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MATCH ITEMS

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Match the following:-

Q1.A (00)* 1 Set of all 0s

B 0(00)* 2 Set of alleven numberof 0s

C 00(00)*+0(00)* 3 Set of all oddnumber of0s

D 0* 4 Set of all 0s

excluding 5 Set of all 0s

which aremultiples ofthree andfour

6 Set of all 0swhich aremultiples ofthree

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6

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(iv) A->2,B->3,C->4,D->1

Q2.

A (00)*(11)* 1 Set of allstrings over{0,1} notcontaining a1

B 0(00)*(11)* 2 Set of alleven numberof 0sfollowed byan evennumber of1s

C 00(00)*+0(00)* 3 Set of all odd

number of0s followedby an evnnumber of1s

D 0* 4 Set of all 0s

excluding 5 Set of all 0swhich are

multiples ofthree andfour

6 Set of all 0s

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which aremultiples ofthree

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q3.

A (0+10)*(+1) 1 Set of allstrings over

{0,1} notcontainingtwoconsecutive0s

B 0(00)* 2 Set of allstrings over

{0,1} notcontainingtwoconsecutive1s

C 00(00)*+0(00)* 3 Set of all odd

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number of0s

D (1+01)*(+0) 4 Set of all 0sexcluding

5 Set of all 0swhich aremultiples ofthree andfour


Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q4.A (0+10)*(+1) 1 Set of allstrings over{0,1} notcontainingtwo

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consecutive0s

B (0+10+110)*(+1+11) 2 Set of allstrings over{0,1} notcontainingtwoconsecutive1s

C (1+01+001)*(+0+00) 3 Set of allstrings over

{0,1} notcontainingthreeconsecutive1s.

D (1+01)*(+0) 4 Set of allstrings

over{0,1}notcontainingthreeconsecutive0s.

5 Set of all 0s


6 Set of all 0swhich are

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multiples ofthree

Answer:


(iv) A->2,B->3,C->4,D->1

Q5.

A (0+10)*(+1) 1 Set of allstrings over{0,1} not

containingtwoconsecutive0s

B (0+10+110)*(+1+11) 2 Set of allstrings over{0,1} not


C [00+11+(01+10)(00+11)*(01+10)]* 3 Set of allstrings over

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{0,1} notcontainingthree

consecutive1s.

D (1+01)*(+0) 4 Set of allstrings over{0,1}containingan evennumber of

0s and anevennumber of1s.

5 Set of all0s whichare


6 Set of all0s whicharemultiples of

three

Answer:

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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q6.

A (11+0)*(00+1)* 1 Set of allstrings over{0,1} not


B (0+10+110)*(+1+11) 2 Set of allstrings over{0,1}where

in somehead of thestring the1s occur inconsecutivepairs andin the tail

of thestring the0s occur inconsecutivepairs

C [00+11+(01+10)(00+11)*(01+10)]* 3 Set of all

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strings over{0,1} notcontaining

threeconsecutive1s.

D (1+01)*(+0) 4 Set of allstrings over{0,1}containingan even

number of0s and anevennumber of1s.

5 Set of all0s which

aremultiples ofthree andfour


multiples ofthree

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Answer:


Q7.

A (11+0)*(00+1)* 1 Set of allstrings over

{0,1} notcontaining twoconsecutive 0s

B (01+10)* 2 Set of allstrings over{0,1}where insome head of

the string the1s occur inconsecutivepairs and inthe tail of thestring the 0soccur in

consecutivepairs

C [00+11+(01+10)(00+11)*(01+10)]* 3 Set of allstrings over{0,1}containingan equal

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number of 0sand 1s whereevery prefix

has at mostone more 0than 1s or atmost one more1 than 0s.

D (1+01)*(+0) 4 Set of allstrings over{0,1}

containing aneven numberof 0s and aneven numberof 1s.


multiples ofthree and four


Answer:

(i) A1,B->2,C->3,D->4

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(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q8.

A (11+0)*(00+1)* 1 Set of allstrings over{0,1} ending in00.

B (01+10)* 2 Set of allstrings over{0,1}where insome head ofthe string the1s occur inconsecutivepairs and in

the tail of thestring the 0soccur inconsecutivepairs

C [00+11+(01+10)(00+11)*(01+10)]* 3 Set of allstrings over

{0,1}containingan equalnumber of 0sand 1s whereevery prefixhas at most

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one more 0than 1s or atmost one more

1 than 0s.D (0+1)*00 4 Set of allstrings over{0,1}containing aneven numberof 0s and aneven number

of 1s.5 Set of all 0s

which aremultiples ofthree and four


multiples ofthree

Answer:


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Q9.

A (11+0)*(00+1)* 1 Set of allstrings over{0,1} notcontaining twoconsecutive 0s

B (01+10)* 2 Set of allstrings over

{0,1}where insome head ofthe string the1s occur inconsecutivepairs and inthe tail of thestring the 0s

occur inconsecutivepairs

C (0+1)*000(0+1)* 3 Set of allstrings over{0,1}containingan equal

number of 0sand 1s whereevery prefixhas at mostone more 0

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than 1s or atmost one more1 than 0s.

D (1+01)*(+0) 4 Set of allstrings over{0,1}containingthreeconsecutive0s.

