1
GATE PI 2014
+2
-0.6
If $$\,\phi = 2{x^3}{y^2}{z^4}$$ then $${\nabla ^2}\phi$$ is
A
$$12x{y^2}{z^4} + 4{x^2}{z^4} + 20{x^3}{y^2}{z^3}$$
B
$$2{x^2}{y^2}z + 4{x^3}{z^4} + 24{x^3}{y^2}{z^2}$$
C
$$12x{y^2}{z^4} + 4{x^2}{z^4} + 24{x^3}{y^2}{z^2}$$
D
$$4x{y^2}z + 4{x^2}{z^4} + 24{x^3}{y^2}{z^2}$$
2
GATE PI 2011
+2
-0.6
The line integral $$\int\limits_{{P_1}}^{{P_2}} {\left( {ydx + xdy} \right)}$$ from $${P_1}\left( {{x_1},{y_1}} \right)$$ to $${P_2}\left( {{x_2},{y_2}} \right)$$ along the semi-circle $${P_1}$$ $${P_2}$$ shown in the figure is
A
$${x_2}{y_2} - {x_1}{y_1}$$
B
$$\left( {y_2^2 - y_1^2} \right) + \left( {x_2^2 - x_1^2} \right)$$
C
$$\left( {{x_2} - {x_1}} \right)\left( {{y_2} - {y_1}} \right)$$
D
$${\left( {{y_2} - {y_1}} \right)^2} + {\left( {{x_2} - {x_1}} \right)^2}$$
3
GATE PI 2011
+2
-0.6
If $$T(x, y, z)$$ $$= {x^2} + {y^2} + 2{z^2}$$ defines the temperature at any location $$(x, y, z)$$ then the magnitude of the temperature gradient at point $$P(1,1,1)$$ is _________.
A
$$2$$$$\sqrt 6$$
B
$$4$$
C
$$24$$
D
$$\sqrt 6$$
4
GATE PI 2007
+2
-0.6
The angle (in degrees) between two planar vectors $$\vec a = {{\sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ and $$\vec b = {{ - \sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ is
A
$$30$$
B
$$60$$
C
$$90$$
D
$$120$$
GATE PI Subjects
Engineering Mechanics
Theory of Machines
Machine Design
Fluid Mechanics
Thermodynamics
Casting
Joining of Materials
Metal Forming
Machine Tools and Machining
Metrology
Industrial Engineering
EXAM MAP
Medical
NEET