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

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.6

The integral $$\,\,\oint\limits_C {\left( {ydx - xdy} \right)\,\,} $$ is evaluated along the circle $${x^2} + {y^2} = {1 \over 4}\,$$ traversed in counter clockwise direction. The integral is equal to

$$0$$

$$ - {\pi \over 4}$$

$$ - {\pi \over 2}$$

$$ {\pi \over 4}$$

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.6

In the following table, $$x$$ is a discrete random variable and $$p(x)$$ is the probability density. The standard deviation of $$x$$ is GATE ME 2014 Set 1 Engineering Mathematics - Probability and Statistics Question 20 English

GATE ME 2014 Set 1 Engineering Mathematics - Probability and Statistics Question 20 English

$$0.18$$

$$0.36$$

$$0.54$$

$$0.6$$

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

Numerical

-0

If $$\,y = f\left( x \right)\,\,$$ is the solution of $${{{d^2}y} \over {d{x^2}}} = 0$$ with the boundary conditions $$y=5$$ at $$x=0,$$ and $$\,{{dy} \over {dx}} = 2$$ at $$x=10,$$ $$f(15)=$$_______.

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