Algebra - General Aptitude - General Aptitude (GA) Previous Year Questions

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2017 · General Aptitude (GA) · General Aptitude · Algebra

Computer Science & Information Technology (CS) 2017 [Session 1]

Consider the following context-free grammar over the alphabet \(\Sigma = \{a, b, c\}\) with \(S\) as the start symbol:
\[S \to abScT \mid abcT\]
\[T \to bT \mid b\]
Which one of the following represents the language generated by the above grammar?

A

\(\{(ab)^n (cb)^n \mid n \geq 1\}\)

B

\(\{(ab)^n cb^{m_1} cb^{m_2} \cdots cb^{m_n} \mid n, m_1, m_2, \cdots, m_n \geq 1\}\)

C

\(\{(ab)^n (cb^m)^n \mid m, n \geq 1\}\)

D

\(\{(ab)^n (cb^n)^m \mid m, n \geq 1\}\)

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2

2017 · General Aptitude (GA) · General Aptitude · Algebra

Computer Science & Information Technology (CS) 2017 [Session 1]

Let T be a tree with 10 vertices. The sum of the degrees of all the vertices in T is ______________.

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3

2017 · General Aptitude (GA) · General Aptitude · Algebra

Computer Science & Information Technology (CS) 2017 [Session 1]

Consider the language L given by the regular expression (a + b)^* b (a + b) over the alphabet {a, b} . The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting L is ______.

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4

2017 · General Aptitude (GA) · General Aptitude · Algebra

Computer Science & Information Technology (CS) 2017 [Session 1]

If G is a grammar with productions S → SaS | aSb | bSa | SS | ε where S is the start variable, then which one of the following strings is not generated by G?

A

abab

B

aaab

C

abbaa

D

babba

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5

2017 · General Aptitude (GA) · General Aptitude · Algebra

Computer Science & Information Technology (CS) 2017 [Session 1]

Consider the context-free grammars over the alphabet {a,b,c} given below. S and T are non-terminals.
G1: S → aSb|T, T → cT|ϵ
G2: S → bSa|T, T → cT|ϵ
The language L(G1) ∩ L(G2) is

A

Finite.

B

Not finite but regular.

C

Context-Free but not regular.

D

Recursive but not context-free.

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6

2017 · General Aptitude (GA) · General Aptitude · Algebra

Computer Science & Information Technology (CS) 2017 [Session 1]

The expression \(\frac{(x+y)-|x-y|}{2}\) is equal to

A

the maximum of x and y

B

the minimum of x and y

C

1

D

none of the above

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