GATE CSE 2013 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2013

MCQ (Single Correct Answer)

-0.6

The line graph $$L(G)$$ of a simple graph $$G$$ is defined as follows:

$$\,\,\,\,$$There is exactly one vertex $$v(e)$$ in $$L$$(G)$$ for each edge $$e$$ in $$G$$

$$\,\,\,\,$$ For any two edges $$e$$ and $$e'$$ in $$G$$, $$L(G)$$ has an edge between $$v(e)$$ and $$v(e')$$, if and only if $$e$$ and $$e'$$

$$\,\,\,\,$$ Which of the following statements is/are TRUE?

(P) The line graph of a cycle is a cycle.
(Q) The line graph of a clique is a clique.
(R) The line graph of a planar graph is planar.
(S) The line graph of a tree is a tree.

P only

P and R only

R only

P, Q and S only

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Which one of the following functions is continuous at $$x=3?$$

$$f\left( x \right) = \left\{ {\matrix{ {2,} & {if} & {x = 3} \cr {x - 1} & {if} & {x > 3} \cr {{{x + 3} \over 3},} & {if} & {x < 3} \cr } } \right.$$

$$f\left( x \right) = \left\{ {\matrix{ {4,} & {if} & {x = 3} \cr {8 - x} & {if} & {x \ne 3} \cr } } \right.$$

$$f\left( x \right) = \left\{ {\matrix{ {x + 3,} & {if} & {x \le 3} \cr {x - 4} & {if} & {x > 3} \cr } } \right.$$

$$f\left( x \right) = {1 \over {{x^3} - 27}},\,if\,\,x \ne 3$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Suppose p is the number of cars per minute passing through a certain road junction between 5PM and 6PM and p has a poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

$$8/(2{e^3})$$

$$9/(2{e^3})$$

$$17/(2{e^3})$$

$$26/(2{e^3})$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.6

A certain computation generates two arrays a and b such that a[i]=f(i)for 0 ≤ i < n and b[i] = g (a[i] )for 0 ≤ i < n. Suppose this computation is decomposed into two concurrent processes X and Y such that X computes the array a and Y computes the array b. The processes employ two binary semaphores R and S, both initialized to zero. The array a is shared by the two processes. The structures of the processes are shown below.

Process X:
private i;
for(i = 0; i < n; i++){
 a [i] = f (i);
 Exit X (R, S);
}

Process Y:
private i;
for(i = 0; i < n; i++){
 Entry Y (R, S);
 b [i] = g (a [i] );
}

Which of the following represents the correct implementations of Exit X and Entry Y?

Exit X (R, S){
  P(R);
  V(S);
}
Entry Y (R, S){
  P(S);
  V(R);
}

Exit X (R, S){
  V(R);
  V(S);
}
Entry Y (R, S){
  P(R);
  P(S);
}

Exit X (R, S){
  P(S);
  V(R);
}
Entry Y (R, S){
  V(S);
  P(R);
}

Exit X (R, S){
  V(R);
  P(S);
}
Entry Y (R, S){
  V(S);
  P(R);
}

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