5 Set of all 0s

which aremultiples ofthree and four


Answer:


Q10.

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A (11+0)*(00+1)* 1 Set of allstrings over{0,1} where

every pair ofconsecutive 0soccurs beforeany pair ofadjacent 1s.

B (01+10)* 2 Set of allstrings over{0,1}where in

some head ofthe string the1s occur inconsecutivepairs and inthe tail of thestring the 0s

occur inconsecutivepairs

C (0+1)*000(0+1)* 3 Set of allstrings over{0,1}containingan equal

number of 0sand 1s whereevery prefixhas at mostone more 0than 1s or at

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most one more1 than 0s.

D (0+10)*(1+10)* 4 Set of all

strings over{0,1}containingthreeconsecutive0s.


multiples ofthree and four


Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q11.

A L=(0+1)*00(0+1)*00(0+1)* 1 Set of all

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Intersection(0+1)*11(0+1)*11(0+1)*consider the complement of

L

strings over{0,1} whereevery pair of

consecutive 0soccurs beforeany pair ofadjacent 1s.

B (01+10)* 2 Set of allstrings over{0,1}containingat most one

pair ofconsecutive 0sand at mostone pair ofconsecutive1s.

C (0+1)*000(0+1)* 3 Set of all

strings over{0,1}containingan equalnumber of 0sand 1s whereevery prefixhas at most

one more 0than 1s or atmost one more1 than 0s.

D (0+10)*(1+10)* 4 Set of allstrings over

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{0,1}containingthree

consecutive0s.

5 Set of all 0swhich aremultiples ofthree and four


multiples ofthree

Answer:


Q12.

A 0*(10*)* 1 Set of all strings over{0,1} where every pairof consecutive 0soccurs before any

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pair of adjacent 1s.

B (01+10)* 2 1*(01*)*

C The complement

of(0+1)*000(0+1)*

3 Set of all strings over

{0,1}containing anequal number of 0sand 1s where everyprefix has at mostone more 0 than 1sor at most one more 1than 0s.

D (0+10)*(1+10)* 4 (1+01+001)*(+0+00) 5 Set of all 0s which

are multiples of threeand four

6 (000)*

Answer:


Q13.

A 0*(10*)* 1 (Ra)* R

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B (01+10)* 2 1*(01*)*

C The complementof

(0+1)*000(0+1)*

3 Set of all strings over{0,1}containing an

equal number of 0sand 1s where everyprefix has at mostone more 0 than 1sor at most one more 1than 0s.

D R (aR)* where aand R are some

regularexpressions

4 (1+01+001)*(+0+00)

5 Set of all 0s whichare multiples of threeand four

6 (000)*

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q14.

A 0*(10*)* 1 (Ra)* R

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B (r*s*)**** 2 1*(01*)*

C The complementof

(0+1)*000(0+1)*

3 (r+s)*

D R (aR)* where aand R are someregularexpressions

4 (1+01+001)*(+0+00)

5 Set of all 0s whichare multiples of threeand four

6 (000)*

Answer:


Q15.A 0*(10*)* 1 (Ra)* R

B (r*s*)**** 2 1*(01*)*

C (+R)* 3 (r+s)*D R (aR)* 4 R*

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where a andR are someregular

expressions 5 Set of all 0swhich aremultiples ofthree andfour

6 (000)*

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q16.

A (R*+S*)*RR 1 (Ra)* R

B (r*s*)**** 2 (R+S)*RRC (+R)* 3 (r+s)*D R (aR)*


4 R*

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expressions



6 (000)*

Answer:


Q17.

A (R*+S*)*RR 1 (Ra)* R

B (R+R+R+R)R 2 (R+S)*RR

C (+R)* 3 RRD R (aR)*

where a and

R are someregularexpressions

4 R


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6 (000)*

Answer:


Q18.

A R(S+T) 1 (Ra)* RB (R+R+R+R)R 2 (RS+RT)

C (+R)* 3 RRD R (aR)*


expressions

4 R


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6 (000)*

Answer:


Q19.

A R(S+T) 1 RT+ST

B (R+R+R+R) 2 RS+RT

C (+R)*R 3 RD (R+S)T 4 RR


6 (000)*

Answer:

(i) A1,B->2,C->3,D->4

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(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q20.

A R(S+T) 1 RT+ST

B (R+R+R+R) 2 RS+RT

C R+S 3 R

D (R+S)T 4 S+R


6 (000)*

Answer:


(iv) A->2,B->3,C->4,D->1

Q21.

A R(S+T)T 1 RT+ST

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B (R+S)+T 2 RST+RTT

C R+S 3 (R+S)+T

D (R+S)T 4 S+R


6 (000)*

Answer:


(iv) A->2,B->3,C->4,D->1

Q22.

A R(S+T)T 1 RT+ST

B (R+S)+T 2 RST+RTT

C R+S 3 (R+S)+T

D (R+S)T 4 S+R5 Set of all 0s

which aremultiples ofthree and

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(iv) A->2,B->3,C->4,D->1

Q24.

A * 1 RT+STB (R+S)+T 2 C (RS)T 3 (R+S)+T

D (R+S)T 4 (RS)T


6 (000)*

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q25.

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A * 1 B (R+S)+T 2 C (RS)T 3 (R+S)+T

D * 4 (RS)T5 Set of all 0s


6 (000)*

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q26.

