1
GATE CE 2004
MCQ (Single Correct Answer)
+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
$$\,{1 \over x} = {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle a$}} + k\,t$$
C
$$x = a\left( {1 - {e^{ - kt}}} \right)$$
D
$$x = a\, + k\,t$$
2
GATE CE 2004
MCQ (Single Correct Answer)
+1
-0.3
A delayed unit step function is defined as $$$u\left( {t - a} \right) = \left\{ {\matrix{ {0,} & {t < a} \cr {1,} & {t \ge a} \cr } } \right.$$$

Its Laplace transform is ____________.

A
$$a\,\,{e^{ - as}}$$
B
$${e^{ - as}}/s$$
C
$${e^{ as}}/s$$
D
$${e^{ - as}}/a$$
3
GATE CE 2004
MCQ (Single Correct Answer)
+2
-0.6
The present population of a community is 28000 with an average water consumption of 4200 $$m^3/d$$. The existing water treatment plant has a design capacity of 6000 $$m^3/d$$. It is expected that the population will increase to 44000 during the next 20 years. The number of years from now when the plant will reach it's design capacity, assuming an arithmetic rate of population growth, will be
A
5.5 years
B
8.6 years
C
15.0 years
D
16.5 years
4
GATE CE 2004
MCQ (Single Correct Answer)
+1
-0.3
Most of the turbidity meters work on the scattering principle. The turbidity value obtained is expressed in
A
CFU
B
FTU
C
JTU
D
NTU
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