GATE ME 2012 | GATE ME Year Wise Previous Years Questions

GATE ME 2012

MCQ (Single Correct Answer)

-0.3

The inverse Laplace transform of the function $$F\left( s \right) = {1 \over {s\left( {s + 1} \right)}}$$ is given by

$$f\left( t \right) = \sin \,t$$

$$f\left( t \right) = {e^{ - t}}\sin \,t$$

$$f\left( t \right) = {e^{ - t}}$$

$$f\left( t \right) = 1 - {e^{ - t}}$$

GATE ME 2012

MCQ (Single Correct Answer)

-0.6

$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$
The system of algebraic equations given above has

a unique solution of $$x=1,y=1$$ and $$z=1$$

only the two solutions of $$x=1, y=1, z=1$$ and $$x=2, y=1, z=0$$

infinite number of solutions.

no feasible solution.

GATE ME 2012

MCQ (Single Correct Answer)

-0.3

For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as

$$\left( {\matrix{ {{1 \over 2}} \cr {{{\sqrt 3 } \over 2}} \cr } } \right)$$

$$\left( {\matrix{ {{1 \over {\sqrt 2 }}} \cr {{{ - 1} \over {\sqrt 2 }}} \cr } } \right)$$

$$\left( {\matrix{ {{3 \over {\sqrt {10} }}} \cr {{{ - 1} \over {\sqrt {10} }}} \cr } } \right)$$

$$\left( {\matrix{ {{1 \over 5}} \cr {{2 \over {\sqrt 5 }}} \cr } } \right)$$

GATE ME 2012

MCQ (Single Correct Answer)

-0.3

The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is

$$1/6$$

$$1/4$$

$$1/3$$

$$1/2$$

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