1
GATE CE 2005
+2
-0.6
Value of the integral $$\,\,\oint {xydy - {y^2}dx,\,\,}$$ where, $$c$$ is the square cut from the first quadrant by the line $$x=1$$ and $$y=1$$ will be (Use Green's theorem to change the line integral into double integral)
A
$$1/2$$
B
$$1$$
C
$$3/2$$
D
$$5/3$$
2
GATE CE 2005
+2
-0.6
The line integral $$\int {\,\,V.dr\,\,}$$ of the vector function $$V\left( r \right) = 2xyz\widehat i + {x^2}z\widehat j + {x^2}y\widehat k\,\,$$ from the origin to the point $$P(1,1,1)$$
A
is $$1$$
B
is zero
C
is $$-1$$
D
cannot be determined without specifying the path
3
GATE CE 2002
+2
-0.6
The directional derivative of the following function at $$(1, 2)$$ in the direction of $$(4i+3j)$$ is : $$f\left( {x,y} \right) = {x^2} + {y^2}$$
A
$$4/5$$
B
$$4$$
C
$$2/5$$
D
$$1$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Joint Entrance Examination