1
GATE IN 2011
+1
-0.3
The matrix $$M = \left[ {\matrix{ { - 2} & 2 & { - 3} \cr 2 & 1 & 6 \cr { - 1} & { - 2} & 0 \cr } } \right]$$ has eigen values $$-3, -3, 5.$$ An eigen vector corresponding to the eigen value $$5$$ is $${\left[ {\matrix{ 1 & 2 & { - 1} \cr } } \right]^T}.$$ One of the eigen vector of the matrix $${M^3}$$ is
A
$${\left[ {\matrix{ 1 & 8 & { - 1} \cr } } \right]^T}$$
B
$${\left[ {\matrix{ 1 & 2 & { - 1} \cr } } \right]^T}$$
C
$${\left[ {\matrix{ 1 & {\root 3 \of 2 } & { - 1} \cr } } \right]^T}$$
D
$${\left[ {\matrix{ 1 & 1 & { - 1} \cr } } \right]^T}$$
2
GATE IN 2011
+1
-0.3
The series $$\,\,\sum\limits_{m = 0}^\alpha {{1 \over {{4^m}}}{{\left( {x - 1} \right)}^{2m}}\,\,\,}$$ converges for
A
$$- 2 < x < 2$$
B
$$- 1 < x < 3$$
C
$$- 3 < x < 1$$
D
$$x < 3$$
3
GATE IN 2011
+2
-0.6
The box $$1$$ contains chips numbered $$3, 6, 9,$$ $$12$$ and $$15$$. The box $$2$$ contains chips numbered $$6, 11, 16, 21$$ and $$26$$. Two chips, one from each box are drawn at random. The numbers written on these chips are multiplied. The probability for the product to be an even number is ______________.
A
$${6 \over {25}}$$
B
$${2 \over {5}}$$
C
$${3 \over {5}}$$
D
$${19 \over {25}}$$
4
GATE IN 2011
+2
-0.6
Consider the differential equation $$\mathop y\limits^{ \bullet \bullet } + 2\,\mathop y\limits^ \bullet + y = 0\,\,$$ with boundary conditions $$y(0)=1$$ & $$y(1)=0.$$ The value of $$y(2)$$ is
A
$$-1$$
B
$$- {e^{ - 1}}$$
C
$$- {e^{ - 2}}$$
D
$${e^2}$$
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