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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 LRU Least Recently Used OPT Optimal Page Replacement MRU Most Recently Used FIFO First In First Out
Page Replacement
125
Dirty bit for a page in a page table helps avoid unnecessary writes on a paging device helps maintain LRU information allows only read on a page None of the above
Page Replacement
125
The inclusion of which of the following sets into S left left 1 2 right left 1 2 3 right left 1 3 5 right left 1 2 4 right left 1 2 3 4 5 right right is necessary and sufficient to make S a complete lattice under the partial order defined by set containment 1 1 2 3 1 1 3 1 1 3 1 2 3 4 1 2 3 5
Partial Order
126
Let S leq be a partial order with two minimal elements a and b and a maximum element c Let P S o True False be a predicate defined on S Suppose that P a True P b False and P x implies P y for all x y in S satisfying x leq y where implies stands for logical implication Which of the following statements CANNOT be true P x True for all x in S such that x u2260 b P x False for all x in S such that x u2260 a and x u2260 c P x False for all x in S such that b u2264 x and x u2260 c P x False for all x in S such that a u2264 x and b u2264 x
Partial Order
126
If the longest chain in a partial order is of length n then the partial order can be written as a _____ of n antichains
Partial Order
126
Consider the set S a b c d Consider the following 4 partitions u03c0_1 u03c0_2 u03c0_3 u03c0_4 on S u03c0_1 overline abcd u03c0_2 overline ab overline cd quad u03c0_3 overline abc overline d u03c0_4 bar a bar b bar c bar d Let prec be the partial order on the set of partitions S u03c0_1 u03c0_2 u03c0_3 u03c0_4 defined as follows u03c0_i prec u03c0_j if and only if u03c0_i refines u03c0_j The poset diagram for S prec is
Partial Order
126
A partial order P is defined on the set of natural numbers as follows Here dfrac x y denotes integer division 0 0 in P a b in P if and only if a 10 leq b 10 and frac a 10 frac b 10 in P Consider the following ordered pairs 101 22 22 101 145 265 0 153 Which of these ordered pairs of natural numbers are contained in P i and iii ii and iv i and iv iii and iv
Partial Order
126
The less than relation lt on reals is a partial ordering since it is asymmetric and reflexive a partial ordering since it is antisymmetric and reflexive not a partial ordering because it is not asymmetric and not reflexive not a partial ordering because it is not antisymmetric and reflexive none of the above
Partial Order
126
Suppose A a b c d and Pi_1 is the following partition of A Pi_1 left left a b c right left d right right List the ordered pairs of the equivalence relations induced by Pi_1 Draw the graph of the above equivalence relation Let Pi_2 left left a right left b right left C right left d right right Pi_3 left left a b c d right right and Pi_4 left left a b right left c d right right Draw a Poset diagram of the poset left langle left Pi_1 Pi_2 Pi_3 Pi_4 right ext refines right rangle
Partial Order
126
Let X 2 3 6 12 24 Let leq be the partial order defined by X leq Y if x divides y Number of edges in the Hasse diagram of X leq is 3 4 9 None of the above
Partial Order
126
A set S together with partial order ll is called a well order if it has no infinite descending chains i e there is no infinite sequence x_1 x_2 ldots of elements from S such that x_ i 1 ll x_i and x_ i 1 eq x_i for all i Consider the set of all words finite sequence of letters a z denoted by W in dictionary order Between aa and az there are only 24 words Between aa and az there are only 2 24 words W is not a partial order W is a partial order but not a well order W is a well order
Partial Order
126
A partial order le is defined on the set S x a1 a2 an y as x le ai for all i and ai le y for all i where n ge 1 The number of total orders on the set S which contain the partial order le is n n 2 n 1
Partial Order
126
The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined
Passage Reading
127
The Gross Domestic Product GDP in Rupees grew at 7 during 2012 2013 For international comparison the GDP is compared in US Dollars USD after conversion based on the market exchange rate During the period 2012 2013 the exchange rate for the USD increased from Rs 50 USD to Rs 60 USD India s GDP in USD during the period 2012 2013 increased by 5 decreased by 13 decreased by 20 decreased by 11
Percentage
128
Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________
Percentage
128
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12
Permutation Combination
129
