195 4 P2 254 5 P3 45 3 P4 364 8 The page size is 1 KB The size of an entry in the page table is 4 bytes The size of an entry in the segment table is 8 bytes The maximum size of a segment is 256 KB The paging method for memory management uses two level paging and its storage overhead is P The storage overhead for the segmentation method is S The storage overhead for the segmentation and paging method is T What is the relation among the overheads for the different methods of memory management in the concurrent execution of the above four processes P lt S lt T S lt P lt T S lt T lt P T lt S lt P | Memory Management | 100 |
Consider a main memory system that consists of 8 memory modules attached to the system bus which is one word wide When a write request is made the bus is occupied for 100 nanoseconds ns by the data address and control signals During the same 100 ns and for 500 ns thereafter the addressed memory module executes one cycle accepting and storing the data The internal operation of different memory modules may overlap in time but only one request can be on the bus at any time The maximum number of stores of one word each that can be initiated in 1 millisecond is ________ | Memory Management | 100 |
A computer installation has 1000k of main memory The jobs arrive and finish in the following sequences Job 1 requiring 200k arrives Job 2 requiring 350k arrives Job 3 requiring 300k arrives Job 1 finishes Job 4 requiring 120k arrives Job 5 requiring 150k arrives Job 6 requiring 80k arrives Draw the memory allocation table using Best Fit and First Fit algorithms Which algorithm performs better for this sequence | Memory Management | 100 |
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