GATE IN 2005 | GATE IN Year Wise Previous Years Questions

GATE IN 2005

MCQ (Single Correct Answer)

-0.6

A scalar field is given by $$f = {x^{2/3}} + {y^{2/3}},$$ where $$x$$ and $$y$$ are the Cartesian coordinates. The derivative of $$'f'$$ along the line $$y=x$$ directed away from the origin at the point $$(8, 8)$$ is

$${{\sqrt 2 } \over 3}$$

$${{\sqrt 3 } \over 2}$$

$${2 \over {\sqrt 3 }}$$

$${3 \over {\sqrt 2 }}$$

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

The probability that there are $$53$$ Sundays in a randomly chosen leap year is

$${1 \over 7}$$

$${1 \over 14}$$

$${1 \over 28}$$

$${2 \over 7}$$

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

The general solution of the differential equation $$\left( {{D^2} - 4D + 4} \right)y = 0$$ is of the form (given $$D = {d \over {dx}}$$ and $${C_1},{C_2}$$ are constants)

$${C_1}\,{e^{2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,{e^{ - 2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,{e^{2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,x\,{e^{2x}}$$

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

Consider the circle $$\left| {z\, - 5\, - 5i} \right|\, = \,2$$ in the complex number plane (x, y) with z = x + iy. The minimum distance from the origin to the circle is

$$5\sqrt 2 - 2$$

$$\sqrt {54} $$

$$\sqrt {34} $$

$$5\sqrt 2 $$

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