We need to choose a team of 11 from a pool of 15 players and also select a captain The number of different ways this can be done is begin pmatrix 15 11 end pmatrix 11 begin pmatrix 15 11 end pmatrix 15 14 13 12 11 10 9 8 7 6 5 15 14 13 12 11 10 9 8 7 6 5 11
Permutations And Combinations
130
Two girls have picked 10 roses 15 sunflowers and 15 daffodils What is the number of ways they can divide the flowers among themselves 1638 2100 2640 None of the above
Permutations And Combinations
130
The number of substrings of all lengths inclusive that can be formed from a character string of length n is n n 2 frac n n 1 2 frac n n 1 2
Permutations And Combinations
130
The number of binary strings of n zeros and k ones in which no two ones are adjacent is n 1 C_k nC_k nC_ k 1 None of the above
Permutations And Combinations
130
Provide short answers to the following questions How many substrings of all lengths inclusive can be formed from a character string of length n Assume all characters to be distinct prove your answer
Permutations And Combinations
130
Match the pairs in the following questions by writing the corresponding letters only A The number distinct binary trees with n nodes P frac n 2 B The number of binary strings of length of 2n with an equal number of 0 u2019s and 1 u2019s Q binom 3n n C The number of even permutation of n objects R binom 2n n D The number of binary strings of length 6n which are palindromes with 2n 0 u2019s S frac 1 1 n binom 2n n
Permutations And Combinations
130
Mala has the colouring book in which each English letter is drawn two times She wants to paint each of these 52 prints with one of k colours such that the colour pairs used to colour any two letters are different Both prints of a letter can also be coloured with the same colour What is the minimum value of k that satisfies this requirement 9 8 7 6
Permutations And Combinations
130
Let A be a sequence of 8 distinct integers sorted in ascending order How many distinct pairs of sequences B and C are there such that each is sorted in ascending order B has 5 and C has 3 elements and the result of merging B and C gives A 2 30 56 256
Permutations And Combinations
130
In how many ways can we distribute 5 distinct balls B1 B2 B5 in 5 distinct cells C1 C2 C5 such that Ball Bi is not in cell Ci u2200i 1 2 5 and each cell contains exactly one ball 44 96 120 3125
Permutations And Combinations
130
How many sub strings of different lengths non zero can be found formed from a character string of length n n n 2 2 n frac n n 1 2
Permutations And Combinations
130
How many 4 digit even numbers have all 4 digits distinct 2240 2296 2620 4536
Permutations And Combinations
130
Find the number of binary strings w of length 2n with an equal number of 1 s and 0 s and the property that every prefix of w has at least as many 0 s as 1 s
Permutations And Combinations
130
n couples are invited to a party with the condition that every husband should be accompanied by his wife However a wife need not be accompanied by her husband The number of different gatherings possible at the party is 2n mathrm C _n imes 2 n 3 n frac 2n 2 n 2n mathrm C _n
Permutations And Combinations
130
m identical balls are to be placed in n distinct bags You are given that m geq kn where k is a natural number geq 1 In how many ways can the balls be placed in the bags if each bag must contain at least k balls left begin array c m k n 1 end array right left begin array c m kn n 1 n 1 end array right left begin array c m 1 n k end array right left begin array c m kn n k 2 n k end array right
Permutations And Combinations
130
In how many ways can a given positive integer n geq 2 be expressed as the sum of 2 positive integers which are not necessarily distinct For example for n 3 the number of ways is 2 i e 1 2 2 1 Give only the answer without any explanation In how many ways can a given positive integer n geq 3 be expressed as the sum of 3 positive integers which are not necessarily distinct For example for n 4 the number of ways is 3 i e 1 2 1 2 1 1 Give only the answer without explanation In how many ways can a given positive integer n geq k be expressed as the sum of k positive integers which are not necessarily distinct Give only the answer without explanation
Permutations And Combinations
130
The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above
Pigeonhole Principle
131
Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM and p has a Poisson distribution with mean 3 What is the probability of observing fewer than 3 cars during any given minute in this interval A dfrac 8 2e 3 B dfrac 9 2e 3 C dfrac 17 2e 3 D dfrac 26 2e 3
