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In a file allocation system which of the following allocation scheme s can be used if no external fragmentation is allowed Contiguous Linked Indexed 1 and 3 only 2 only 3 only 2 and 3 only
File System
58
In the index allocation scheme of blocks to a file the maximum possible size of the file depends on the size of the blocks and the size of the address of the blocks the number of blocks used for the index and the size of the blocks the size of the blocks the number of blocks used for the index and the size of the address of the blocks None of the above
File System
58
Indicate whether the following statement is true or false providing a short explanation to substantiate your answers If a language L is accepted by an NFA with n states then there is a DFA with no more than 2 n states accepting L
Finite Automata
59
Consider the following first order logic formula in which R is a binary relation symbol u2200x u2200y R x y implies R y x The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
First Order Logic
60
def graph ext Graph def connected ext Connected Let graph x be a predicate which denotes that x is a graph Let connected x be a predicate which denotes that x is connected Which of the following first order logic sentences DOES NOT represent the statement qquad ext Not every graph is connected lnot forall x Bigl graph x implies connected x Bigr exists x Bigl graph x land lnot connected x Bigr lnot forall x Bigl lnot graph x lor connected x Bigr forall x Bigl graph x implies lnot connected x Bigr
First Order Logic
60
Let a x y b x y and c x y be three statements with variables x and y chosen from some universe Consider the following statement qquad exists x forall y a x y wedge b x y wedge eg c x y Which one of the following is its equivalent forall x exists y a x y vee b x y o c x y exists x forall y a x y vee b x y wedge eg c x y eg forall x exists y a x y wedge b x y o c x y eg forall x exists y a x y vee b x y o c x y
First Order Logic
60
b Consider the following first order formula left matrix forall x exists y R x y 1em Large land 1em forall x forall y Bigl R x y implies lnot R y x Bigr 1em Large land 1em forall x forall y forall z Bigl R x y land R y z implies R x z Bigr 1em Large land 1em forall x lnot R x x right Does it have finite models Is it satisfiable If so give a countable model for it
First Order Logic
60
Consider the following first order logic formula in which R is a binary relation symbol u2200x u2200y R x y implies R y x The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
First Order Logic
60
What is the first order predicate calculus statement equivalent to the following Every teacher is liked by some student u2200 x left ext teacher left x right u2192 u2203 y left ext student left y right u2192 ext likes left y x right right right u2200 x left ext teacher left x right u2192 u2203 y left ext student left y right u2227 ext likes left y x right right right u2203 y u2200 x left ext teacher left x right u2192 left ext student left y right u2227 ext likes left y x right right right u2200 x left ext teacher left x right u2227 u2203 y left ext student left y right u2192 ext likes left y x right right right
First Order Logic
60
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right
Fixed Point Representation
61
Consider a combination of T and D flip flops connected as shown below The output of the D flip flop is connected to the input of the T flip flop and the output of the T flip flop is connected to the input of the D flip flop Initially both Q_ 0 and Q_ 1 are set to 1 before the 1st clock cycle The outputs Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 00 respectively Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 01 respectively Q_ 1 Q_ 0 after the 3rd cycle are 00 and after the 4th cycle are 11 respectively Q_ 1 Q_ 0 after the 3rd cycle are 01 and after the 4th cycle are 01 respectively
Flip Flop
62
Consider a combination of T and D flip flops connected as shown below The output of the D flip flop is connected to the input of the T flip flop and the output of the T flip flop is connected to the input of the D flip flop Initially both Q_ 0 and Q_ 1 are set to 1 before the 1st clock cycle The outputs Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 00 respectively Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 01 respectively Q_ 1 Q_ 0 after the 3rd cycle are 00 and after the 4th cycle are 11 respectively Q_ 1 Q_ 0 after the 3rd cycle are 01 and after the 4th cycle are 01 respectively
Flip Flop
62
In an SR latch made by cross coupling two NAND gates if both S and R inputs are set to 0 then it will result in Q 0 Q 1 Q 1 Q 0 Q 1 Q 1 Indeterminate states
Flip Flop
62
A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100
Flip Flop
62
A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100
