1
GATE ECE 2005
+1
-0.3
The value of the integral $$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{\scriptstyle {{x^2}}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 8}}}}} \,\,dx\,\,\,$$ is ________.
A
$$1$$
B
$${\pi }$$
C
$$2$$
D
$${2\pi }$$
2
GATE ECE 1997
+1
-0.3
The curve given by the equation $${x^2} + {y^2} = 3axy$$ is
A
Symmetrical about $$x$$-axis
B
Symmetrical about $$y$$-axis
C
Symmetrical about the line $$y=x$$
D
Tangential to $$x=y=a/3$$
3
GATE ECE 1995
+1
-0.3
By reversing the order of integration $$\int\limits_0^2 {\int\limits_{{x^2}}^{2x} {f\left( {x,y} \right)dy\,dx} }$$ may be represented as ______.
A
$$\int\limits_0^2 {\int\limits_{{x^2}}^{2x} {f\left( {x,y} \right)dy\,dx} }$$
B
$$\int\limits_0^2 {\int\limits_y^{\sqrt y } {f\left( {x,y} \right)dy\,dx} }$$
C
$$\int\limits_0^4 {\int\limits_{y/2}^{\sqrt y } {f\left( {x,y} \right)dy\,dx} }$$
D
$$\int\limits_{{x^2}}^{2x} {\int\limits_0^2 {f\left( {x,y} \right)dy\,dx} }$$
4
GATE ECE 1995
+1
-0.3
The third term in the taylor's series expansion of $${e^x}$$ about $$'a'$$ would be ________.
A
$${e^a}\left( {x - a} \right)$$
B
$${{{e^a}} \over 2}{\left( {x - a} \right)^2}$$
C
$${{{e^a}} \over 2}$$
D
$${{{e^a}} \over 6}{\left( {x - a} \right)^3}$$
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