A * 1 B (R+S)+T 2 C R(ST) 3 (R+S)+TD * 4 (RS)T

5 Set of all 0swhich aremultiples of

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three andfour

6 (000)*

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q27.

A * 1 B (R+S)+T 2 C (00)*(1+01) 3 (R+S)+TD * 4 0*1


6 (000)*

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Answer:


Q28.

A * 1 B ((0+1)(0+1)(0+1))*+((0+1)(0+1)(0+1)(0+1))* 2 C (RS)T 3 Set of all

stringsover{0,1}whicharemultiples

of threeor four

D * 4 (RS)T5 Set of all

0swhichare

multiplesof threeand four

6 Set of allstrings

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over{0,1}which

aremultiplesof threeand four

Answer:


Q29.

A * 1 B ((0+1)(0+1)(0+1))*+((0+1)(0+1)(0+1)(0+1))* 2 C

Consider the set accepted by the finiteautomata

3 Set of allstringsover

{0,1}whicharemultiplesof threeor four

a

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D

Consider the set accepted by the finiteautomata

4 +a

5 Set of all

0swhicharemultiplesof threeand four

6 Set of all

stringsover{0,1}whicharemultiplesof three

and four

Answer:

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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q30.

A Consider the setaccepted by thefinite automata,

M=({q},{0,1},,{q})(q,0)=q,(q,1)=q

1

B Consider the setaccepted by thefinite automata,

M=({q},{0,1},,{q})(q,0)=q,(q,1)=

2 (0+1)*(0+1)*

C Consider the setaccepted by thefinite automata,

M=({q},{0,1},,{q})(q,0)=,(q,1)=q

3 0*0*0*

D (Consider the setaccepted by the

finite automata,M=({q},{0,1},,{q})(q,0)=(q,1)=

4 1*1*1*


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6 (000)*

Answer:


Q31.

A Consider the set acceptedby the finite automata,

M=({a,b,c},{0,1},,{q})(a,0)=a,(a.1)=b,(b,1)=b,

(b,0)=c,(c,0)=c,(c,1)=c

1

B Consider the set acceptedby the finite automata,

M=({q},{0,1},,{q})(q,0)=q,(q,1)=

2 0*0*1*1*

C Consider the set acceptedby the finite automata,

M=({q},{0,1},,{q})3 0*0*0*

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(q,0)=,(q,1)=qD (Consider the set accepted

by the finite automata,

M=({q},{0,1},,{q})(q,0)=(q,1)=

4 1*1*1*

5 Set of all0s whicharemultiplesof threeand four

6 (000)*

Answer:


Q32.

A Consider the set accepted bythe finite automata,

M=({q},{0,1},,{q})(q,0)=q,(q,1)=q

1 (01+10)*

B Consider the set accepted by 2 (0+1)*(0+1)*

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the finite automata,

M=({q},{0,1},,{q})(q,0)=q,(q,1)=

C Consider the set accepted bythe finite automata,

M=({q},{0,1},,{q})(q,0)=,(q,1)=q

3 0*0*0*

D Consider the set accepted bythe finite automata,

M=({q0,q1,q2,q3},{0,1},,{q})(q0,0)=q1,(q0,1)=q2,(q1,1)=q0,(q1,0)=q3,(q2,0)=q0,(q2,1)=q3,(q3,0)=q3,(q3,1)=q3

4 1*1*1*

5 Set of all 0swhich aremultiples of

three andfour

6 (000)*

Answer:


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Q33.A Consider the set accepted bythe finite automata,

M=({q},{0,1},,{q})(q,0)=q,(q,1)=q

1 Set of allstringsover {0,1}with anequalnumber of0s and 1s

whereeveryprefix hasat mostone more0 than 1 orat most

one more1 than a 0.

B Consider the set accepted bythe finite automata,

M=({q},{0,1},,{q})(q,0)=q,(q,1)=

2 The set ofall stringsover {0,1}

C Consider the set accepted by

the finite automata,M=({q},{0,1},,{q})

(q,0)=,(q,1)=q

3 The set of

all 0s


4 The set ofall 1s

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5 Set of all0s whicharemultiplesof three

and four6 (000)*

Answer:


(iv) A->2,B->3,C->4,D->1

Q34.

A Consider the regular setdenoted by

(1+01+001)*(+0+00)1 Set of all

stringsover {0,1}with anequal

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number of0s and 1swhere

everyprefix hasat mostone more 0than 1 orat mostone more 1than a 0.

B Consider the set denoted by(0+1)*(00+11)

2 Theminimalfiniteautomatahas threestates

C Consider the set accepted by

the finite automata,M=({q},{0,1},,{q})

(q,0)=,(q,1)=q

3 The

minimalfiniteautomatahas 5states



4 The set ofall 1s

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multiplesof threeand four

6 (000)*

Answer:


Q35.