Flip Flop
62
A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100
Flip Flop
62
A sequential circuit takes an input stream of 0 s and 1 s and produces an output stream of 0 s and 1 s Initially it replicates the input on its output until two consecutive 0 s are encountered on the input From then onward it produces an output stream which is the bit wise complement of input stream until it encounters two consecutive 1 s whereupon the process repeats An example input and output stream is shown below The input stream 101100 01001011 0 11 The desired output 101100 10110100 0 11 J K master slave flip flops are to be used to design the circuit Give the state transition diagram
Flip Flop
62
A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100
Flip Flop
62
A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100
Flip Flop
62
The exponent of a floating point number is represented in excess N code so that The dynamic range is large The precision is high The smallest number is represented by all zeros Overflow is avoided
Floating Point Representation
63
A 32 bit floating point number is represented by a 7 bit signed exponent and a 24 bit fractional mantissa The base of the scale factor is 16 The range of the exponent is ___________
Floating Point Representation
63
Given the following binary number in 32 bit single precision IEEE 754 format large 00111110011011010000000000000000 The decimal value closest to this floating point number is 1 45 10 1 1 45 10 1 2 27 10 1 2 27 10 1
Floating Point Representation
63
Given the following binary number in 32 bit single precision IEEE 754 format large 00111110011011010000000000000000 The decimal value closest to this floating point number is 1 45 10 1 1 45 10 1 2 27 10 1 2 27 10 1
Floating Point Representation
63
Consider the following floating point format Mantissa is a pure fraction in sign magnitude form The normalized representation for the above format is specified as follows The mantissa has an implicit 1 preceding the binary radix point Assume that only 0 u2019s are padded in while shifting a field The normalized representation of the above number 0 239 imes 2 13 is 0A 20 11 34 49 D0 4A E8
Floating Point Representation
63
Given the following binary number in 32 bit single precision IEEE 754 format large 00111110011011010000000000000000 The decimal value closest to this floating point number is 1 45 10 1 1 45 10 1 2 27 10 1 2 27 10 1
Floating Point Representation
63
The exponent of a floating point number is represented in excess N code so that The dynamic range is large The precision is high The smallest number is represented by all zeros Overflow is avoided
Floating Point Representation
63
The following is a scheme for floating point number representation using 16 bits Bit Position 15 14 9 8 0 s e m Sign Exponent Mantissa Let s e and m be the numbers represented in binary in the sign exponent and mantissa fields respectively Then the floating point number represented is begin cases 1 s left 1 m imes 2 9 right 2 e 31 amp ext if the exponent eq 111111 0 amp ext otherwise end cases What is the maximum difference between two successive real numbers representable in this system 2 40 2 9 2 22 2 31
Floating Point Representation
63
The exponent of a floating point number is represented in excess N code so that The dynamic range is large The precision is high The smallest number is represented by all zeros Overflow is avoided
Floating Point Representation
63
A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1
Fork
64
A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1
Fork
64
Consider the following code fragment if fork 0 a a 5 printf d p n a amp a else a a 5 printf d p n a amp a Let u v be the values printed by the parent process and x y be the values printed by the child process Which one of the following is TRUE u x 10 and v y u x 10 and v y u 10 x and v y u 10 x and v y
Fork
64
A process executes the code fork fork fork The total number of child processes created is 3 4 7 8
Fork
64
A process executes the code fork fork fork The total number of child processes created is 3 4 7 8
Fork
64
A process executes the code fork fork fork The total number of child processes created is 3 4 7 8
Fork
64
A process executes the following code for i 0 i lt n i fork The total number of child processes created is n 2n 1 2n 2n 1 1
Fork
64
A process executes the code fork fork fork The total number of child processes created is 3 4 7 8
Fork
64
A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1
Fork
64
A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1
Fork
64
A process executes the following code for i 0 i lt n i fork The total number of child processes created is n 2n 1 2n 2n 1 1
Fork
64
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND
Functional Completeness
65
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND
