1
GATE IN 2005
MCQ (Single Correct Answer)
+1
-0.3
$$f = {a_0}\,{x^n} + {a_1}\,{x^{n - 1}}\,y + - - + \,{a_{n - 1}}\,x\,{y^{n - 1}} + {a_n}\,{y^n}$$
where $$\,\,{a_i}\,\,$$ ($$i=0$$ to $$n$$) are constants then $$x{{\partial f} \over {\partial x}} + y{{\partial f} \over {\partial y}}\,\,\,$$ is
A
$${f \over n}$$
B
$${n \over f}$$
C
$$n$$ $$f$$
D
$$n\sqrt f $$
2
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
$$\overrightarrow R \times \overrightarrow R {{d\overrightarrow R } \over {dt}}$$
3
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
$${3 \over {\sqrt 2 }}$$
4
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
$${2 \over 7}$$
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