1
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-0.3
Which one of the following functions is continuous at $$x=3?$$
A
$$f\left( x \right) = \left\{ {\matrix{ {2,} & {if} & {x = 3} \cr {x - 1} & {if} & {x > 3} \cr {{{x + 3} \over 3},} & {if} & {x < 3} \cr } } \right.$$
B
$$f\left( x \right) = \left\{ {\matrix{ {4,} & {if} & {x = 3} \cr {8 - x} & {if} & {x \ne 3} \cr } } \right.$$
C
$$f\left( x \right) = \left\{ {\matrix{ {x + 3,} & {if} & {x \le 3} \cr {x - 4} & {if} & {x > 3} \cr } } \right.$$
D
$$f\left( x \right) = {1 \over {{x^3} - 27}},\,if\,\,x \ne 3$$
2
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-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?
A
$$8/(2{e^3})$$
B
$$9/(2{e^3})$$
C
$$17/(2{e^3})$$
D
$$26/(2{e^3})$$
3
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-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?
A
This algorithm is equivalent to the first-come-first-serve algorithm.
B
This algorithm is equivalent to the round-robin algorithm.
C
This algorithm is equivalent to the shortest-job-first algorithm.
D
This algorithm is equivalent to the shortest-remaining-time-first algorithm.
4
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-0.3
Three concurrent processes X, Y, and Z execute three different code segments that access and update certain shared variables. Process X executes the P operation (i.e., wait) on semaphores a, b and c; process Y executes the P operation on semaphores b, c and d; process Z executes the P operation on semaphores c, d, and a before entering the respective code segments. After completing the execution of its code segment, each process invokes the V operation (i.e., signal) on its three semaphores. All semaphores are binary semaphores initialized to one. Which one of the following represents a deadlock-free order of invoking the P operations by the processes?
A
X:P(a)P(b)P(c)
Y:P(b)P(c)P(d)
Z:P(c)P(d)P(a)
B
X:P(b)P(a)P(c)
Y:P(b)P(c)P(d)
Z:P(a)P(c)P(d)
C
X:P(b)P(a)P(c)
Y:P(c)P(b)P(d)
Z:P(a)P(c)P(d)
D
X:P(a)P(b)P(c)
Y:P(c)P(b)P(d)
Z:P(c)P(d)P(a)
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