1
GATE CE 2004
+2
-0.6
Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equation $$\,{{d\,x} \over {dt}} + k\,{x^2} = 0,$$ where $$k$$ is the reaction rate constant. If $$x=a$$ at $$t=0$$ then solution of the equation is
A
$$x = a\,{e^{ - kt}}$$
B
$$\,{1 \over x} = {\raise0.5ex\hbox{1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{a}} + k\,t$$
C
$$x = a\left( {1 - {e^{ - kt}}} \right)$$
D
$$x = a\, + k\,t$$
2
GATE CE 2001
+2
-0.6
The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \right) = - 3$$ is where $${{{d^2}y} \over {d{x^2}}} = 3x - 2$$
A
$$y = {{{x^3}} \over 3} - {{{x^2}} \over 2} = 3x - 2$$
B
$$y = 3{x^3} - {{{x^2}} \over 2} - 5x + 2$$
C
$$y = {{{x^3}} \over 2} - {x^2} - 5{x \over 2} + 2$$
D
$$y = {x^3} - {{{x^2}} \over 2} + 5x + {3 \over 2}$$
3
GATE CE 1998
Subjective
+2
-0
Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$
4
GATE CE 1997
+2
-0.6
The differential equation $${{dy} \over {dx}} + py = Q,$$ is a linear equation of first order only if,
A
$$P$$ is a constant but $$Q$$ is a function of $$y$$
B
$$P$$ and $$Q$$ are functions of $$y$$ (or) constants
C
$$P$$ is a function of $$y$$ but $$Q$$ is a constant
D
$$P$$ and $$Q$$ are functions of $$x$$ (or) constants
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
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude
EXAM MAP
Joint Entrance Examination