GATE ECE 2005 | Calculus Question 54 | Engineering Mathematics

GATE ECE 2005

MCQ (Single Correct Answer)

-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 ________.

$$1$$

$${\pi }$$

$$2$$

$${2\pi }$$

GATE ECE 1997

MCQ (Single Correct Answer)

-0.3

The curve given by the equation $${x^2} + {y^2} = 3axy$$ is

Symmetrical about $$x$$-axis

Symmetrical about $$y$$-axis

Symmetrical about the line $$y=x$$

Tangential to $$x=y=a/3$$

GATE ECE 1995

MCQ (Single Correct Answer)

-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 ______.

$$\int\limits_0^2 {\int\limits_{{x^2}}^{2x} {f\left( {x,y} \right)dy\,dx} } $$

$$\int\limits_0^2 {\int\limits_y^{\sqrt y } {f\left( {x,y} \right)dy\,dx} } $$

$$\int\limits_0^4 {\int\limits_{y/2}^{\sqrt y } {f\left( {x,y} \right)dy\,dx} } $$

$$\int\limits_{{x^2}}^{2x} {\int\limits_0^2 {f\left( {x,y} \right)dy\,dx} } $$

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

The third term in the taylor's series expansion of $${e^x}$$ about $$'a'$$ would be ________.

$${e^a}\left( {x - a} \right)$$

$${{{e^a}} \over 2}{\left( {x - a} \right)^2}$$

$${{{e^a}} \over 2}$$

$${{{e^a}} \over 6}{\left( {x - a} \right)^3}$$

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