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1

### GATE CSE 2007

Consider the following two statements:

P: Every regular grammar is LL(1)
Q: Every regular set has a LR(1) grammar

Which of the following is TRUE?
A
Both P and Q are true
B
P is true and Q is false
C
P is false and Q is true
D
Both P and Q are false
2

### GATE CSE 2006

Consider the following grammar:

\eqalign{ & S \to FR \cr & R \to *S\,|\,\varepsilon \cr & F \to id \cr}

In the predictive parser table, M, of the grammar the entries $$M\left[ {S,id} \right]$$ and $$M\left[ {R,\ } \right]$$ respectively.

A
$$\left\{ {S \to FR} \right\}$$ and $$\left\{ {R \to \varepsilon } \right\}$$
B
$$\left\{ {S \to FR} \right\}$$ and $$\left\{ {\,\,} \right\}$$
C
$$\left\{ {S \to FR} \right\}$$ and $$\left\{ {R \to * S} \right\}$$
D
$$\left\{ {F \to id} \right\}$$ and $$\left\{ {R \to \varepsilon } \right\}$$
3

### GATE CSE 2006

In the correct grammar of the previous question, what is the length of the derivation (number of steps starring from S) to generate the string $${a^l}{b^m}$$ with $$l \ne m$$?
A
$$\max (l,m) + 2$$
B
$$l + m + 2$$
C
$$l + m + 3$$
D
$$\max (l,m) + 3$$
4

### GATE CSE 2006

Which one of the following grammars generates the following language?

$$L = \left( {{a^i}{b^j}|i \ne j} \right)$$
A
\eqalign{ & S \to AC\,|\,CB \cr & C \to aCb\,|\,a\,|\,b \cr & A \to aA\,|\, \in \cr & B \to Bb\,|\, \in \cr}
B
$$S \to aS\,|\,Sb\,|\,a\,|\,b$$
C
\eqalign{ & S \to AC\,|\,CB \cr & C \to aCb\,|\, \in \cr & A \to aA\,|\, \in \cr & B \to Bb\,|\, \in \cr}
D
\eqalign{ & S \to AC\,|\,CB \cr & C \to aCb\,|\, \in \cr & A \to aA\,|\,a \cr & B \to Bb\,|\,b \cr}

### Joint Entrance Examination

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NEET

Class 12