1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider this C code to swap two integers and these five statements:
void swap(int *px, int *py) 
{ 
    *px = *px - *py; 
    *py = *px + *py; 
    *px = *py - *px; 
}
S1: will generate a compilation error

S2: may generate a segmentation fault at runtime depending on the arguments passed

S3: correctly implements the swap procedure for all input pointers referring to integers stored in memory locations accessible to the process

S4: implements the swap procedure correctly for some but not all valid input pointers

S5: may add or subtract integers and pointers.
A
S1
B
S2 and S3
C
S2 and S4
D
S2 and S5
2
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
If $$s$$ is a string over $${\left( {0 + 1} \right)^ * }$$ then let $${n_0}\left( s \right)$$ denote the number of $$0'$$ s in $$s$$ and $${n_1}\left( s \right)$$ the number of $$1'$$s in $$s.$$ Which one of the following languages is not regular?
A
$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {{n_0}\left( s \right)\,\,} \right.} \right.$$ is a $$3$$-digit prime$$\left. \, \right\}$$
B
$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {\,\,} \right.} \right.$$ for every prefix $$s'$$ of $$s.$$ $$\,\left| {{n_0}\left( {{s^,}} \right) - {n_1}\left( {{s^,}} \right)\left| { \le \left. 2 \right\}} \right.} \right.$$
C
$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^*}\left\| {{n_0}\left( s \right) - {n_1}\left( s \right)\left| { \le \left. 4 \right\}} \right.} \right.} \right.$$
D
$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }} \right.\left| {{n_0}\left( s \right)} \right.$$ mod $$7 = {n_1}\left( s \right)$$ mod $$5 = \left. 0 \right\}$$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Let $${L_1}$$ be a regular language, $${L_2}$$ be a deterministic context-free language and $${L_3}$$ a recursively enumerable, but not recursive, language. Which one of the following statement is false?
A
$${L_1} \cap {L_2}$$ is deterministic $$CFL$$
B
$${L_3} \cap {L_1}$$ is recursive
C
$${L_1} \cup {L_2}$$ is context-free
D
$${L_1} \cap {L_2} \cap {L_3}$$ is recursively enumerable
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
For $$s \in {\left( {0 + 1} \right)^ * },$$ let $$d(s)$$ denote the decimal value of $$s(e. g.d(101)=5)$$
Let $$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {\,d\left( s \right)\,} \right.} \right.$$ mod $$5=2$$ and $$d(s)$$ mod $$\left. {7 \ne 4} \right\}$$

Which of the following statement is true?

A
$$L$$ is recursively enumerable, but not recursive
B
$$L$$ is recursive, but not context-free
C
$$L$$ is context-free, but not regular
D
$$L$$ is regular
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12