A Consider the regular setdenoted by

(1+01+001)*(+0+00)1 The

minimalfiniteautomatahas four

statesB Consider the set denoted by(0+1)*(00+11)

2 Theminimalfiniteautomatahas three

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states

C Consider the set denoted bythe regular expression

(00)*+(0000)*+(000000)*

3 Theminimal

finiteautomatahas 5states



4 Theminimalfiniteautomata

has twostates

5 Set of all0s whicharemultiples

of threeand four

6 (000)*

Answer:


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(iv) A->2,B->3,C->4,D->1

Q36.A Consider the regular setdenoted by(0+1)*1(0+1)(0+1)(0)

1 Theminimalfiniteautomatahas fourstates

B Consider the set denoted by(0+1)*(00+11)

2 Theminimalfiniteautomatahas 8states

C Consider the set denoted bythe regular expression

(00)*+(0000)*+(000000)*

3 Theminimal

finiteautomatahas 5states



4 Theminimalfinite

automatahas twostates

5 Set of all

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0s whicharemultiples

of threeand four

6 (000)*

Answer:


Q37.A Consider the

regular setthe set of allstrings over{0,1} notcontaining 1

as asubstring

1 The minimalfiniteautomatahas 5 states

B Consider theregular setthe set of allstrings over


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{0,1} notcontaining11 as a

substringC Consider theregular setthe set of allstrings over{0,1} notcontaining111as a

substring


D Consider theregular setthe set of allstrings over{0,1} notcontaining

1111 as asubstring



6 (000)*

Answer:

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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q38.

A Consider theregular set theset of all

strings over{0,1} notcontaining101 as asubstring

1 The minimalfiniteautomata

has 3 states

B Consider theregular set the

set of allstrings over{0,1} startingwith a 1 thatinterpreted asthe binaryrepresentation

of an integerare congruentto 0 modulo 5

2 The minimalfinite

automatahas 4 states

C Consider theregular set theset of all

3 The minimalfiniteautomata

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strings over{0,1} wherethe 10th

symbol fromthe right endis a 1

has 7 states

D Consider theregular set theset of allstrings over{0,1} ending

in 00

4 The minimalfiniteautomatahas 1024states

5 Tsheminimalfiniteautomatahas 1000states

6 No minimalfiniteautomataexists

Answer:


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(iv) A->2,B->3,C->4,D->1

Q39.A Consider theregular setthe set of allstrings over{0,1} wherethe 1s aredivisible by

10 and the0s aredivisible by11


B Consider theregular setthe set of all

strings over{0,1} wherethe 0ss aredivisible the3 and the 1sby 2

2 The minimalautomatahas 110

states

C Consider the

regular setthe set of allstrings over{0,1} wherethe 0s aredivisible by 6

3 The minimal

finiteautomatahas 6 states

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and the 1sdivisible by 8

D Consider the

regular setthe set of allstrings over{0,1} notcontaining1111 as asubstring

4 The minimal


5 The minimal


6 The minimalfiniteautomatahas 890

states

Answer:

(i) A

1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

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Q40.

A Consider adeterministic

finiteautomatawith inputalphabet{0,1} of10^1000states whichhas no final

state

1 The empty string isnot accepted

B Consider adeterministicfiniteautomatawith inputalphabet

{0,1} of10^1000states whereall the statesare finalstates

2 The emptyset isaccepted

C Consider a

deterministicfiniteautomataover thealphabet{0,1} of

3 (0+1)* is

accepted

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10^1000states wherethe start state

is the finalstate

D Consider adeterministicfiniteautomata of10^1000states over

the alphabet{0,1} wherethe start stateis not a finalstate

4 The emptystring isacepted

5 0 is accepted

6 1 is accepted

Answer:


Q41.

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A Consider anondeterministicfinite automata

with inputalphabet {0,1} of10^1000 stateswhich has nofinal state

1 The empty string isnot accepted

B Consider anondeterministicfinite automata

with inputalphabet {0,1} of10^1000 stateswhere all thestates are finalstates

2 The emptyset isaccepted

C Consider a

nondeterministicfinite automataover thealphabet {0,1} of10^1000 stateswhere the startstate is the final

state

3 (0+1)* is

accepted

D Consider anondeterministicfinite automataof 10^1000states over the

4 The emptystring isacepted

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alphabet {0,1}where the startstate is not a

final state 5 0 is accepted

6 1 is accepted

Answer:


Q42.A Deterministic

finite automata1 r.e. sets

B Deterministicpush downautomata

2 Regular sets

C Nondeterministic

linear boundedauotmata

3 Deterministic

context freelanguages

D Deterministicturing machines

4 Contextsensititvelanaugages

5 Context free

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languages

6 Recursivesets

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q43.

A Nondeterministic

finite automata

1 r.e. sets

B push downautomata

2 Regular sets

C Nondeterministiclinear boundedauotmata

3 context freelanguages

D Nondeterministic

turing machines

4 Context sensitive

lanaugages5 Deterministiccontext freelanguageslanguages

6 Recursive sets

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Answer:


Q44.

A Two waydeterministicfinite automata

1 r.e. sets

B Deterministicpush down

automata

2 Regular sets


3 Deterministiccontext freelanguages

D Multitape turingmachines

4 Contextsensitivelanaugages

5 Context freelanguages

6 Recursivesets

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Answer:


Q46.

A Halting 100pushdown tapemachines

1 r.e. sets


automata

2 Recursivesets



D 10000 countermachines



6 Regular sets

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Answer:


Q47.

A Turing machinesthat have no ink

1 r.e. sets


automata

2 Regular sets






6 Recursivesets

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sets

Answer:


Q50.

