1
JEE Main 2014 (Offline)
+4
-1
Let the population of rabbits surviving at time $$t$$ be governed by the differential equation $${{dp\left( t \right)} \over {dt}} = {1 \over 2}p\left( t \right) - 200.$$ If $$p(0)=100,$$ then $$p(t)$$ equals:
A
$$600 - 500\,{e^{t/2}}$$
B
$$400 - 300\,{e^{-t/2}}$$
C
$$400 - 300\,{e^{t/2}}$$
D
$$300 - 200\,{e^{-t/2}}$$
2
JEE Main 2013 (Offline)
+4
-1
At present, a firm is manufacturing $$2000$$ items. It is estimated that the rate of change of production P w.r.t. additional number of workers $$x$$ is given by $${{dp} \over {dx}} = 100 - 12\sqrt x .$$ If the firm employs $$25$$ more workers, then the new level of production of items is
A
$$2500$$
B
$$3000$$
C
$$3500$$
D
$$4500$$
3
AIEEE 2012
+4
-1
The population $$p$$ $$(t)$$ at time $$t$$ of a certain mouse species satisfies the differential equation $${{dp\left( t \right)} \over {dt}} = 0.5\,p\left( t \right) - 450.\,\,$$ If $$p(0)=850,$$ then the time at which the population becomes zero is :
A
$$2ln$$ $$18$$
B
$$ln$$ $$9$$
C
$${1 \over 2}$$$$ln$$ $$18$$
D
$$ln$$ $$18$$
4
AIEEE 2011
+4
-1
Let $$I$$ be the purchase value of an equipment and $$V(t)$$ be the value after it has been used for $$t$$ years. The value $$V(t)$$ depreciates at a rate given by differential equation $${{dv\left( t \right)} \over {dt}} = - k\left( {T - t} \right),$$ where $$k>0$$ is a constant and $$T$$ is the total life in years of the equipment. Then the scrap value $$V(T)$$ of the equipment is
A
$$I - {{k{T^2}} \over 2}$$
B
$$I - {{k{{\left( {T - t} \right)}^2}} \over 2}$$
C
$${e^{ - kT}}$$
D
$${T^2} - {1 \over k}$$
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