1
GATE CE 2004
+1
-0.3
The value of the function, $$f\left( x \right) = \mathop {Lim}\limits_{x \to 0} {{{x^3} + {x^2}} \over {2{x^3} - 7{x^2}}}\,\,\,$$ is
A
$$0$$
B
$${-1 \over 7}$$
C
$${1 \over 7}$$
D
$$\infty$$
2
GATE CE 2002
+1
-0.3
The following function has local minima at which value of $$x,$$ $$f\left( x \right) = x\sqrt {5 - {x^2}}$$
A
$${{ - \sqrt 5 } \over 2}$$
B
$${\sqrt 5 }$$
C
$$\sqrt {{5 \over 2}}$$
D
$$-\sqrt {{5 \over 2}}$$
3
GATE CE 2002
+1
-0.3
The value of the following definite integral in $$\int\limits_{{\raise0.5ex\hbox{\scriptstyle { - \pi }} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}^{{\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}} {{{Sin2x} \over {1 + \cos x}}dx = \_\_\_\_\_\_\_\_.}$$
A
$$-2log$$ $$2$$
B
$$2$$
C
$$0$$
D
None
4
GATE CE 2001
+1
-0.3
Limit of the following series as $$x$$ approaches $${\pi \over 2}$$ is
$$f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - - -$$
A
$${{2\pi } \over 3}$$
B
$${\pi \over 2}$$
C
$${\pi \over 3}$$
D
$$1$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Environmental Engineering
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Medical
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