A Multidimensional,multitape,multiheadedturing machines

with 1098 pushdown tapes but noink

1 r.e. sets


2 Regular sets

C Nondeterministic

linear boundedauotmata

3 Deterministic




5 Context free

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languages

6 Recursivesets

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q51.

A Deterministicfinite automata

1 Recursivesets


2 Regular sets



D Deterministic

halting turingmachines

4 Context

sensititvelanaugages


6 R.e. sets

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Answer:


Q52.

A Type 3grammars

1 r.e. sets

B LR(k)grammars

2 Regular sets

C Type 1

grammars

3 Deterministic


D Type 0grammars

4 Contextsensititvelanaugages


6 Recursivesets

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Answer:


Q53.

A Deterministicfinite automata

1 Type 0languages


2 Type 3languages



D Deterministic

turing machines

4 Type 1

languages5 Type 2

languages

6 Recursivesets

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

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(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q54.

A Deterministicfiniteautomata

1 Proceduresthatare notnecessarilyalgorithms


2 Regular sets

C Halting twopushdowntapemachines


D Deterministicturing

machines

4 Algorithms


6 Recursive sets

Answer:


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(iv) A->2,B->3,C->4,D->1

Q55.A The set of allstrings over{0,1} withany numberof 0s andany numberof 1s

1 Recursive setthat is notcontextsensitive

B The set of allstrings over{0,1} with anequalnumber of0s and 1s

2 Regular setbut not a dcfl

C The set of all

strings over{0,1,2} withan equalnumber of0s, 1s and2s.

3 Deterministic

context freelanguage

D The set of

regularexpressionswhosecomplementis empty

4 Context

sensititvelanguagethat is notcontext free

5 r.e but not

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recursive

6 Finite set

Answer:


(iv) A->2,B->3,C->4,D->1

Q56.

A The set of allstrings over{0,1} with

any numberof 0s andany numberof 1s

1 Recursive setthat is notcontext

sensitive

B The set of allpalidromesover {0,1}


C The set of allstrings over{0,1,2} withan equalnumber of0s, 1s and

3 context freelanguage

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strings over{0,1} with anequal

number of0s and 1s

but not a dcfl

C The set of allstrings over{0,1,2}of theform wwwhere w is astring in

{0,1,2}+

3 Deterministiccontext freelanguage

D The set ofregularexpressionswhosecomplementis empty

4 Contextsensititvelanguagethat is notcontext free

5 r.e but notrecursive

6 Finite set

Answer:


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Q58.

A The set of allstrings over{0,1} withany numberof 0s andany numberof 1s

1 Recursive set

B The set of allstrings over{0,1} not ofthe form ww,w in {0,1}+


C The set of allstrings over{0,1,2} with

an equalnumber of0s, 1s and2s.


D The set ofregularexpressions

whoseintersectionis empty

4 Contextsensititvelanguage

that is notcontext free


6 Finite set

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Answer:


Q59.

A The set of allstrings over{0,1} withany numberof 0s and

any numberof 1s

1 Recursive set

B The set of allstrings over{0,1} with anunequalnumber of

0s and 1s


C The set of allstrings over{0,1,2} withan equalnumber of


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0s, 1s and2s.

D The set of

regularexpressionswhosecomplementis empty

4 Context

sensititvelanguagethat is notcontext free


6 Finite set

Answer:


Q61.

A The set of all

strings over{0,1} notcontainingthreeconsecutive0s and not

1 Recursive set

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containingthreeconsecutive

1s.B The set of allstrings over{0,1,2} withan unequalnumber of0s and 1sor an

unequalnumber of1s and 2s


C The set of allstringsprimes inunary.


D The set ofregularexpressionswhosecomplementis empty


5 r.e but not

recursive6 Finite set

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Answer:


(iv) A->2,B->3,C->4,D->1

Q62.

A The set of allpowers of 2in binary

1 Recursive set

B The set of allstringspalidromesover a finite

alphabet


C The set of allstringsprimes inunary.


D The set ofregular

expressionswhosecomplementis empty

4 Contextsensititve

languagethat is notcontext free


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6 Finite set

Answer:


Q63.

A The set of allpowers of 2in binary

1 Recursive set

B The set of all

strings withan equalnumber of0s and 1sor with twiceas many 0sas 1s.

2 Regular set

but not a dcfl

C The set of allstrings thatare notprimes inbinary.


The set of 4 ContextD

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complement is empty languagethat is notcontext free


6 Finite set

Answer:


Q65.A The set of all powers of

20 in base 201 Recursive

set

B {0^m1^n0^(m+n)|m,n>1} 2 Regular setbut not adcfl

C {wwRw|w in {0,1}+} 3 context

freelanguage

D The set of regularexpressions whosecomplement is empty

4 Contextsensititvelanguagethat is not

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context free


6 Finite set

Answer:


Q66.

A The set of all powers of

20 in base 20

1 Recursive

setB {0^m1^n0^(m+n)|m,n>1} 2 Regular set

but not adcfl

C {a^nb^n^2|n>1} 3 contextfreelanguage



5 r.e but not

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recursive

6 Finite set

Answer:


(iv) A->2,B->3,C->4,D->1

Q67.

