GATE CSE 2015 Set 2 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2015 Set 2

Numerical

-0

The number of onto functions (subjective functions) from set $$X = \left\{ {1,2,3,4} \right\}$$ to set $$Y = \left\{ {a,b,c} \right\}$$ is __________________.

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GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.6

Which one of the following well formed formulae is a tautology?

$$\forall x\,\exists y\,R\left( {x,y} \right) \leftrightarrow \exists y\forall x\,R\left( {x,y} \right)$$

$$\left( {\forall x\left[ {\exists y\,R\left( {x,y} \right) \to S\left( {x,y} \right)} \right]} \right) \to \forall x\exists y\,S\left( {x,y} \right)$$

$$\left[ {\forall x\,\exists y\,\left( {P\left( {x,y} \right)} \right. \to R\left( {x,y} \right)} \right] \leftrightarrow \left[ {\forall x\,\exists y\,\left( {\neg P\left( {x,y} \right)V\,R\left( {x,y} \right)} \right.} \right]$$

$$\forall x\,\forall y\,P\left( {x,y} \right) \to \forall x\forall y\,P\left( {y,x} \right)$$

GATE CSE 2015 Set 2

Numerical

-0

The larger of the two eigenvalues of the matrix $$\left[ {\matrix{ 4 & 5 \cr 2 & 1 \cr } } \right]$$ is ______.

Your input ____

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.6

Let $$\,\,f\left( x \right) = {x^{ - \left( {1/3} \right)}}\,\,$$ and $${\rm A}$$ denote the area of the region bounded by $$f(x)$$ and the $$X-$$axis, when $$x$$ varies from $$-1$$ to $$1.$$ Which of the following statements is/are TRUE?
$${\rm I}.$$ $$f$$ is continuous in $$\left[ { - 1,1} \right]$$
$${\rm I}{\rm I}.$$ $$f$$ is not bounded in $$\left[ { - 1,1} \right]$$
$${\rm I}{\rm I}{\rm I}.$$ $${\rm A}$$ is nonzero and finite

$${\rm I}$$$${\rm I}$$ only

$${\rm I}$$$${\rm I}$$$${\rm I}$$ only

$${\rm I}$$$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ only

$${\rm I}$$, $${\rm I}$$$${\rm I}$$, and $${\rm I}$$$${\rm I}$$$${\rm I}$$

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