GATE CSE 2013 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Which of the following statements is/are TRUE for undirected graphs?
P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even.

P only

Q only

Both P and Q

Neither P and Q

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 of the following does not equal
$$\left| {\matrix{ 1 & x & {{x^2}} \cr 1 & y & {{y^2}} \cr 1 & z & {{z^2}} \cr } } \right|?$$

$$\left| {\matrix{ 1 & {x\left( {x + 1} \right)} & {x + 1} \cr 1 & {y\left( {y + 1} \right)} & {y + 1} \cr 1 & {z\left( {z + 1} \right)} & {z + 1} \cr } } \right|$$

$$\left| {\matrix{ 1 & {x + 1} & {{x^2} + 1} \cr 1 & {y + 1} & {{y^2} + 1} \cr 1 & {z + 1} & {{z^2} + 1} \cr } } \right|$$

$$\left| {\matrix{ 0 & {x - y} & {{x^2} - {y^2}} \cr 0 & {y - z} & {{x^2} - {z^2}} \cr 1 & z & {{z^2}} \cr } } \right|$$

$$\left| {\matrix{ 2 & {x + y} & {{x^2} + {y^2}} \cr 2 & {y + z} & {{x^2} + {z^2}} \cr 1 & z & {{z^2}} \cr } } \right|$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

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

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

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

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

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

PREVIOUS NEXT

GATE CSE Papers

2024