Poisson Distribution
132
In a multi user operating system on an average 20 requests are made to use a particular resource per hour The arrival of requests follows a Poisson distribution The probability that either one three or five requests are made in 45 minutes is given by 6 9 imes 10 6 imes e 20 1 02 imes 10 6 imes e 20 6 9 imes 10 3 imes e 20 1 02 imes 10 3 imes e 20
Poisson Distribution
132
If a random variable X has a Poisson distribution with mean 5 then the expectation E X 2 2 equals ___
Poisson Distribution
132
If the cube roots of unity are 1 omega and omega 2 then the roots of the following equation are x 1 3 8 0 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2
Polynomials
133
A polynomial p x satisfies the following p 1 p 3 p 5 1 p 2 p 4 1 The minimum degree of such a polynomial is 1 2 3 4
Polynomials
133
A polynomial p x is such that p 0 5 p 1 4 p 2 9 and p 3 20 The minimum degree it should have is 1 2 3 4
Polynomials
133
A non zero polynomial f x of degree 3 has roots at x 1 x 2 and x 3 Which one of the following must be TRUE f 0 f 4 lt 0 f 0 f 4 gt 0 f 0 f 4 gt 0 f 0 f 4 lt 0
Polynomials
133
If f x 2x 7 3x 5 which of the following is a factor of f x left x 3 8 right x 1 2x 5 x 1
Polynomials
133
A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______
Precedence Graph
134
Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc
Prime Implicants
135
Let f x y z bar x bar y x xz be a switching function Which one of the following is valid bar y x is a prime implicant of f xz is a minterm of f xz is an implicant of f y is a prime implicant of f
Prime Implicants
135
A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order
Priority Queue
136
Two n bit binary strings S_1 and S_2 are chosen randomly with uniform probability The probability that the Hamming distance between these strings the number of bit positions where the two strings differ is equal to d is dfrac n C_ d 2 n dfrac n C_ d 2 d dfrac d 2 n dfrac 1 2 d
Probability
137
Two friends agree to meet at a park with the following conditions Each will reach the park between 4 00 pm and 5 00 pm and will see if the other has already arrived If not they will wait for 10 minutes or the end of the hour whichever is earlier and leave What is the probability that the two will not meet
Probability
137
Two dice are thrown simultaneously The probability that at least one of them will have 6 facing up is frac 1 36 frac 1 3 frac 25 36 frac 11 36
Probability
137
The security system at an IT office is composed of 10 computers of which exactly four are working To check whether the system is functional the officials inspect four of the computers picked at random without replacement The system is deemed functional if at least three of the four computers inspected are working Let the probability that the system is deemed functional be denoted by p Then 100p _____________
Probability
137
Seven distinct car accidents occurred in a week What is the probability that they all occurred on the same day dfrac 1 7 7 dfrac 1 7 6 dfrac 1 2 7 dfrac 7 2 7
Probability
137
Let P E denote the probability of the event E Given P A 1 P B dfrac 1 2 the values of P A mid B and P B mid A respectively are left dfrac 1 4 right left dfrac 1 2 right left dfrac 1 2 right left dfrac 1 4 right left dfrac 1 2 right 1 1 left dfrac 1 2 right
Probability
137
E1 and E2 are events in a probability space satisfying the following constraints Pr E1 Pr E2 Pr E1 u222a E2 1 E1 and E2 are independent The value of Pr E1 the probability of the event E1 is 0 dfrac 1 4 dfrac 1 2 1
Probability
137
A program consists of two modules executed sequentially Let f_1 t and f_2 t respectively denote the probability density functions of time taken to execute the two modules The probability density function of the overall time taken to execute the program is given by f_1 t f_2 t int_0 t f_1 x f_2 x dx int_0 t f_1 x f_2 t x dx max f_1 t f_2 t
Probability
137
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
137
A die is rolled three times The probability that exactly one odd number turns up among the three outcomes is a frac 1 6 b frac 3 8 c frac 1 8 d frac 1 2
Probability
137
The probability that top and bottom cards of a randomly shuffled deck are both aces is frac 4 52 imes frac 4 52 frac 4 52 imes frac 3 52 frac 4 52 imes frac 3 51 frac 4 52 imes frac 4 51
Probability
137
The probability that it will rain today is 0 5 The probability that it will rain tomorrow is 0 6 The probability that it will rain either today or tomorrow is 0 7 What is the probability that it will rain today and tomorrow 0 3 0 25 0 35 0 4