A The set of all powers of20 in base 20

1 Recursiveset

B {0^m1^n0^(m+n)|m,n>1} 2 Regular set

but not adcfl

C {a^Ib^j|gcd(I,j)=1} 3 contextfreelanguage

D The set of regularexpressions whose

complement is empty

4 Contextsensititve

languagethat is notcontext free


6 Finite set

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Answer:


Q68.

A The set of all powers of200 in base 200

1 Recursiveset

B {0^m1^n0^(m+n)|m,n>1} 2 Regular setbut not adcfl

C {a^Ib^jc^k|I not equal toj not equal to k}

3 contextfreelanguage


4 Contextsensititvelanguagethat is not

context free 5 r.e but notrecursive

6 Finite set

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Answer:


Q69.

A The set of all strings ovesr{0,1} not containing0000000001111111100000as a substring

1 Finite set

B {0^m1^n0^(m+n)|m,n>1} 2 Regular set

but not adcfl

C {a^Ib^jc^k|I not equal to jnot equal to k}

3 contextfreelanguage

D {0^n1^n| n

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set notnecessarilya context

sensitivelanguage

Answer:


Q70.

A S-a|aS|b|bS 1 Finite setB SaSb|ab 2 Regular set

but not a dcfl

C {a^Ib^jc^k|Inot equal to jnot equal to

k}


D {0^n1^n|n

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6 Recursive set

notnecessarily acontextsensitivelanguage

Answer:


Q71.

A S-a|aS|b|bS 1 Finite setB SaSa|bSb|a|b 2 Regular set

but not a

dcflC {a^Ib^jc^k|Inot equal to jnot equal to k}


D {0^n1^n|n

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lakh} languagethat is notcontext free


6 Recursive setnotnecessarily acontextsensitivelanguage

Answer:


(iv) A->2,B->3,C->4,D->1

Q72.

A S-a|aS|b|bS 1 Finite setB S

aSa|bSb|a|b 2 Regular setbut not a

dcfl

C SaSBC|aBCCBBCaBab


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bBbbbCbccCcc

D S

a|b|c|d 4 Contextsensititvelanguagethat is notcontext free



Answer:


(iv) A->2,B->3,C->4,D->1

Q73.

A S-a|aS|b|bS 1 Finite setB SaSa|bSb|a|b 2 Regular set but not

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B SaSa|bSb|a|b 2 Regular set but nota dcfl

C SaSBC|aBCCB

BCaBabbBbbbCbccCcc

3 context free

language

D SCWaDWaaaWWDEWaEEaCECWWDFWaFWFwaCFW

4 The set{a^nb^nc^n|n>=1}


6 Recursive set notnecessarily acontext sensitivelanguage

Answer:


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(iv) A->2,B->3,C->4,D->1

Q75.A S-a|aS|b|bS 1 Unrestrictedgrammar

B SaSa|bSb|a|b 2 Regulargrammar

C SaSBC|aBCCBBCaBabbBbbbCbccCcc

3 Context freegrammar

D SCWaDWaaaWWDEWaEEaCECWWDFWaFWFwaCFW

4 Contextsensitivegrammar


6 Recursive set

notnecessarily acontextsensitivelanguage

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Answer:


Q76.

A S-a|aS|b|bS 1 Type 0B SaSa|bSb|a|b 2 Type 3C SaSBC|aBC

CBBCaBabbBbbbCbccCcc

3 Type 2

D SCWaDWaaaWWDEWaEEaCE

CWWDFWaFWFwaCFW

4 Type 1


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6 Type 4

Answer:


Q77.

A All C programs 1 Unrestrictedgrammar

B SaSa|bSb|a|b 2 ProceduresC SaSBC|aBC

CBBCaBabbBbbbCbccCcc

3 Context free

grammar

D SCWaDWaaaWWD

EWaEEaCECWWDFWaFWFwaCFW

4 Contextsensitive

grammar

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5 Not r.e.

6 Recursive setnot

necessarily acontextsensitivelanguage

Answer:


Q78.

A Halting C andJava programs

1 Unrestrictedgrammar

B SaSa|bSb|a|b 2 AlgorithmsC SaSBC|aBC

CBBCaB

abbBbbbCbccCcc

3 Context freegrammar

D SCWaDWaaaW

4 Contextsensitive

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WDEWaEEaCECWWD

FWaFWFwaCFW

grammar



Answer:


Q79.

A r.e. sets 1 Closed undercomplementbut notunder union

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orintersection

B Recursive

sets

2 Not closed

undercomplementbut closedunder unionandintersection

C Context freelanguages

3 Closed underunion,

intersectionandcomplement

D Deterministiccontext freelanguages

4 Closed underunion andintersectionbut not

undercomplement

5 Not closedunder unionbut closedunderintersection

6 Not closedunder unionorcomplement

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4 Closed underunion andintersection

but notundercomplement



Answer:


Q81.

A Finite sets 1 Closed undercomplementbut not

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under unionorintersection

B Recursivesets 2 Not closedundercomplementbut closedunder unionandintersection

C Context free

languages

3 Closed under

union,intersectionandcomplement


4 Closed underunion andintersection

but notundercomplement

5 Not closedunder unionbut closedunder

intersection6 Not closedunder unionorcomplement

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Answer:


Q82.

