GATE ME 2006 | GATE ME Year Wise Previous Years Questions

GATE ME 2006

MCQ (Single Correct Answer)

-0.3

For $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 4{{dy} \over {dx}} + 3y = 3{e^{2x}},\,\,$$ the particular integral is

$${1 \over {15}}{e^{2x}}$$

$${1 \over {5}}{e^{2x}}$$

$$3{e^{2x}}$$

$${c_1}{e^{ - x}} + {c_2}{e^{ - 3x}}$$

GATE ME 2006

MCQ (Single Correct Answer)

-0.6

Multiplication of matrices $$E$$ and $$F$$ is $$G.$$ Matrices $$E$$ and $$G$$ are
$$E = \left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr {sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$ and $$G = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
What is the matrix $$F?$$

$$\left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr {sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$

$$\left[ {\matrix{ {\cos \theta } & {\cos \theta } & 0 \cr { - \cos \theta } & {sin\theta } & 0 \cr 0 & 0 & 1 \cr } } \right]\,$$

$$\left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr { - sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]\,$$

$$\left[ {\matrix{ {sin\theta } & { - \cos \theta } & 0 \cr {\cos \theta } & {sin\theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$

GATE ME 2006

MCQ (Single Correct Answer)

-0.6

Eigen values of a matrix $$S = \left[ {\matrix{ 3 & 2 \cr 2 & 3 \cr } } \right]$$ are $$5$$ and $$1.$$ What are the eigen values of the matrix $${S^2} = SS?$$

$$1$$ and $$25$$

$$6,4$$

$$5,1$$

$$2,10$$

GATE ME 2006

MCQ (Single Correct Answer)

-0.3

The solution of the differential equation $${{dy} \over {dx}} + 2xy = {e^{ - {x^2}}}\,\,$$ with $$y(0)=1$$ is

$$\left( {1 + x} \right)\,\,{e^{{x^2}}}$$

$$\left( {1 + x} \right)\,\,{e^{ - {x^2}}}$$

$$\left( {1 - x} \right)\,\,{e^{{x^2}}}$$

$$\left( {1 - x} \right)\,\,{e^{ - {x^2}}}$$

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