1
GATE IN 2005
MCQ (Single Correct Answer)
+1
-0.3
If a vector $$\overrightarrow R \left( t \right)$$ has a constant magnitude then
A
$$\overrightarrow R .{{d\overrightarrow R } \over {dt}} = 0$$
B
$$\overrightarrow R \times {{d\overrightarrow R } \over {dt}} = 0$$
C
$$\overrightarrow R .\overrightarrow R {{d\overrightarrow R } \over {dt}}$$
D
$$\overrightarrow R \times \overrightarrow R {{d\overrightarrow R } \over {dt}}$$
2
GATE IN 2005
MCQ (Single Correct Answer)
+2
-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
A
$${{\sqrt 2 } \over 3}$$
B
$${{\sqrt 3 } \over 2}$$
C
$${2 \over {\sqrt 3 }}$$
D
$${3 \over {\sqrt 2 }}$$
3
GATE IN 2005
MCQ (Single Correct Answer)
+1
-0.3
The probability that there are $$53$$ Sundays in a randomly chosen leap year is
A
$${1 \over 7}$$
B
$${1 \over 14}$$
C
$${1 \over 28}$$
D
$${2 \over 7}$$
4
GATE IN 2005
MCQ (Single Correct Answer)
+1
-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)
A
$${C_1}\,{e^{2x}}$$
B
$${C_1}\,{e^{2x}} + {C_2}\,{e^{ - 2x}}$$
C
$${C_1}\,{e^{2x}} + {C_2}\,{e^{2x}}$$
D
$${C_1}\,{e^{2x}} + {C_2}\,x\,{e^{2x}}$$
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