1

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 _________.

2

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)

3

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

4

GATE CE 2002

MCQ (Single Correct Answer)

+2

-0.6

The directional derivative of the following function at $$(1, 2)$$ in the direction of $$(4i+3j)$$ is : $$f\left( {x,y} \right) = {x^2} + {y^2}$$

Questions Asked from Vector Calculus (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CE Subjects

Engineering Mechanics

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude