GATE CSE 2013 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2013

MCQ (More than One Correct Answer)

-0

Which one of the following is NOT logically equivalent to $$\neg \exists x\left( {\forall y\left( \alpha \right) \wedge \left( {\forall z\left( \beta \right)} \right)} \right)?$$

$$\forall x\left( {\exists z\left( {\neg \beta } \right) \to \forall y\left( \alpha \right)} \right)$$

$$\forall x\left( {\forall z\left( \beta \right) \to \exists y\left( {\neg \alpha } \right)} \right)$$

$$\forall x\left( {\forall y\left( \alpha \right) \to \exists z\left( {\neg \beta } \right)} \right)$$

$$\forall x\left( {\exists y\left( {\neg \alpha } \right) \to \exists z\left( {\neg \beta } \right)} \right)$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

A Binary operation $$ \oplus $$ on a set of integers is defined as $$x$$ $$ \oplus $$ $$y$$ $$ = {x^2} + {y^2}$$. Which one of the following statements is TRUE about $$ \oplus $$ ?

Commutative but not associative

Both commutative and associative

Associative but not Commutative

Neither commutative nor associative

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

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

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

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

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

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

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Function $$f$$ is known at the following points: GATE CSE 2013 Discrete Mathematics - Calculus Question 32 English

The value of $$\int\limits_0^3 {f\left( x \right)dx} $$ computed using the trapezoidal rule is

$$8.983$$

$$9.003$$

$$9.017$$

$$9.045$$

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