1
GATE CE 2002
MCQ (Single Correct Answer)
+2
-0.6
The value of the following improper integral is $$\,\int\limits_0^1 {x\,\log \,x\,dx} = \_\_\_\_\_.$$
A
$${1 \over 4}$$
B
$$0$$
C
$${{ - 1} \over 4}$$
D
$$1$$
2
GATE CE 2000
MCQ (Single Correct Answer)
+2
-0.6
The Taylor series expansion of sin $$x$$ about $$x = {\pi \over 6}$$ is given by
A
$${1 \over 2} + {{\sqrt 3 } \over 2}\left( {x - {\Pi \over 6}} \right) - {1 \over 4}{\left( {x - {\Pi \over 6}} \right)^2} - {{\sqrt 3 } \over {12}}{\left( {x - {\Pi \over 6}} \right)^3} + - -$$
B
$$x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - -$$
C
$${{x - {\Pi \over 6}} \over {1!}} - {{{{\left( {x - {\Pi \over 6}} \right)}^3}} \over {3!}} + {{{{\left( {x - {\Pi \over 6}} \right)}^5}} \over {5!}} - {{{{\left( {x - {\Pi \over 6}} \right)}^7}} \over {7!}} + - - - -$$
D
$${1 \over 2}$$
3
GATE CE 2000
MCQ (Single Correct Answer)
+2
-0.6
Limit of the function
$$f\left( x \right) = {{1 - {a^4}} \over {{x^4}}}\,\,as\,\,x \to \infty$$ is given by
A
$$1$$
B
$${e^{ - {a^4}}}$$
C
$$\infty$$
D
$$0$$
4
GATE CE 2000
MCQ (Single Correct Answer)
+2
-0.6
If $$f\left( {x,y,z} \right) =$$
$${\left( {{x^2} + {y^2} + {z^2}} \right)^{{\raise0.5ex\hbox{\scriptstyle { - 1}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}},$$ $${{{\partial ^2}f} \over {\partial {x^2}}} + {{{\partial ^2}f} \over {\partial {y^2}}} + {{{\partial ^2}f} \over {\partial {z^2}}}$$ is equal to _______.
A
$$0$$
B
$$1$$
C
$$2$$
D
$$- 3{\left( {{x^2} + {y^2} + {z^2}} \right)^{{\raise0.5ex\hbox{\scriptstyle { - 5}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}$$
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
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CBSE
Class 12