GATE CSE 2013 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Which of the following does not equal
$$\left| {\matrix{ 1 & x & {{x^2}} \cr 1 & y & {{y^2}} \cr 1 & z & {{z^2}} \cr } } \right|?$$

$$\left| {\matrix{ 1 & {x\left( {x + 1} \right)} & {x + 1} \cr 1 & {y\left( {y + 1} \right)} & {y + 1} \cr 1 & {z\left( {z + 1} \right)} & {z + 1} \cr } } \right|$$

$$\left| {\matrix{ 1 & {x + 1} & {{x^2} + 1} \cr 1 & {y + 1} & {{y^2} + 1} \cr 1 & {z + 1} & {{z^2} + 1} \cr } } \right|$$

$$\left| {\matrix{ 0 & {x - y} & {{x^2} - {y^2}} \cr 0 & {y - z} & {{x^2} - {z^2}} \cr 1 & z & {{z^2}} \cr } } \right|$$

$$\left| {\matrix{ 2 & {x + y} & {{x^2} + {y^2}} \cr 2 & {y + z} & {{x^2} + {z^2}} \cr 1 & z & {{z^2}} \cr } } \right|$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

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

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

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

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

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

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Suppose p is the number of cars per minute passing through a certain road junction between 5PM and 6PM and p has a poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

$$8/(2{e^3})$$

$$9/(2{e^3})$$

$$17/(2{e^3})$$

$$26/(2{e^3})$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero (the lowest priority). The scheduler re-evaluates the process priorities every $$T$$ time units and decides the next process to schedule. Which one of the following is TRUE if the processes have no $${\rm I}/O$$ operations and all arrive at time zero?

This algorithm is equivalent to the first-come-first-serve algorithm.

This algorithm is equivalent to the round-robin algorithm.

This algorithm is equivalent to the shortest-job-first algorithm.

This algorithm is equivalent to the shortest-remaining-time-first algorithm.

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