1
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
$$-\sqrt {{5 \over 2}}$$
2
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
3
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
$$1$$
4
GATE CE 2000
+1
-0.3
Consider the following integral $$\mathop {Lim}\limits_{x \to 0} \int\limits_1^a {{x^{ - 4}}} dx$$ ________.
A
diverges
B
converges to $$1/3$$
C
converges to $${ - {1 \over {{a^3}}}}$$
D
converges to $$0$$
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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