Probability
137
The probability of an event B is P_1 The probability that events A and B occur together is P_2 while the probability that A and bar B occur together is P_3 The probability of the event A in terms of P_1 P_2 and P_3 is _____________
Probability
137
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 HEADS or HEADS TAILS then output N and stop Step 4 If the outcomes are TAILS TAILS then go to Step 1 The probability that the output of the experiment is Y is up to two decimal places ____________
Probability
137
A bag contains 10 white balls and 15 black balls Two balls are drawn in succession The probability that one of them is black and the other is white is frac 2 3 frac 4 5 frac 1 2 frac 1 3
Probability
137
Which combination of the following features will suffice to characterize an OS as a multi programmed OS More than one program may be loaded into main memory at the same time for execution If a program waits for certain events such as I O another program is immediately scheduled for execution If the execution of a program terminates another program is immediately scheduled for execution a a and b a and c a b and c
Process
138
The process state transition diagram of an operating system is as given below Which of the following must be FALSE about the above operating system It is a multiprogrammed operating system It uses preemptive scheduling It uses non preemptive scheduling It is a multi user operating system
Process
138
The process state transition diagram in the below figure is representative of a batch operating system an operating system with a preemptive scheduler an operating system with a non preemptive scheduler a uni programmed operating system
Process
138
We wish to schedule three processes P1 P2 and P3 on a uniprocessor system The priorities CPU time requirements and arrival times of the processes are as shown below Process Priority CPU time required Arrival time hh mm ss P1 10 highest 20 sec 00 00 05 P2 9 10 sec 00 00 03 P3 8 lowest 15 sec 00 00 00 We have a choice of preemptive or non preemptive scheduling In preemptive scheduling a late arriving higher priority process can preempt a currently running process with lower priority In non preemptive scheduling a late arriving higher priority process must wait for the currently executing process to complete before it can be scheduled on the processor What are the turnaround times time from arrival till completion of P2 using preemptive and non preemptive scheduling respectively 30 sec 30 sec 30 sec 10 sec 42 sec 42 sec 30 sec 42 sec
Process Schedule
139
The sequence u2026 u2026 is an optimal non preemptive scheduling sequence for the following jobs which leaves the CPU idle for u2026 u2026 u2026 unit s of time Job Arrival Time Burst Time 1 0 0 9 2 0 6 5 3 1 0 1 3 2 1 1 2 1 3 0 3 2 1 0 1 2 3 5
Process Schedule
139
In a computer system where the u2018best fit u2019 algorithm is used for allocating u2018jobs u2019 to u2018memory partitions u2019 the following situation was encountered Partitions size in KB 4K 8K 20K 2K Job sizes in KB 2K 14K 3K 6K 6K 10K 20K 2K Time for execution 4 10 2 1 4 1 8 6 When will the 20K job complete
Process Schedule
139
Fill in the blanks The highest response ratio next scheduling policy favours ___________ jobs but it also limits the waiting time of _________ jobs
Process Schedule
139
Consider three processes process id 0 1 2 respectively with compute time bursts 2 4 and 8 time units All processes arrive at time zero Consider the longest remaining time first LRTF scheduling algorithm In LRTF ties are broken by giving priority to the process with the lowest process id The average turn around time is 13 units 14 units 15 units 16 units
Process Schedule
139
Consider the following set of processes with the arrival times and the CPU burst times gives in milliseconds Process Arrival Time Burst Time P1 P2 P3 P4 0 1 2 4 5 3 3 1 What is the average turnaround time for these processes with the preemptive shortest remaining processing time first SRPT algorithm 5 50 5 75 6 00 6 25
Process Schedule
139
Assume that the following jobs are to be executed on a single processor system Job Id CPU Burst Time p 4 q 1 r 8 s 1 t 2 The jobs are assumed to have arrived at time 0 and in the order p q r s t Calculate the departure time completion time for job p if scheduling is round robin with time slice 1 4 10 11 12 None of the above
Process Schedule
139