Functional Completeness
65
The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete
Functional Completeness
65
The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete
Functional Completeness
65
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND
Functional Completeness
65
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND
Functional Completeness
65
The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete
Functional Completeness
65
The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete
Functional Completeness
65
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND
Functional Completeness
65
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND
Functional Completeness
65
The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete
Functional Completeness
65
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND
Functional Completeness
65
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND
Functional Completeness
65
Form the following instance of a relation schema R A B C we can conclude that A B C 1 1 1 1 1 0 2 3 2 2 3 2 A functionally determines B and B functionally determines C A functionally determines B and B does not functionally determine C B does not functionally determine C A does not functionally determine B and B does not functionally determine C
Functional Dependencies
66
Relation R has eight attributes ext ABCDEFGH Fields of R contain only atomic values F ext CH u2192G A u2192BC B u2192CFH E u2192A F u2192EG is a set of functional dependencies FDs so that F is exactly the set of FDs that hold for R How many candidate keys does the relation R have 3 4 5 6
Functional Dependencies
66
What is the generating function G z for the sequence of Fibonacci numbers
Generating Functions
68
The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________
Generating Functions
68
The coefficient of x 3 in the expansion of 1 x 3 2 x 2 10 is 2 14 31 left frac 3 3 right left frac 10 1 right left frac 3 3 right 2 left frac 10 1 right left frac 3 3 right left frac 10 1 right 2 9
Generating Functions
68
The coefficient of x 3 in the expansion of 1 x 3 2 x 2 10 is 2 14 31 left frac 3 3 right left frac 10 1 right left frac 3 3 right 2 left frac 10 1 right left frac 3 3 right left frac 10 1 right 2 9
Generating Functions
68
The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________
Generating Functions
68
The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________
Generating Functions
68
If the ordinary generating function of a sequence big a_n big _ n 0 infty is large frac 1 z 1 z 3 then a_3 a_0 is equal to ___________
Generating Functions
68
If the ordinary generating function of a sequence big a_n big _ n 0 infty is large frac 1 z 1 z 3 then a_3 a_0 is equal to ___________
Generating Functions
68
The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________
Generating Functions
68
The coefficient of x 3 in the expansion of 1 x 3 2 x 2 10 is 2 14 31 left frac 3 3 right left frac 10 1 right left frac 3 3 right 2 left frac 10 1 right left frac 3 3 right left frac 10 1 right 2 9
Generating Functions
68
If the ordinary generating function of a sequence big a_n big _ n 0 infty is large frac 1 z 1 z 3 then a_3 a_0 is equal to ___________
Generating Functions
68
A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96
Geometry
69
A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96
Geometry
69
In a triangle PQR PS is the angle bisector of angle QPR ext and angle QPS 60 circ What is the length of PS left dfrac q r qr right left dfrac qr q r right large sqrt q 2 r 2 left dfrac q r 2 qr right
Geometry
69
In a triangle PQR PS is the angle bisector of angle QPR ext and angle QPS 60 circ What is the length of PS left dfrac q r qr right left dfrac qr q r right large sqrt q 2 r 2 left dfrac q r 2 qr right
Geometry
69
When a point inside of a tetrahedron a solid with four triangular surfaces is connected by straight lines to its corners how many new internal planes are created with these lines
Geometry
69
A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96
Geometry
69
A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96
Geometry
69
A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96
Geometry
69
A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96
Geometry
69
In a triangle PQR PS is the angle bisector of angle QPR ext and angle QPS 60 circ What is the length of PS left dfrac q r qr right left dfrac qr q r right large sqrt q 2 r 2 left dfrac q r 2 qr right
Geometry
69
A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96
Geometry
69
When a point inside of a tetrahedron a solid with four triangular surfaces is connected by straight lines to its corners how many new internal planes are created with these lines
Geometry
69
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70
An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code
Goto
70