1

GATE CE 2007

MCQ (Single Correct Answer)

+2

-0.6

The velocity vector is given as $${\mkern 1mu} \vec V = 5xy\widehat i + 2{y^2}\widehat j + 3y{z^2}\widehat k.{\mkern 1mu} {\mkern 1mu} $$ The divergence of this velocity vector at $$(1,1,1)$$ is

2

GATE CE 2006

MCQ (Single Correct Answer)

+2

-0.6

The directional derivative of $$\,\,f\left( {x,y,z} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at the point $$P(2,1,3)$$ in the direction of the vector $${\mkern 1mu} \vec a = \widehat i - 2\widehat k{\mkern 1mu} $$ is _________.

3

GATE CE 2005

MCQ (Single Correct Answer)

+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)

4

GATE CE 2005

MCQ (Single Correct Answer)

+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 $$P(1,1,1)$$

Questions Asked from Vector Calculus (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

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

Environmental Engineering

Engineering Mathematics

Structural Analysis

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

General Aptitude