GATE CSE 2015 Set 3 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-0.3

In the given matrix $$\left[ {\matrix{ 1 & { - 1} & 2 \cr 0 & 1 & 0 \cr 1 & 2 & 1 \cr } } \right],$$ one of the eigenvalues is $$1.$$ The eigen vectors corresponding to the eigen value $$1$$ are

$$\left\{ {\alpha \left( {4,2,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$

$$\left\{ {\alpha \left( { - 4,2,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$

$$\left\{ {\alpha \left( {\sqrt 2 ,0,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$

$$\left\{ {\alpha \left( { - \sqrt 2 ,0,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-0.3

Suppose $$𝑈$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T \right|$$ denote the number of elements in $$𝑇$$ and $$T'$$ denote the complement of $$𝑇.$$ For any $$T,R \in U,$$ let $$T\backslash R$$ be the set of all elements in $$𝑇$$ which are not in $$𝑅.$$ Which one of the following is true?

$$\forall X \in U\,\,$$ $$\left( {\left| X \right| = \left| {X'} \right|} \right)$$

$$\exists X \in U$$ $$\exists Y \in U\,\,$$ $$\left( {\left| X \right| = 5,\left| Y \right| = 5} \right.$$ and $$\left. {X \cap Y = \phi } \right)$$

$$\forall X \in U\,$$ $$\forall Y \in U\,\,$$ $$\,\,\left( {\left| X \right| = 2,\left| Y \right| = 3{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} and{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} X\backslash Y = \phi } \right)$$

$$\forall X \in U\,\,$$ $$\forall Y \in U\,\,$$ $$\,\left( {X\backslash Y = Y'\backslash X'} \right)$$

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-0.6

For the processes listed in the following table, which of the following scheduling schemes will give the lowest average turnaround time?

Process	Arrival Time	Processing Time
A	0	3
B	1	6
D	4	4
E	6	2

First Come First Serve

Non-preemptive Shortest Job First

Shortest Remaining Time

Round Robin with Quantum value two

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-0.3

The maximum number of processes that can be in $$Ready$$ state for a computer system with $$n$$ $$CPUs$$ is

$$n$$

$${n^2}$$

$${2^n}$$

Independent of $$n$$

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