GATE CSE 2013 | GATE CSE Year Wise Previous Years Questions

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

$$8.983$$

$$9.003$$

$$9.017$$

$$9.045$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Consider an undirected random$$^ \circ $$ graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?

$$1/8$$

$$1$$

$$7$$

$$8$$

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