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

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-0.6

Let $$R$$ be a relation on the set of ordered pairs of positive integers such that $$\left( {\left( {p,q} \right),\left( {r,s} \right)} \right) \in R$$ if and only if $$p - s = q - r.$$ Which one of the following is true about $$R$$?

Both reflexive and symmetric

Reflexive but not symmetric

Not reflexive but symmetric

Neither reflexive nor symmetric

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

If the following system has non - trivial solution $$$px+qy+rz=0$$$ $$$qx+ry+pz=0$$$ $$$rx+py+qz=0$$$

Then which one of the following Options is TRUE?

$$p-q+r=0$$ or $$p=q=-r$$

$$p+q-r=0$$ or $$p=-q=r$$

$$p+q+r=0$$ or $$p=q=r$$

$$p-q+r=0$$ or $$p=-q=-r$$

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-0.3

A function $$f(x)$$ is linear and has a value of $$29$$ at $$x=-2$$ and $$39$$ at $$x=3.$$ Find its value at $$x=5.$$

$$59$$

$$45$$

$$43$$

$$35$$

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