GATE IN 2005 | GATE IN Year Wise Previous Years Questions

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GATE IN 2005

MCQ (Single Correct Answer)

-0.3

If a vector $$\overrightarrow R \left( t \right)$$ has a constant magnitude then

$$\overrightarrow R .{{d\overrightarrow R } \over {dt}} = 0$$

$$\overrightarrow R \times {{d\overrightarrow R } \over {dt}} = 0$$

$$\overrightarrow R .\overrightarrow R {{d\overrightarrow R } \over {dt}}$$

$$\overrightarrow R \times \overrightarrow R {{d\overrightarrow R } \over {dt}}$$

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)

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

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

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

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

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2017