A uni processor computer system only has two processes both of which alternate 10 ms CPU bursts with 90 ms I O bursts Both the processes were created at nearly the same time The I O of both processes can proceed in parallel Which of the following scheduling strategies will result in the least CPU utilization over a long period of time for this system First come first served scheduling Shortest remaining time first scheduling Static priority scheduling with different priorities for the two processes Round robin scheduling with a time quantum of 5 ms
Process Schedule
139
Four jobs to be executed on a single processor system arrive at time 0 in the order A B C D Their burst CPU time requirements are 4 1 8 1 time units respectively The completion time of A under round robin scheduling with time slice of one time unit is 10 4 8 9
Process Schedule
139
Four jobs are waiting to be run Their expected run times are 6 3 5 and x In what order should they be run to minimize the average response time Write a concurrent program using ext par begin par end to represent the precedence graph shown below
Process Schedule
139
Consider three CPU intensive processes which require 10 20 and 30 time units and arrive at times 0 2 and 6 respectively How many context switches are needed if the operating system implements a shortest remaining time first scheduling algorithm Do not count the context switches at time zero and at the end 1 2 3 4
Process Schedule
139
Consider n processes sharing the CPU in a round robin fashion Assuming that each process switch takes s seconds what must be the quantum size q such that the overhead resulting from process switching is minimized but at the same time each process is guaranteed to get its turn at the CPU at least every t seconds q leq frac t ns n 1 q geq frac t ns n 1 q leq frac t ns n 1 q geq frac t ns n 1
Process Schedule
139
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 algorithms would minimize the average waiting time in the ready queue Shortest remaining time first Round robin with the time quantum less than the shortest CPU burst Uniform random Highest priority first with priority proportional to CPU burst length
Process Schedule
139
When the result of a computation depends on the speed of the processes involved there is said to be cycle stealing race condition a time lock a deadlock
Process Synchronization
140
The following solution to the single producer single consumer problem uses semaphores for synchronization define BUFFSIZE 100 buffer buf BUFFSIZE int first last 0 semaphore b_full 0 semaphore b_empty BUFFSIZE void producer while 1 produce an item p1 put the item into buff first first first 1 BUFFSIZE p2 void consumer while 1 c1 take the item from buf last last last 1 BUFFSIZE c2 consume the item Complete the dotted part of the above solution Using another semaphore variable insert one line statement each immediately after p1 immediately before p2 immediately after c1 and immediately before c2 so that the program works correctly for multiple producers and consumers
Process Synchronization
140
The concurrent programming constructs fork and join are as below fork lt label gt which creates a new process executing from the specified label join lt variable gt which decrements the specified synchronization variable by 1 and terminates the process if the new value is not 0 Show the precedence graph for S1 S2 S3 S4 and S5 of the concurrent program below N 2 M 2 Fork L3 Fork L4 S1 L1 join N S3 L2 join M S5 L3 S2 Goto L1 L4 S4 Goto L2 Next
Process Synchronization
140
Match the pairs in the following questions a Critical region p Hoare s monitor b Wait Signal q Mutual exclusion c Working Set r Principle of locality d Deadlock s Circular Wait
Process Synchronization
140
Let m 0 m 4 be mutexes binary semaphores and P 0 P 4 be processes Suppose each process P i executes the following wait m i wait m i 1 mode 4 release m i release m i 1 mod 4 This could cause Thrashing Deadlock Starvation but not deadlock None of the above
Process Synchronization
140
Each Process P_i i 1 9 is coded as follows repeat P mutex Critical section V mutex forever The code for P_ 10 is identical except it uses V mutex in place of P mutex What is the largest number of processes that can be inside the critical section at any moment 1 2 3 None
Process Synchronization
140
Draw the process state transition diagram of an OS in which i each process is in one of the five states created ready running blocked i e sleep or wait or terminated and ii only non preemptive scheduling is used by the OS Label the transitions appropriately
Process Synchronization
140
