1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
$$F$$ is an $$n$$ $$x$$ $$n$$ real matrix. $$b$$ is an $$n$$ $$x$$ $$1$$ real vector. Suppose there are two $$n$$ $$x$$ $$1$$ vectors, $$u$$ and $$v$$ such that $$u \ne v$$, and $$Fu = b,\,\,\,\,Fv = b$$

Which one of the following statements is false?

A
Dererminant of $$F$$ is zero
B
There are an infinite number of solutions to $$Fx$$ $$=$$ $$b$$
C
There is an $$x \ne 0$$ such that $$Fx = 0$$
D
$$F$$ must have two identical rows
2
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
What are the eigen values of the matrix $$P$$ given below? $$$P = \left( {\matrix{ a & 1 & 0 \cr 1 & a & 1 \cr 0 & 1 & a \cr } } \right)$$$
A
$$a,a - \sqrt {2,} a + \sqrt 2 $$
B
$$a,a,a$$
C
$$0,a,2a$$
D
$$ - a,2a,2a$$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+1
-0.3
Consider three $$CPU$$-intensive process, which require $$10,20$$ and $$30$$ time units and arrive at times $$0,2$$ and $$6$$ respectively. How many context switches are needed if the operating system implements a shortest remaining time first scheduling algorithm? Do not count the context switches at time zero and at the end.
A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider three processes (process id $$0,1,2,$$ respectively) with compute time bursts $$2, 4,$$ and $$8$$ time units. All processes arrive at time zero. Consider the longest remaining time first $$(LRTF)$$ scheduling algorithm. In $$LRTF$$ ties are broken by giving priority to the process with the lowest process id. The average turn around time is
A
$$13$$ units
B
$$14$$ units
C
$$15$$ units
D
$$16$$ units
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