(1) If X is a viable word sequence ending with A then a B can be added at the end.
(2) If CX is a viable word sequence then so is CXX.
(3) If there are three A’s i.e. AAA then the trio can be replaced by a single B.
(4) If there are two B’s i.e. BB then the pair can be dropped altogether.
It is known that CA is a viable word.
Example: To obtain CBAAB from CA, the minimum number of steps is:
Step 1: CA
Step 2: CAA
Step 3: CAAAA
Step 4: CBA
Step 5: CBAB
Step 6: CBABBAB
Step 7: CBAAB
In one step only one operation can be carried out
What is the minimum number of steps required to obtain CBBBA from CA?
- 8
- 9
- 10
- 11
The Correct Option is A
Solution and Explanation
From the question we know that,
3 A's can be replaced with B
and 2 B's can be dropped altogether.
so,
To get CBBBA, we have to,
Start with CA.
CA→CAA
CAA→CAAA
CAAA→CBA
CBA→CBAB
CBAB→CBABBAB
CBABBAB→CBBAB
CBBAB→CBBBA
Total Steps = 8
The correct option is (A): 8
How many steps are required to get CABAB from CA?
- 3
- 4
- 5
- 6
The Correct Option is C
Solution and Explanation
From the question we know that,
3 A's can be replaced with B
and 2 B's can be dropped altogether.
so,
To get CABAB, we have to,
Start with CA.
CA→ CAA
CAA→CAAAA
CAAAA→CBA
CBA→CABAB
Total Steps = 5
The correct option is (C): 5
What is the minimum number of steps required to obtain CBBAA from CA?
- 5
- 6
- 8
- 7
The Correct Option is D
Solution and Explanation
From the question we know that,
3 A's can be replaced with B
and 2 B's can be dropped altogether.
so,
To get CBBAA, we have to,
Start with CA.
CA→CAA
CAA→CAAA
CAAA→CBA
CBA→CBAB
CBAB→CBABBAB
CBABBAB→CBBAA
Total Steps = 7
The correct option is (D): 7
What is the minimum number of steps required to obtain BC from CA?
- 3
- 5
- 6
- not possible
The Correct Option is A
Solution and Explanation
From the question we know that,
3 A's can be replaced with B
and 2 B's can be dropped altogether.
so,
To get BC, we have to,
Start with CA.
CA→ CAA
CAA→ CBA
CBA→ BC
Total Steps = 3
The correct option is (A): 3
Starting from CBAB, what is the minimum number of steps required to obtain CBBAB
- 5
- 4
- 6
- 7
The Correct Option is B
Solution and Explanation
From the question we know that,
3 A's can be replaced with B
and 2 B's can be dropped altogether.
so,
To get CBBAB, we have to,
Start with CBAB.
CBAB→CBABBAB
CBABBAB→ CBBAAA
CBBAAA→CBBAB
Total Steps = 4
The correct option is (B): 4
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