1
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
How many of the following matrices have an eigen value $$1$$?
$$\left[ {\matrix{ 1 & 0 \cr 0 & 0 \cr } } \right],\,\,\left[ {\matrix{ 0 & 1 \cr 0 & 0 \cr } } \right],\,\,\left[ {\matrix{ 1 & { - 1} \cr 1 & 1 \cr } } \right]\,\,and\,\,\left[ {\matrix{ { - 1} & 0 \cr 1 & { - 1} \cr } } \right]$$
A
one
B
two
C
three
D
four
2
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
If $$M$$ is a square matrix with a zero determinant, which of the following assertion(s) is (are) correct?
$$S1$$ : Each row of $$M$$ can be represented as a linear combination of the other rows
$$S2$$ : Each column of $$M$$ can be represented as a linear combination of the other columns
$$S3$$ : $$MX$$ $$=$$ $$0$$ has a nontrivial solution
$$S4$$ : $$M$$ has an inverse
A
$$S3$$ and $$S2$$
B
$$S1$$ and $$S4$$
C
$$S1$$ and $$S3$$
D
$$S1$$, $$S2$$, and $$S3$$
3
GATE CSE 2008
MCQ (Single Correct Answer)
+1
-0.3
The value of $$\int\limits_0^3 {\int\limits_0^x {\left( {6 - x - y} \right)dxdy\,\,\,} } $$ is _____.
A
$$13.5$$
B
$$27.0$$
C
$$40.5$$
D
$$54.0$$
4
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
A process executes the following code
for (i = 0; i < n; i + +) fork ( ); 
The total number of child processes created is
A
$$n$$
B
$${2^n} - 1$$
C
$${2^n}$$
D
$${2^{n + 1}} - 1$$
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