1
GATE CE 2014 Set 1
Numerical
+2
-0
A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2$$ $$sin$$ $$(5t),$$ where $$x, y$$ and $$z$$ show variations of the distance covered by the particle (in cm) with time $$t$$ (in $$s$$). The magnitude of the acceleration of the particle (in cm/s2) at $$t=0$$ is _______.
2
GATE CE 2009
+2
-0.6
For a scalar function $$\,f\left( {x,y,z} \right) = {x^2} + 3{y^2} + 2{z^2},\,\,$$ the directional derivative at the point $$P(1,2,-1)$$ in the direction of a vector $$\widehat i - \widehat j + 2\widehat k\,\,$$ is
A
$$-18$$
B
$$-3\sqrt 6$$
C
$$3\sqrt 6$$
D
$$18$$
3
GATE CE 2007
+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
A
$$9$$
B
$$10$$
C
$$14$$
D
$$15$$
4
GATE CE 2006
+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 _________.
A
$$-2.785$$
B
$$-2.145$$
C
$$-1.789$$
D
$$1.000$$
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
NEET