GATE ME 2014 Set 1 | GATE ME Year Wise Previous Years Questions

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.6

The matrix form of the linear system $${{dx} \over {dt}} = 3x - 5y$$ and $$\,{{dy} \over {dt}} = 4x + 8y\,\,$$ is

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 3 & { - 5} \cr 4 & 8 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 3 & 8 \cr 4 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & { - 5} \cr 3 & 8 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & 8 \cr 3 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.3

Given that the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 0 \cr 2 & 6 & 4 \cr { - 1} & 0 & 2 \cr } } \right]$$ is $$-12$$, the determinant of the matrix $$\left[ {\matrix{ 2 & 6 & 0 \cr 4 & {12} & 8 \cr { - 2} & 0 & 4 \cr } } \right]$$ is

$$-96$$

$$-24$$

$$24$$

$$96$$

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.3

Which one of the following describes the relationship among the three vectors, $$\widehat i + \widehat j + \widehat k,\,\,2\widehat i + 3\widehat j + \widehat k$$ and $$5\widehat i + 6\widehat j + 4\widehat k?$$

The vectors are mutually perpendicular

The vectors are linearly dependent

The vectors are linearly independent

The vectors are unit vectors

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.3

$$\mathop {Lt}\limits_{x \to 0} {{x - \sin x} \over {1 - \cos x}}$$ is

$$0$$

$$1$$

$$3$$

not defined

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