A The cliqueproblem

1 Decidable

B The 2-CNFproblem

2 NP-complete

C The

equivalenceof context-freelanguages

3 Is in P

D Equivalenceof finiteautomata

4 Undecidable

5 Not closed

under unionbut closedunderintersection

6 Not closed

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under unionorcomplement

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q83.

A TheHamiltonian

circuitproblem

1 Decidable

B The 2-CNFproblem

2 NP-complete

C Theequivalenceof a context-

free to *where isthe inputvocabulary.

3 Is in P

D The 4 Undecidable

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membershipproblem ofcontext

sensitivelanguages


6 Not closed


Answer:


Q84.

A Theknapsackproblem

1 Decidable

B The 2-CNF 2 NP-complete

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problem

C Theequivalence

of twodeterministicturingmachines

3 Is in P

D Whether acontext freelanguage isfinite,

infinite orempty

4 Undecidable



Answer:


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(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q86

A All formallanguages

1 Decidable

B The class ofregular sets

2 Areuncountable

C Whether aturingmachine willhalt on blanktape

3 Countablyinfinite

D Whether aturingmachine willever leave an

input region

4 Undecidable


6 Not closed


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Answer:


Q87.

A {w$w| w in (0+1)*} 1 Finite set

B {wwR|in (0+1)*} 2 Deterministiccontext freelanguage

C {wwwwwwwwR|w

in(0+1)+}

3 Context free

languagethat is notdeterministic

D The set of all stringsnot containing0000000000001111000over {0,1} of length

less than 10^100000

4 Contextsensitivelanguagethat is not

context free5 Not closedunder unionbut closedunderintersection

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6 Not closedunder unionor

complement

Answer:


Q88

A {0^100n 1^1000n|n>=1} 1 Finite set

B {0^n1^n|n>=1^n1^2n|n>=1 2 Deterministiccontext freelanguage

C {wwwwwwwwR|w in(0+1)+} 3 Context freelanguagethat is notdeterministic

D The set of all strings notcontaining0000000000001111000 over{0,1} of length less than10^100000

4 Contextsensitivelanguagethat is notcontext free

5 Not closed

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under unionbut closedunder

intersection6 Not closedunder unionorcomplement

Answer:


Q89

A {ww| w in (0+1)*} 1 Thecomplementis not afinite set but

the set isfinite

B {wwR|in (0+1)*} 2 Thecomplementis a cfl

C {w$w|n(0+1)+} 3 The

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complementis not a clf

D The set of all strings

not containing0000000000001111000over {0,1} of lengthless than 10^100000

4 The

complementis a dcfl

5 Recursivebut not a csl


Answer:


Q90.

A Sa 1 The langugegenerated isambiguouswith aninfinitenumber ofderivations

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for a

B SaSAA

a

2 Thelanguage

generated isunambiguous

C SaSA|BAaBb

3 Thelanguagegenerated isambiguouswith twoderivations

for aD SSS|a| 4 The

languagegenerated isambiguouswith threedistinct

derivationsfor a

5 Thelanguagegenerated isinherentlyambigugous

6 Thelanguagegenerated isr.e but notrecursive

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Answer:


Q91.

A EE+E|E*E|(E)|i 1 The langugegenerated isambiguouswith aninfinite

number ofderivationsfor a

B SaSAAa

2 Thelanguagegenerated isambiguous

and is the setof all Cexpressionsover + and *

C SaSA|B

3 Thelanguage

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AaBb

generated isambiguouswith two

derivationsfor a

D SSS|a| 4 Thelanguagegenerated isambiguouswith threedistinct

derivationsfor a



Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

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(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q92.

A EE+E|E*E|(E)|i 1 Thelanguagegenerated isambiguouswith aninfinite

number ofderivationsfor a

B EE+E|E.E|(E)|a|b|| 2 Thelanguagegenerated isambiguous

and is theset of all Cexpressionsover + and *

C SaSA|BAaB

b

3 Thelanguagegenerated is

ambiguousand is theset of allregularexpressionsover {a,b}

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D SSS|a| 4 Thelanguagegenerated is

ambiguouswith threedistinctderivationsfor a


inherentlyambigugous


Answer:


Q93.

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A EE+E|E*E|(E)|i 1 Thelanguagegenerated is

ambiguouswith aninfinitenumber ofderivationsfor a

B EE+E|E.E|(E)|a|b|| 2 Thelanguage

generated isambiguousand is the setof all Cexpressionsover + and *

C EE+T|TTT*F|FF(E)|i

3 The

languagegenerated isanunambiguousgrammar forarithmeticexpressions

D S

SS|a| 4 Thelanguagegenerated isambiguouswith threedistinct

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derivationsfor a

5 The

languagegenerated isinherentlyambigugous

6 Thelanguagegenerated isr.e but not

recursive

Answer:


Q94.

A E

E+E|E*E|(E)|i 1 Thelanguagegenerated isall stringsover {a,b} notof the form

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languagegenerated isr.e but not

recursive

Answer:


Q95.

A EE+E|E*E|(E)|i 1 Thelanguagegenerated isambiguousand is the setof all stringsover {a,b}with an equal

number ofas and bs.


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and is the setof all Cexpressions

over + and *C EE+T|TTT*F|FF(E)|i

3 Thelanguagegenerated isanunambiguousgrammar forarithmetic

expressionsD SaSbS|bSaS| 4 The

languagegenerated isambiguouswith threedistinct

derivationsfor a



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Answer:


Q96.