Consider the following program segment for concurrent processing using semaphore operators P and V for synchronization Draw the precedence graph for the statements S1 to S9 var a b c d e f g h i j k semaphore begin cobegin begin S1 V a V b end begin P a S2 V c V d end begin P c S4 V e end begin P d S5 V f end begin P e P f S7 V k end begin P b S3 V g V h end begin P g S6 V i end begin P h P i S8 V j end begin P j P k S9 end coend end
Process Synchronization
140
Consider Peterson s algorithm for mutual exclusion between two concurrent processes i and j The program executed by process is shown below repeat flag i true turn j while P do no op Enter critical section perform actions then exit critical section Flag i false Perform other non critical section actions Until false For the program to guarantee mutual exclusion the predicate P in the while loop should be flag j true and turn i flag j true and turn j flag i true and turn j flag i true and turn i
Process Synchronization
140
A solution to the Dining Philosophers Problem which avoids deadlock is to ensure that all philosophers pick up the left fork before the right fork ensure that all philosophers pick up the right fork before the left fork ensure that one particular philosopher picks up the left fork before the right fork and that all other philosophers pick up the right fork before the left fork None of the above
Process Synchronization
140
A certain processor provides a test and set instruction that is used as follows TSET register flag This instruction atomically copies flag to register and sets flag to 1 Give pseudo code for implementing the entry and exit code to a critical region using this instruction
Process Synchronization
140
Draw a precedence graph for the following sequential code The statements are numbered from S_1 to S_6 S_1 read n S_2 i 1 S_3 if i gt n next S_4 a i i 1 S_5 i i 1 S_6 next write a i Can this graph be converted to a concurrent program using parbegin parend construct only
Process Synchronization
140
a Fill in the boxes below to get a solution for the reader writer problem using a single binary semaphore mutex initialized to 1 and busy waiting Write the box numbers 1 2 and 3 and their contents in your answer book L1 int R 0 W 0 Reader wait mutex if W 0 R R 1 u25ad ______________ 1 else u25ad ______________ 2 goto L1 do the read wait mutex R R 1 signal mutex L2 Writer wait mutex if u25ad _________ 3 signal mutex goto L2 W 1 signal mutex do the write wait mutex W 0 signal mutex b Can the above solution lead to starvation of writers
Process Synchronization
140
A critical section is a program segment which should run in a certain amount of time which avoids deadlocks where shared resources are accessed which must be enclosed by a pair of semaphore operations P and V
Process Synchronization
140
Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii
Programming Constructs
141
The goal of structured programming is to have well indented programs be able to infer the flow of control from the compiled code be able to infer the flow of control from the program text avoid the use of GOTO statements
Programming Paradigms
142
Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1
Programming Paradigms
142
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 it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02
Proportions
143
What is the converse of the following assertion I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go
Propositional Logic
144
The proposition p wedge sim p vee q is a tautology logically equivalent to p wedge q logically equivalent to p vee q a contradiction none of the above
Propositional Logic
144
Obtain the principal canonical conjunctive normal form of the propositional formula p wedge q vee eg q wedge r where wedge is logical and vee is inclusive or and eg is negation
Propositional Logic
144
Let p q r s represents 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 x is a prime number The integer x geq2 which satisfies eg left left p Rightarrow q right wedge left eg r vee eg s right right is ____________
Propositional Logic
144
Let p and q be propositions Using only the Truth Table decide whether p Longleftrightarrow q does not imply p o lnot q is True or False
Propositional Logic
144
Let a b c d be propositions Assume that the equivalence a u21d4 b vee eg b and b u21d4c hold Then the truth value of the formula a u2227 b u2192 a u2227 c u2228 d is always True False Same as the truth value of b Same as the truth value of d
Propositional Logic
144
If the proposition lnot p o v is true then the truth value of the proposition lnot p lor left p o q right where lnot is negation lor is inclusive OR and o is implication is a True b Multiple Values c False d Cannot be determined
Propositional Logic
144