GATE CSE 2003 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2003

MCQ (Single Correct Answer)

-0.3

Consider the following C function.

float f,(float x, int y) {
    float p, s; int i;
    for (s=1,p=1,i=1; i < y; i++) {
         p *= x/i;
         s+=p;
    }
return s;
}

For large values of y, the return value of the function f best approximates

X^y

e^x

$$\ln (1 + x)$$

X^x

GATE CSE 2003

MCQ (Single Correct Answer)

-0.3

Consider the set $$\sum {^ * } $$ of all strings over the alphabet $$\,\sum { = \,\,\,\left\{ {0,\,\,\,1} \right\}.\sum {^ * } } $$ with the concatenation operator for strings

Does not from a group

Forms a non-commutative group

Does not have a right identity element

Forms a group if the empty string is removed from $${\sum {^ * } }$$

GATE CSE 2003

MCQ (Single Correct Answer)

-0.3

The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the same set as

$$\left( {{1^ * }0} \right){}^ * {1^ * }$$

$$0 + \left( {0 + 10} \right){}^ * $$

$$\left( {0 + 1} \right){}^ * 10\left( {0 + 1} \right){}^ * $$

None of the above.

GATE CSE 2003

MCQ (Single Correct Answer)

-0.6

Define Languages $${L_0}$$ and $${L_1}$$ as follows
$${L_0} = \left\{ { < M,\,w,\,0 > \left| {M\,\,} \right.} \right.$$ halts on $$\left. w \right\}$$
$${L_1} = \left\{ { < M,w,1 > \left| M \right.} \right.$$ does not halts on $$\left. w \right\}$$

Here $$ < M,\,w,\,i > $$ is a triplet, whose first component, $$M$$ is an encoding of a Turing Machine, second component, $$w$$, is a string, and third component, $$t,$$ is a bit.
Let $$L = {L_0} \cup {L_1}.$$ Which of the following is true?

$$L$$ is recursively enumerable, but $$\overline L $$ is not

$$\overline L $$ is recursively enumerable, but $$L$$ is not

Both $$L$$ and $$\overline L $$ are recursive

Neither $$L$$ nor $$\overline L $$ is recursive enumerable

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