A EE+E|E*E|(E)|i 1 Thelanguagegenerated isambiguousand is the set

of all stringsover{a,b}with twice asmany as asbs.

B EE+E|E.E|(E)|a|b|| 2 Thelanguage

generated isambiguousand is the setof all Cexpressionsover + and *

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anunambiguousgrammar forarithmeticexpressions

D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated is


5 Thelanguage

generated isinherentlyambigugous


recursive

Answer:

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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q97.

A AaAb|abA1a|a A1SA1|A1 S|


ambiguousand is the setof all stringsover{a,b}with twice asmany as asbs.

B EE+E|E.E|(E)|a|b|| 2 Thelanguagegenerated isthe set of allstrings over{a,b} with theas greater

than the bs.C EE+T|TTT*F|FF(E)|i

3 Thelanguagegenerated isanunambiguous

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languagegenerated isambiguous

with threedistinctderivationsfor a

5 Thelanguagegenerated isinherently

ambigugous6 The

languagegenerated isr.e but notrecursive

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q99.

A EE+E|E*E|(E)|i 1 The

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languagegenerated is{a^I b^J

c^K|I notequal to J orJ not equal toK}


and is the setof all Cexpressionsover + and *




D SA1|B1|C1|A1 C1SA1 A|A1 A C1S

B C1| A1 B C1AaAb|abBaBb|abA1a| a A1B1b|b B1C1c|c C1

4 Thelanguage

generated isambiguouswith threedistinctderivationsfor a

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inherentlyambigugous


Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q100.

A SaSa|bSb|cSc|dSd 1 Thelanguage

generated isambiguousand is the setof all stringsover{a,b}with twice as

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many as asbs.

B EE+E|E.E|(E)|a|b|| 2 Thelanguagegenerated isthe set of allpalidromesover {a,b,c,d}




D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguage


5 The


6 Thelanguage

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generated isr.e but notrecursive

Answer:

(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q101.


generated isambiguousand is theset of allstringsover{a,b}with twice

as many asas bs.

B {a^I b^J c^K|I=max(J,K)} 2 Thelanguagegenerated isthe set of all

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palidromesover{a,b,c,d}

C E

E+T|TTT*F|FF(E)|i

3 Thelanguagegenerated isa a csl andnot a cfl



5 Thelanguage



recursive

Answer:

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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q102.


generated isambiguousand is theset of allstringsover{a,b}with twice

as many asas bs.

B {a^I b^J c^K|I=min(J,K} 2 Thelanguagegenerated isthe set of allpalidromes

over{a,b,c,d}


3 Thelanguagegenerated isa csl which

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is not a cfl

D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguage


5 Thelanguage



recursive

Answer:

(i) A

1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

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Q103.

A SaSa|bSb|cSc|dSd 1 Thelanguagegenerated isambiguousand is theset of allstringsover{a,b}with twice

as many asas bs.

B {a^n B^n c^I|I not equal ton}

2 Thelanguagegenerated isthe set of allpalidromes

over{a,b,c,d}


3 Thelanguagegenerated isa csl whichis not a cfl

D S

aSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated isambiguouswith threedistinct

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derivationsfor a

5 The



recursive

Answer:


Q104.

A S

aSa|bSb|cSc|dSd 1 Thelanguagegenerated isambiguousand is theset of all

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stringsover{a,b}with twice

as many asas bs.

B {a^m B^n c^I|n lies betweenm and 2I}

2 Thelanguagegenerated isthe set of allpalidromesover

{a,b,c,d}C EE+T|T

TT*F|FF(E)|I


D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated isambiguouswith threedistinctderivationsfor a


6 The

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languagegenerated isr.e but not

recursive

Answer:


Q105.

A SaSa|bSb|cSc|dSd 1 Thelanguagegenerated isambiguousand is theset of allstrings

over{a,b}with twiceas many asas bs.


2 Thelanguage

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generated isthe set of allpalidromes

over{a,b,c,d}

C {a^I b^J c^K|K=I+J} 3 Thelanguagegenerated isa csl whichis not a cfl

D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated isa dcfl whichis notregular

5 Thelanguage



recursive

Answer:

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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5

(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1

Q106.

A SaSa|bSb|cSc|dSd 1 Thelanguagegenerated is

ambiguousand is theset of allstringsover{a,b}with twiceas many as

as bs.B {a^n B^n c^I|I not equal to

n}2 The

languagegenerated isthe set of allpalidromesover

{a,b,c,d}C {a^I b^J c^K|K

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a cfl whichis not a dcfl


6 The

languagegenerated isr.e but notrecursive

Answer:


Q106.

A {a^I b^J c^J d^2 e^3I} 1 Thelanguage

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generated isambiguousand is the

set of allstringsover{a,b}with twiceas many asas bs.


2 Thelanguage is

a cfl and ifwe take thefirst half ofthe stringswe ger alanguagewhich is not

a cflC EE+T|T

TT*F|FF(E)|i


D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated isambiguouswith threedistinctderivations

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for a

5 Thelanguage



Answer:


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NOTE:-The answer for all the above questions is choice(IV)

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QVIII

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Transcript of QVIII